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Metode SMART4 | Utility | Risk
SMART (Simple Multi-attribute Rating Technique) Metode
AFHRL-TR-88-3
AIR FORCE S%
MULTIATTRIBUTE DECISION MODELING
(%JEV
Jonathan C.Fast
Metrica, Incorporated
8301 Broadway
Larry T. Looper
MANPOWER AND PERSONNEL DIVISION
Air Force Base, Texas 718235-5601
Final Report for Period September 1986 - September 1987
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Multiattribute Decision Modeling Techniques:
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Looper, L.T.
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mltiattribute decision models
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This research developed a taxonomy of decision modeling techniques and accomplished a comparative analysis of
two techniques developed and used by the Air Force in the areas of personnel selection, job classification, and
The two techniques, policy capturing and policy specifying, were shown to have several characteristics
which allowed them to be aligned with existing decision analytical theory. A set of criteria for evaluating the
usefulness of a particular technique in a particular decision context was developed, and four techniques were
policy capturing, policy specifying, Simple
selected for more detailed study and evaluation.
and Hierarchical Additive Weighting Method (HAWN).
Multiattribute Rating Technique (SMART),
A panel of experts rated each
respectively, examples of utility assessment and hierarchical decision models.
The panel then rated the match
technique over the set of 16 criteria, first without regard to decision context.
between each of the four techniques and the need for particular criteria in each of three Air Force decision
person-job match, promotion, and research and development project prioritization.
ratings are pre-;ented and suggegtiont made for enhancing the Air Force's ability to conduct decision analytical
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policy specifying and policy capturing. As part of this task. H/ ByI The task also produced a set of criteria for evaluating the potential usefulness of a decision modeling technique in a particular context. Accession For NTIS GRA&I DTIC TAB Unannounced El Distribution!__ Availnblliti Co(2cs 4/ 11 __ . policy specifying fits only roughly into the class of direct estimation techniques. HAVWM (Hierarchical Additive Weighting Method). and policy capturing. it should be applied to decision contexts different from the other three methods. the four techniques were then evaluated in three separate decision contexts. but was not similar enough to any technique to conform to an existing axiomatic base. however. Policy capturing was found to have many characteristics that make it a very useful decision modeling tool. The criteria and resulting rating scheme proved to be useful for determining the utility of each technique in each decision context. in order to determine their strengthsAiand weaknesses. These two techniques. were developed by AFHRL and have been used in a variety of decision modeling contexts. since it is primarily a holistic technique. and an Air Force promotion hoard. The four techniques studied were: SMART (Simple Multiattribute Rating Technique). at first without regard to context. Policy capturing fell clearly within the well-founded and empirically tested field of statistical/holistic decision modeling. These criteria were applied to four modeling techniques.SUMMARY This task evaluated two decision modeling techniques used by the Air Force Human Resources Laboratory (AFH-RL). the relationship between the two techniques and other decision modeling analysis techniques had not been previously investigated. the research team produced a taxonomy of decision modeling techniques and found that thcie was a place ii. However. policy specifying. research and development project prioritization. zhz dzcis. Policy specifying was found to be a technique which.oa mo-1liug 1idiurue for the two AFHRL techniques. although possessing some unique characteristics. The three decision contexts studied were: person-job match. Using a rating scheme developed to determine the utility of each technique in any decision context. However. could be modified to make it more useful.
Jr. or the United States Air Force. and Dr.PREFACE The work documented in this report is a component of the Force Acquisition and Distribution System Subthrust of the Manpower and Personnel Division's research and development program.. Ward. Mr. Detlof Von Winterfeldt. William StillweU. Dr. Thomas Martin. and will provide tools for personnel managers and force planners to make more informed resource allocation decisions to achieve the Air Force's defense mission. Von Winterfeldt substantially authored section II and Append. of General Physics Corporation. The evaluation and comparative study of decision modeling tools will improve the conduct of person-job match and promotion system research. the MAXIMA Corporation. Dr. Jonathan Fast of Metrica. IV. Metrica Inc. Patrick T. Dr. and Mr. independent consultant.. V. Harker. Dr. Looper of the Air Force Human Resources Laboratory contributed sections I1. Dr. of Decision Insights.. of the Wharton School at the University of Pennsylvania. mU . of the MAXIMA Corporation. The contract team working on this project included Mr. Inc. Larry T. The opinions expressed in this rcport do not necessarily represent the views of all the authors.x A to this report. Joe H. and VI. David Seaver. Fast and Mr.
..................... TAXONOMY OF TECHNIQUES .............. Ill.......... The Expected Utility Model .......................................... E licitation of W eights ......................... Elicitation of H olistic Judgm ents ............................................ SM A RT ................. Policy Specifying ............................................. Conjoint M easurem ent ... INTRO D U CTIO N ............... The Hierarchical Additive Weighting Method (HAWM) ..... and Multilinear Utility Functions ........... M odel D evelopm ent ......... Policy Specifying Evaluation ... ................................................................................................ Elicitation of W eights .......................................................................... Multiplicative.................... C om m on Exam ple ..................... HAWM Evaluation ................................................... Additive.................................. Elicitation of Single-Attribute Value Functions ........... Risky Indifference Procedures .. Evaluation R esults ............. SMART Evaluation ............................................................................................................... SMA R T ........... Surface Fitting Procedure .......... ........... Aggregation of Weights and Single-Attribute Values ...... EVALUATION OF TECHNIQUES ....................... .......................... Policy Capturing Evaluation ......................... Holistic Orthogonal Parameter Estimation (HOPE) ..................................................................................... I II................................................. Policy Specifying ................................. H ierarchical Structure . The Analytic Hierarchy Process .......................TABLE OF CONTENTS Page I................................................................... Policy Capturing.......................................................................... Statistical/H olistic Procedures ........................................................... ............ Evaluation A pproach ....... Policy Capturing ........................................... Preference Scores ............................................................................................ V alue M easurem ent .............. A ggregation R ule ......................................................................................... Direct Estim ation Procedures ......... i iii 13 ..................................................................................................... Riskiess Indifference Procedures .............................................. 2 3 4 5 5 6 7 7 8 9 9 11 11...................................................................................................................................... 13 13 14 15 17 18 18 19 20 21 21 22 23 23 26 27 30 33 33 33 34 .........................................................................
...................................................................................... EVALUATION OF CONTEXT/TECHNIQUE MATCH .......... 34 34 35 V........................................................................................... improvements to Policy Capturing ........................................ IMPLICATIONS FOR POTENTIAL IMPROVEMENTS TO DECISION MODELING TECHNIQUES ........... An Axiomatic Basis for Judgments Required in Policy Specifying ...... iv 61 61 62 ....................................... Decision C ontexts ...................................TABLE OF CONTENTS (CONCLUDED) Page IV.................. 40 Person-Job-M atch Context ........................... 40 44 Research and Development Project Context .. 52 52 52 53 TECHNICAL REFERENCES .... 48 VI........................... CONTEXT EVALUATION RESULTS ...... Promotion Board Context ............ Improvements to Policy Specifying .............. Suggested Improvements to the Overall AFHRL Policy Modeling Capability ............. Evaluation A pproach ....... 54 BIBLIO G RA PH Y ................................................................... 57 APPENDIX: AXIOMATIC BASIS FOR POLICY SPECIFYING .......... An Axiomatic Foundation for Polynomial Model Forms ....................................................................................................................................
................................xt Weighting Matrix ...... 7 Example: Judgment Profile for Policy Capturing in Promotion Application .............................................................................................. 8 Promotion Policy Specifying Hierarchy .......................................................................................... 13 Context Scoring M atrix .................... 10 JKT-GOK Worst/Best Payoff Table ................................................ 6 Illustration of the HAWM Aggregation Process ................. ................................ A-1 Tree Structure to Illustrate Hierarchical Utility Assessment ................ 9 JKT-GOK Relationship ............................ 2 Example of a Rating Scale for Assessing a Single-Attribute Value Function .. 11 Decision Attributes .......................... 5 Illustration of an Analytic Hierarchy ................................................... 3 Example of the Curve Drawing Technique to Assess a Single-Attribute Value Function . 12 Technique Scoring M atrix ...... ....... I~l IV II 11 14 14 16 18 21 22 24 25 25 28 31 36 38 39 63 ......................................LIST OF FIGURES Figure Page 1 Modified Lens Model ............ ...... 14 Hierarchical Structure .................... 4 Illustration of a Hierarchical Tree Structure with Hierarchical Weights .......... 15 Cont-...........
............................................ Overall Utilities: R&D Project Context ................................................................................. R&D Project Context ............................................................. Prom otion Board Context . Overall Utilities: PJM Context ..................... PJM Context W eights .................... edyotts ior R aoi rroject Context .......... 55.......................................... 20 27 32 37 41 42 43 44 45 46 47 48 49 50 51 52 ....... Illustrative Weight Ratio Assessment ........... Technique Scoring Results ........... R&D Project Context Weights ........................................ 16 17 19 7 8 9 10 11 12 13 14 15 16 17 18 i9 20 21 Vi .......... Illustration of the Computation of Aggregate Value for a Promotion Candidate ..................... Payoffs for Promotion Board Context ......... PJM C ontext .................................. Overall Utilities: Promotion Board Context ........................................... 15 3 4 5 6 Illustration of Hierarchical Swing Weighting .................................LIST OF TABLES Table Page I Polynomial Forms of Conjoint Measurement (3 Attributes) .... Payoffs for PJM Context ................. Promotion Board Context Weights .................................... 2 Illustration of the Swing Weighting Technique .......................................................................................... Payoff of Context/Technique Match .................. ......................................... Illustration of Relative Preference Assessments for Five Promotion Candidates on the JKT Attribute ............................................................ JKT-GOK Payoff Table ..................................................................................................................
but their relationship to the recognized fields of utility and value theory has not been well established. 2. Nine methods representing four theoretical areas were reviewed during this task. and guides the user in making the most appropriate choice of technique for a particular application. have been very useful in the military personnel decision contexts for which they were developed. For Section III of this report. The procedures are classified into four groups: 1.cy specifying. 4. Section IV describes the methodology used to extend this analysis to three Air Force decision making contexts. The examination of these techniques needs to be extended to include the effect of prol~ci context on the determination of usefulness of a technique. 3. INTRODUCTION This is the final report of a task to examine and improve two policy modeling techniques developed at the Air Force Human Resources Laboratory (AFHRL). . and discusses the results of evaluating these techniques without regard to context. Szction V contains the results of the methodology's being applied through the use of expert judgment.1. and are reported in Section II of this report. Drawing upon this analysis. During this research four objectives were accomplished: 1. Although advancements are still being made in these techniques. 2. Section VI contains suggestions for modifying policy capturing and policy specifying in order to make more appropriate and defensible applications of these two techniques. Speciflcktion of the relative strengths and weaknesses of each approach. Decision theorists and decision analysts have developed a number of closely related decision modeling approaches such as multiattribute utility/value assessment and hierarchical analysis and have applied these techniques to a number of non-military problems. four more commonly used techniques (including policy capturing and policy specifying) were selected for further analysis. Development of criteria for comparison of procedures and methods of measuring technical performance. 3. TAXONOMY OF TECHNIQUES This section of the report provides a summary of nine multiattribute decision modeling and evaluation procedures that may be useful for military applications such as person-job-matching and other personnel utilization decisions in the Air Force. policy capturing and po!. ii. Riskless indifference procedures Risky indifference procedures Direct estimation procedures Statistical procedures. there is a need to compare and assess these techniques with those being used in military contexts in ordcr to enable analysts and decision makers to make more informed choices among the available techniques in a particular decision context. Evaluation of the usefulness and applicability of each technique in selected typical problem contexts. using difference measurement theory. The ultimate goal of this research and development (R&D) effort is an intelligent comptotcrbased system that contains alternate techniques. Survey and review of the available theories and techniques. Appendix A includes a discussion of a theoretical underpinning for the judgments made in policy specifying. 4. This report contains the results of this context-depcndcnt evaluation of the techniques. This section also contains a description of the development of criteria and rating scales for evaluating the four methodologies. These techniques.
. Riskless indifference procedures construct utility functions and scaling fact'rs (step 4 above) by observing tradeoff and indifference judgments.. Identify and structure the dimensions on which the objects are to be evaluated. They aggregate these judgments in a variety of forms.he attributes are labelled A(i)." and leads to weaker representations. j= 1. multiplicative. but the decision maker is risk neutral. 4.. It is therefore often called 'value measurement. and assumptions. The first is built on the notion of "strengths of preference" or "preference intensities" and leads to interval scale value functions.. because they attempt to evaluate decision alternatives on a set of prc-spcified value relevant attributes. Develop a formal value or utility model that quantifies the tradeoffs among the attribute scales and the attributes. 5. Identify the objects that are to be evaluated and the purpose of the evaluation. this may be done in a hierarchy with general objectives at the top and specific attributes at the bottom.. Two broad classes of riskless indifference procedures exist." Of the two. in spite of these differences. Aggregation rules (step 5) vary from extremely simple additive rules to complex interactive rules." The second is built on the simpler notion of "preference" or "indifference. i. which have interval quality only in a restricted sense. Most multiattribute procedures go through several or all of the following steps: 1. and. to deriving models from holistic ratings of objects via regression or similar model fitting techniques. i 1. elicitation techniques. these objects are labelled 0(j). This class is usually called conoint measurement. if it appears reasonable to select risky objects according to the expected value of their riskless evaluations. this may be done by developing a utility (value) function u(i) for each scale X(i) and by assigning scaling factors (weights) w(i) to each scale. multilinear. Jointly. Recombine the pieces developed in steps 1-4 through some formal aggregation rule that assigns a single value or utility to each object. polynomial rules. Riskless Indifference Procedures Riskless indifference procedures attempt to evaluate objects in the absence of any risk. the structural similarities among various approaches are very strong. 2t . in the case of conjoin. value measurement has gained increasing acceptance in decision and management science. 6. including additive.m. Yet. and many appliers of multiattribute decision modeling techniques are convinced that the structuring steps (1-3) drive much of the subsequent analysis.Each procedure will be described by its historical origin and main references. The main differences among the procedures discussed in this paper occur in steps 4 and 5.! measurement. it is helpful to identify the commonalities among them. the quantification of tradeoffs and re-aggregation. 2.n. They are also applicable in those instances in which risk is present. model forms. Develop scales for each of the lower level attributes on which the objects are to be evaluated.e. the procedures are often called multiattribute procedures. Before discussing the separate procedures. Perform sensitivity analyses and select the object(s) with the highest overall value or utility. 3. the most common form is the weighted additive aggregation rule but more complex polynomial forms have been used. the scales are assumed to be measured numerically (real values) and they are labelled X(i). independently of the techniques for quantifying tradeoffs or aggregation rules. Techniques for tradeoff assessment (step 4) range from simple rating and weighting techniques based on indifference procedures to construct single-attribute utility functions and scaling factors.
The first creates a single-attribute value function vi for each scale X.e. finding the point on the scale ihat is just midway in value between the best and worst scale levels. the midpoint then receives a value of 50. The second elicitation creates the scaling factors required for the aggregation of the single-attribute value functions vi. Arbitrarily assigning the best and worst scale levels a value of X) and 0. and Keeney and Raiffa (1976) provided sonic generalizations. namely "strengths of preferences. (1971). Elicitation Techniques Two types of elicitations are required for the value measurement models. which are then formed into ratio scales and re-normalized. 1986). including multiplicative versions. i. 1979) or "multiplicative difference independencc" (Von Winterfeldt & Edwards. In value measurement these are obtained by comparing value differences created by stepping from the worst to the best levels in the attribute scales X. A slightly more complex model is the multiplicative model: n l+wv(oJ) 'r i=1 [l+wwivi + (X1i)]. The most simple difference value model is the additive model: v(oj) = n 2 Wiv1 (Xj) i=1 It assumes that value differences judged in one attribute are independent of the scale levels in other attributes. This creates a ratiu scale of value differences which are mapped into weights w i by renormalization. Another. It assumes that relative value differences judged in any subset of attributes are independent of fixed scale levels in the other attributes. Dyer and Sarin (1979).Nalur %leasurvment flistor' jnd n References. The decision maker is first asked to rank order these value increments. 1971) in which segments of equal value differences are "pieced together.? This procedure again creates a rank order of value differences. In it.. This assumption is sometimes called "difference independence" (Dyer & Sarin.:. less common technique is standard sequences (Krantz et al. Fishburn (1970).. 1986). Farquahr (1984) provides sonic discussion of "strengths of preferences" as do Von Winterfeldt and Edwards (1986). This assumption is sometimes called "weak difference independence" (Dyer & Sarin. third. and further developed in Krantz. which second.. Value measurement has its origin in difference measurement theories first created v Suppes and Winct (1955). etc. Model Forms and Assumptions. and Tverskv (1971). all attributes are measured on the same sca. 1960).e. Which scale level would he or she most like to change from worst to best." has remained somewhat obscure. as in time streams of income). using results by Krantz et al. not apprepriate in the indifference framework are direct rating and category estimation (Torgerson.. he or she has to make a judgment as to how much the increments differ. 3 . A variant of this method is the "swing weight" procedure (Von Winterfeldt & Edwards. Luce. the decision maker is asked to imagine he or she is to be "stuck" with an alternative that is worst on all scales. the status of the judgments required. In addition. Suppes. 1979) or "additive difference independence" (Von Winterfeldt & Edwards. Although there has been much literature on the model forms and the axiomatic basis of the value model. Further bisections can refine the value function to any level of detail. 1986). strictly speaking. The most common technique for this step is bisection." Approximation techniques which are. Fi~hburn (1770) provided an additive extension of difference measurement for the simple case of homogcncous juributis (i.
these authors developed what was at that time a new theory of fundamental preference measurement. and they are therefore not discussed here. etc. Conjoint measurement theory has not been applied as frequently as difference value measurement. as currently applied. based merely on indifference judgments. the singleattribute value functions can be fitted. Conjoint Measurement History and Origin.) i-l' I It assumes that preferences among objects that vary only on a subset of attributes do not change if the remaining (fixed) scale levels are changed. conjoint measurement theory was additive. the w. (1971) included the multiplicative form as well as simple polynomials. and since all value functions are calibrated against the same step. Since now each scale X(k) is subdivided into steps of equivalent value. there is no need for weighting. However.n explored in the conjoint measurement context. additional scaling factors have to be assessed. the procedure guarantees that the resulting value functions are appropriately matched in their units of scales. (1971). there is no separation of procedures for assessing single-attribute value functions and weights. jdes and concepts of conjoint measurement theory have found their way in a technique called "conjoint measurement" by Green. n v i (Xij). 4 . later extensions by Krantz et al." It begins by identifying an arbitrary step in value on an arbitrary scale X(i). For the multiplicative and the multilinear models. the w. The multiplicative form. Table 1 summarizes the functional forms that have bc." by Krantz et al. In its original form.The most general difference value model is the multilinear model of the form: n v(oj) = n E wivi(Xi) + iT WikVi(Xij)Vk(Xkj) +. is a derivative of the measurement theory model developed by Luce and Tukey (1964) and by Krantz (1964). This procedure is described by Fishburn (1967) as "lock step.. Subsequently a series of steps are laid off on other scales X(k) such that the subjective value increments among these steps are identical to the original arbitrary increment. These assessments are described in Dyer and Sarin (1979). has been explored by Krantz et al. the independence assumptions become somewhat unintuitive. 1971). Carmone.'s. i=l i<k i=1 It assumes that the relative value differences judged in any single attribute are unaffected by fixed scale levels in the remaining attributes. Independently." and by Keeney and Raiffa (1976) as "toothsaw. + w "- W 1. the wik 's. Elicitation Techniques. In classical conjoint measurement theory. This assumption is called "joint independence" (Krantz et al. as well as simple polynomials. namely. and they are completely analogous to the assessments for Keeney and Raiffa's (1976) multiplicative and multilinear utility functions. Weights for the additive model are constructed exactly as described above. As one moves to the more complicated polynomials. Instead. Conjoint measurement. and Wind (1972) and Green and Rao (1974) which basically fits an additive value function to overall evaluations of objects in an orthogonal design of attribute levels. Model Forms and Assumptions. (1971) as "dual standard sequence. Luce and Tukey built this theory essentially "from scratch" whereas Krantz built it on a reduction of the theory of extensive measurement.. The most common form is again the additive form: n V(O) J Z f (X...-.
If the decision maker was risk neutral. and 5 . Utility theorists argue. Polynomial Forms of Conjoint Measurement (3 Attributes) ADDITIVE: MULTIPLICATIVE: v = fI+ f2 + f3 v = f. The Expected Utility Model History and Origin. Savage (1954) extended the EU model to include subjective probabilities. In the variable probability method. The risky indifference procedures discussed here all assume that the decision maker wants to maximize expected utility. the decision maker is asked to specify a level of p such that he or she would be indifferent between playing the gamble or taking the intermediate outcome for sure. Holloway. however. Elicitation Techniques. the EU model is widely used as the logical normative cornerstone of decision analysis (e. Setting the utility of the worst and best outcomes to be 0 and 1. and the purpose of constructing a utility function is both to map preferences among outcomes and to map preferences among gambles. the decision maker is presented with a gamble created by an (unspecified) probability p of obtaining the best possible outcome versus a probability (1-p) of obtaining the worst outcome. and it is equally customary to use indifference techniques for the elicitation of utilities. The decision maker is presented with a 50-50 gamble for the best versus the worst outcome. Edwards (1954. Today."f2 f3 DISTRIBUTIVE: v = (fI+ f2 ) ' f3 DUAL DISTRIBUTIVE: v = f1* f2 + f3 GENERAL: m blk b2k b3 k v = Eakfl f2 f3 k=1 Risky Indifference Procedures Risky indifference procedures require the decision maker to state preferences or indifferences among probabilistic gamble which have multiattributed outcomes. that most decision makers are risk averse or risk prone and that property is not captured in the value functions resulting from applying riskless indifference procedures or the value functions these procedures produce. the expected utility caculus implies that the utility of the intermediate outcome must be p. Keeney & Raiffa. The variable certainty equivalent procedure is similar to the bisection procedure in difference value measurement. 1979. 1961) introduced the EU model to psychologists and led a series of experimental investigations into its descriptive validity.. The direct estimation of probabilities usually takes the form of asking an expert: What is the probability of this event? Or: What are the odds? The two indifference methods to elicit utilities are the variable probability method and the variable certainty equivalent method (Von Winterfeldt & Edwards. Thus. Although the expected utility (EU) model has many possible founders. a utility is attached to the outcomes of the gambles and the gambles themselves are ordered by taking the expectation of the utilities of their outcomes. Von Neumann and Morgenstern (1947) are usually credited for the first axiomatic foundation of expected utility measurement. 1976). it would be perfectly appropriate to construct a value function and to use it to calculate expected values to guide preferences under uncertainty.Table 1. For each intermediate outcome. In other words. the evaluation objects are uncertain. respectively. 1986). The expected utility model requires elicitation of two entities: probabilities for events and utilities for outcomes.g. It is standard practice to use direct numerical estimation techniques for eliciting probabilities.
Model Forms and Assumptions.e. It says that preferences among gamble." a utility of . Of those. Elicitation Techniques.. 1972). multiplicative. where it has the best scale value. more exotic aggregation rules being valid. multiattribute utility functions require construction of single-attribute utility functions and scaling factors.has to idcntify an intermediate outcome such that he or she is indifferent between gambling or taking the intermediate outcome for sure. These are derivec from indifference judgments similar to those made to obtain the p(i)'s... and that outcome have multiple attributes and scales. As in the difference value models.O(k). This solves the problem for the additive case. The decision maker is presented with a gamble with (unspecified) probability p(i) of winning the outcome which has the best scale values in all attributes and probability 1-p(i) of obtaining the outcome with the worst scale values in all attributes. and Multilinear Utility Functions Origin and History. Having obtained this "midpoint. Giver that the utility for the most desirable outcome is 1 and for the least desirable outcome is 0. the expected utilit) calculus implies that the scaling factor for the i-th attribute (i. P u(O). To construct scaling factors. and Raiffa (1969) developed multiplicative models.. etc. its weight) is exactly p(i). Multiplicative. In the multiplicative and multilinear cases. and more exotic forms involving independent product terms were latei introduced by Farquahr (1975) and Fishburn (1976). Polla (1967). Keeney (1974) extended the multiplicative models to multilinear ones. and if the utility function is denoted by u and the probabilities of the k events are p(l)... mllll m i I (Xij).E(k) which are associated with unique (possibly multiattributed) outcomes O(l). These extensions all begin with the assumption that the expected utility model is valid. since it can be shown that the sum of the p(i)'s must be I if the model is indeed additive.p(k). This gamble is compared to a sure thing thai has the worst scale values on all but the i-th attribute. The bisection procedure is then followed by offering 50-50 gambles between the worst outcome and the midpoint versus a "sure thing" that lies in between.5 is assigned to it... additional parameters have to be assessed. that vary only in a subset of events should be unaffected by the (common) outcomes in the remaining events Other assumptions arc more technical. the substitution principle is perhaps the most important one It requires that it not matter whether a gamble is presented in stages or whether it is presented in one stage b) multiplying the probabilities down through the possible paths of the multistage version. j=l J J The main structural assumption in this model is the sure thing principle. The decision maker i asked to adjust the probability p(i) until he or she is indifferent between the gamble and the sure thing. Model Form and Assumptions. the following variable probability method is used. Both substitution and sur. the variable probability or variable certainty equivalent methods described previously are used. Multiattribute extensions of the expected utility model date back to Fishburn's seminal article (1965a) in which he proved the additive form given certain strong independence assumptions. If a gamble G can be described by k events E(l). multilineaz or other. Keeney (1968. They then employ independence assumptions of varying degrees ol restrictiveness and depending on the validity of these assumptions result in additive. The additive utility model is very similar in structure to the additive valuc model: u(Oj) = n E kiu i=6 . thing principles are consistently violated as descriptive principles of preferences.. then the expected utility model can be expressed by k EU[GJ = . U Illlm II 6 .. Additive. To construct utility functions.. which is implied by the EU calculus.
i=1 It requires that preferences among gambles which vary only on a subset of attributes be independent of fixed levels in other attributes. either by rating the scale values (if scales are discrete) or by linear approximations (if scales are continuous). the multilinear model has the form: n u(O. This assumption has been called "utility independence" (Keency & Raiffa.dependence" (Von Winterfeldt & Edwards. In its simplest form.multiplicative utility independence" (Von Winterfeldt & Edwards. and the like. it requires that certainty equivalents for gambles which are uncertain in only one attribute do not depend on the levels of the outcomes in the other attributes. which Edwards found extremcy stimulating but of limited practical usefulness because of the complexities in model forms and elicitation techniques. and are instead grounded in the theory and practice of psychophysical judgments. and "additive utility ir. 1986). n uI(Xi). 1986).. 1986).-+ Ir kl. Edwards (1971) developed the Simple Multiattribute Rating Technique (SMART) as a direct response to Raiffa's (1969) article on multiattribute utility theory. Their advocates claim that there exist practical advantages of these procedures over the more elegant. 1975). Finally. 1969). In particular. ratios. The most recent versions of SMART arc extremely close to the value measurement techniques but still retain much of the simplification spirit that motivated the early version. SMART was meant to capture the spirit of Raiffa's multiattribute utility procedures. i=I i=1 It assumes that preferences among single-attribute gambles are unaffected by fixed values of the outcome in the remaining attributes. 1986). while at the same time being simple enough to be useful for practical-minded decision makers. This assumption is called "marginality" (Raiffa. SMART Orig and References. Through the years Edward's procedure went through several metamorphoses. SMART uses direct rating and ratio weighting procedures for constructing utility functions (Gardiner & Edwards. scales are converted into value functions. These procedures tend to lack the axiomatic base of indifference techniques. Direct Estimation Procedures The common thread among the direct estimation procedures is that all parameters of the value/utility function are directly estimated as numbers.This model assumes that gambles should be indifferent (have equal utility) whenever they have identical marginal (single-attribute) probability distributions. Elicitation Techniques. 7 .) = n Z kiui(Xij) + Tr kikUi(Xij)Uk(Xkj) +. 1976) and . First. yet more complex indifference methods. "additive independence" (Keeney & Raiffa. 1976). 1976) or "multilincar utility independence" (Von Winterfcldt & Edwards. This assumption is called "utility independence" (Keeney & Raiffa.. so that today SMART stands more for a collection of techniques rather than a single procedure (Von Winterfeldt & Edwards. The multiplicative model has the form: I + n ku(O) =r [1 + kkiui(Xd1j).
and typically produces an inconsistent set of n(n-l)/2 ratio weight assessments. & John. This rating is interpreted as the ratio of the importance between the two attributes. the lowest level of the analytic hierarchy is further split into the alternatives that are to be evaluated. but elicitation methods are different and there are several algorithms for reconciliation of inconsistent judgments and for consistency checks that are not available in any of the utility procedures. the lowest level weights most closely correspond to single-attribute value judgments or ratings in utility theory. Because of the range insensitivity of importance weights (see Gabrielli & Von Winterfeldt. i= I The Analytic Hfierarchy Process rii and References. as used in SMART. weights are elicited at all levels in the value tree and the final weights for attributes are calculated by "multiplying down the tree. which Saaty calls "analytic hierarchies. The procedure then goes through an cigenvalue computation. and secondly. they have not been spelled out explicitly. The lowest ranked attribute is given an importance weight of 10. This procedure is repeated at each level of the tree. 1980) developed. Thus the tree is a mixture of ends (upper levels) and means (lower level). the procedure elicits pairwise judgments of how much more of the next level attribute one alternative possesses than another. In tree applications of SMART. and the widespread application appears to be pushed further along by the introduction of commercially available software packages that implement the AHP algorithms. It is structurally similar to SMART. These judgments are again reconciled using the eigenvalue procedure. 1987) as it facilitates the judgments and allows separation of weighting tasks in an organization between experts (lower level weights) and policy makers (higher level weights)." There are no attempts to define or opcrationalize attributes in terms of scales.Next. The process is most different from utility and value elicitation procedures in its elicitation of "weights" at the lowest level of the tree. 1978. Keeney & Raiffa. The only model form that has been applied in the SMART context is the weighted additive model: v(O) n E wiv. The AHP has been applied vigorously since its first practical exposition in Saaty's (1980) book." which is virtually identical to the weighting methods described in the value difference measurement models.(Xij ) . Thus. recent SMART weighting methods have been changed to include "swing weighting. his Analytic Hierarchy Process (AHP). 1976). Von Winterfeldt. rates the relative importance on a ninepoint scale. The theoretical assumptions are similar to those of ratio measurement. attributes are rank ordered in the order of their importance. The AHP builds heavily on value trees." This procedure has a number of advantages (see Stiliwcll. The procedure elicits more pairwise comparisons than would be necessary to solve for a unique set of weights analytically. Saaty (1977. The model form is the simple additive model. At each level. Model Form and Assumptions. although. SMART applications have often used value trees. Instead. the importance of the others is expressed in terms of multiples of 10. 8 . Recalling that the lowest level consists of the alternatives 0(j). rather than building the multiattribute model simply on the level of the attributes. with the exception of an attempt by Vargas (1984). This comparison first establishes which of two attributes is more important. a complete set of pairwise comparisons is made between attributes. Elicitation Methods. The resulting "raw"weights are normalized to add to 1. to find a set of weights that best fits the weight ratios provided by the decision maker. Model Form. apparently independently of utility theory approaches.
The model forms can be substantially more complex than any of the additive. Two primary characteristics distinguishing one statistical procedure from another are: (a) whether the component attribute scales are discrete and not clearly ordered with respect to overall alternative worth. The assessment process begins by specifying worst and best levels for each attribute and assigning ratings (from 0 to 100) to all four corner points. ng QhjgAnd References. which generates. usually via some subjective-estimate method. rather complicated overall model structures. Policy specifying was developed specifically for analyzing complex hierarchical models for which simple additive forms are inadequate (Ward. 9 . it would seem in principle to be able to provide independence tests for the policy specified models. Elicitation Techniques. There are no explicit assumptions for the model forms developed in the policy specifying context. 1977. the total number of holistic judgments can be substantially reduced by substituting either a fractional replication design or an orthogonal design for the complete factorial design normally employed. Once all functional forms and value functions at each lower level pair are constructed. Assuming that there are no serious three. and so on. a hierarchy is constructed which is very similar to a value tree. 1979). and (b) the number of holistic judgments used to build the statistical model. & Roberts. This constraint is due to the limits of the practicability of the elicitation procedure for more than two attributes. it will be rare to see model forms that are different from simple polynomials (Krantz et al. the judgmental task becomes almost identical to the holistic procedures discussed in the statistical models. 1971). At the higher levels. One constraint is that there should be only two branches at each node. . two theoretical underpirn. and finally. such as rating scales or magnitude estimation. Holistic evaluations of alternatives or hypothetical alternatives are obtained in various ways. Assessments are then made for each pair of attributes in the hierarchy. as long as the model forms remain in the context of simple polynomials. monotonic scales by choosing fixed points along the continuum to represent discrete levels of the dimension. Statistical/Holistic Procedures Statistical procedures all attempt to build a linear statistical model that relates holistic judgments of the overall worth of alternatives to their attribute levels. It combines elements of value and utility models with those of analytic hierarchies. This is due to the nested process of model building.. If further developed. All such procedures rely heavily on obtaining large numbers of subjective holistic judgments. Ward. Both of these considerations combine to determine the exact statistical model employed. Ward et al. these analysis techniques can also be used for continuous. the aggregation rule is defined that fits the four corner points. First. multiplicative. or multilinear ones discussed earlier. Pina. (1979) described the policy specifying procedure in some detail. 1971) and a hierarchical t rory of multilinear dependence in the difference value measurement sense. Its main application areas are in Air Force person-job-matching problems. the functional form for the value function in each attribute is specified. physical features. even at moderate degrees of higher level model complexities. of course. This second theory is explored further in Appendix A to this report. Fast. Component scales for attributes of the alternatives are usually observable. however. analysis of variance or regression analysis is used whenevet attribute scales are discrete or nonmonotonic. are possible: the conjoint measurement theory of simple polynomials (Krantz et al.Po I Seclf..or moreway interactions. However. Although there are no theoretical restrictions of the complexities of the model forms in the policy specifying process. In general. the analysis moves on to higher levels and creates functions of functions. Model Forms A Assumptions. some procedures include scaling of component attributes when the number of possible levels is small. Next.
1975).e. Various terms were used to describe this research. Policy capturing owes its conceptual heritage to Egon Brunswik's probabilistic functionalism approach to psychology (Hammond. scales are built for each of the attributes. Meehl. Stewart. 10 ." These judgments are normally obtained via a rating scale or subjective estimate response mode. 1966). model predictions and/or model parameters may be fed back to the expert decision maker. these cases are by far the exception to the rule. The lens model was also applied in real-world settings to study how expert decision makers combin. Although there are certain prescriptive components of policy capturing. what little research there is derives from study of the effects of response modes in perceptual research. 1970b. Sawyer. with the decision rule being to choose those alternatives with the highest model scores. In any event. The formulae for obtaining least squares estimates of the model parameters (weights) are well known. Elicitation Techniques. Martin. either in determination of relevant attributes. and the experimenter studies subjects' learning of the (arbitrary) relationship. In a typical MCPL experiment. and (c) linearly (or at least monotonically) related to overall worth.. interval level measures). 1975. 1968. adapting the notation used by Dudycha and Naylor (1966) to policy capturing termiology. Slovic and Lichtenstein (1971) provided a good historical overview of this research. physical characteristics. Model Forms and Assumptions. a statistical parameter estimation technique such as multiple linear regression is applied to the data. One robust conclusion of the policy capturing literature is that a linear model built from the expert's judgments will outperform the expert when applied to a new stimulus sample (Goldberg. One or more experts are then asked to judge these alternatives with respect to some aggregate criterion. Mannis." Initially. and/or (c) nonmonotonically related to overall worth. known as the "multiple cue probability learning" (MCPL) paradigm. and new holistic judgments may be obtained. it may be used to evaluate alternatives quantitatively. A schematic of Brunswik's lens model is presented in Figure 1. (b) subjectively judged. and the attribute scales are treated as the predictor variables. information on relevant dimensions to form an overall evaluation. the primary historical concern has been descriptive. Other work in policy capturing has utilized this finding to focus on the normative properties of policy capturing models (Hammond. such as "overall desirability. the parameters and implications of the model are usually discussed with the expert in an informal manner to check for any obvious errors. 1954. the relationship between stimulus dimensions and overall worth is manipulated. 1965. The expert's holistic judgments are treated as the dependent (or criterion) variable. 1966). & Steinmann. Brehinei. specification of attribute scales. these are (a) continuous (i. In some cases. 1970a. Once the expert's model is agreed to. or in holistic judgments of overall worth. and many computer programs are available for this purpose. the goal of policy capturing research was also descriptive (Christal. The next step is to collect a sample of either real or hypothetical alternatives that are in some sense representative of the population of alternatives likely to be evaluated with the resulting model. Once they have been determined. Summers & Wagner. There is no formal procedure for determining the relevant attributes for inclusion in the policy capturing analysis. There is virtually no empirical work in the policy capturing literature on the effects of the exact response mode used to obtain holistic judgments. including "policy capturing" and "bootstrapping.Policy Capturing Histo and Origin. In most cases. Jones. Brunswik's "lens model" has spawned a great deal of laboratory research on how people combine information about different aspects of a stimulus to form an overall evaluation of the stimulus. Although the policy capturing approach can accommodate attributes that are (a) less than interval level. (b) observable. 1967). Once an expert's holistic judgments are obtained.
. HOPE requires the decision 11 . XI € 'tmo FimreI.2 k= 1 for profile j. (a.. from the model the Variations on the standard least squares regression formulation include nonlinear transformations on a is mod derived the of attribute scales and estimation methods other than least square. b0 is a constant term... I. osre . Of course. . The usual policy capturing procedure is to calculate the least squares estima. n is the number of attributes...ATTRISJU . ..I (r). bk is the raw score regression weight judgment where y. .tes of the weighting parameters in: . Estimation (HOPE) Holistic Orthoeonal Parameter j. as defined by Keeney and Raiffa (1976). matchn .I. is the expert's on attriibute it. The usefulness (as (Y) values criterion (unobservable) the match (Ye) function of how closely the predicted expert responses measured by re).i.T n esMdl ON P VALUE m Y. Barron and Person (1979) first proposed HOPE as an alternate method for eliciting multiplicative value and utility functions.. odfie r" otted lin the d withi . .eiil. Xi is the value of attribute k on alternative j. fo atrtiv fro th Ir moe A th exer and Orizin.. . a consistency index (re)' as well as predicted expert responses (Y¢).. can be calculated.. .X + b+Eb yj bk+. UPEN . .. ye . CW1 C. and ej is the residual error b d the expert for alternative j." rdcaiiy(r) or achievement..X.I.
(For example. and thus the notation and equation are the same as in the above discussion of multiplicative value and utility models. for example. The basic strategy. many applications of conjoint measurement have used fractional replication designs in place of complete factorials when higher order interactions are deemed unimportant (Green. Elicitation Techniques. Of course. An orthogonal design of choice alternatives is then constructed based on the attributes and discrete levels identified. These judgments are then used to generate n equalities. 12 . If the sum of the evaluations of the two complementary alternatives is equal to the evaluation of the alternative best on all attributes. d parameters. an extreme type of fractional replication design. the complement of an alternative worst on attribute A(j) and best on all others is that alternative best on attribute A(j) and worst on all others. Once w (or k) is estimated and the model form is selected. Likewise. Any of the elicitation methods used in conjoint measurement or policy capturing is acceptable.i-. and Barron and Person (1979) suggested choosing one comprised of "believable" alternatives. In the additive value case. Holistic evaluations of the alternatives inthe orthogonal design are then obtained from the decision maker. The orthogonal designs of HOPE are simply "highly fractional replications" in which all interaction effects are nonrecoverable. the decision maker may be able to spend more time reflecting on each alternative than is the case when a full factorial design is used. one extra evaluation is required of an alternative that is the complement of one of the alternatives in the orthogonal design. Once value-relevant attributes have been identified. Model Forms and Assumptions. The essential difference between HOPE and the methods proposed by Keeney and Raiffa (1976) is in the flexibility afforded by HOPE in selecting the alternatives upon which judgments are based. w(i) is simply the difference between the average evaluation of alternatives best on attribute A(i) and the average evaluation of alternatives worst on attribute A(i). from which n parameter estimates can be solved. latin square. equations are generated to estimate the single-attribute value (utility) associated with each level of each attribute in the orthogonal design. In addition to the judgments of alternatives in the orthogonal design. but differs in terms of the judgments required to estimate single-attribute value (utility) S. Because of the large number of judgments often required in complete factorial designs. The indifference probability then plays the role of the riskiess rating scale holistic judgments.. of solving n unknowns is the same. in the model. HOPE is applied within the general framework of a multiplicative value (or utility) model. 1974). the elicited holistic judgments are used to generate an equation for each of the scaling parameters. however.) The complementary alternatives are used to estimate the value of w (or k) in the multiplicative value (or utility) model. since many fewer judgments are required. and some rating in between to the remaining alternatives. greco-latin square). Barron and Person (1979) suggested that risky utility functions can be assessed by treating each alternative in the orthogonal design as a sure thing consequence in comparison to a standard gamble with alternatives best on all dimensions and worst on all dimensions as the uncertain outcomes. Barron and Person (1979) suggested assigning a rating of 0 to the alternative worst on all attributes and 100 to the alternative best on all attributes. In addition.g. discrete levels representative of the range of available alternatives are determined for each attribute. There is always more than one orthogonal design. The mathematics necessary to solve the n equations for n unknowns is identical to that resulting from applying a standard ANOVA (or regression with dummy coded variables) to the orthogonal design. then w (or k) is zero or near zero. and the multiplicative model can be reduced to the additive model. w(i) or k(i). The HOPE methodology closely follows the value and utility elicitation techniques described earlier. The alternatives are chosen to form an orthogonal design (e.maker to provide holistic interval level evaluations of a relatively small subset of m choice alternatives. HOPE shares assessment of holistic judgments and use of orthogonal designs with the more traditional approaches of conjoint measurement techniques.
SMART Wc will describe the most recent version of SMART as discussed in Von Winterfeldt and Edwards (1986). and a software implementation of AHP called the Hierarchical Additive Weighting Method (HAWM). SMART and HAWM were also selected because they are gaining widespread acceptance as techniques that are very useful in modeling policies and decisions across a variety of contexts. EVALUATION OF TECHNIQUES in this section disciusion will foeus on four of the techniques that will be examined in more detail. 1977) with the difference measurement theory proposed by Dyer and Sarir. Both SMART and HAWM are also relatively easy to use and understand. In most cases. Common Examle In order to clarify the exact form of the techniques that are being evaluated in this study. Policy capturing and policy specifying are included because they are two techniques often used by the Air Force in many decision contexts. These techniques are: policy capturing. (c) time in service (TIS). and (f) an individual performance rating (IPR). In this example. In this promotion system. Each test results in a score on a percent correct scale (that is. The example selected is that of a hypothetical Air Force enlisted promotion system. This version merges the original SMART technique proposed by Edwards (1971. (e) awards and decorations (AD). This system uses a number of personnel attributes to determine a rating for each candidate. The IPR. six attributes were chosen for use in developing these decision models: (a) scores from a job knowledge test (JKT). (d) time in grade (TIG). with an example of the application of that technique to a common personnel problem--promotion decisions. a system which would be used by the Air Force to determine which individuals eligible for promotion will in fact be selected for promotion. In addition. This section is directed toward making clear exactly the form and application of each technique being evaluated in this study. and many decision analysts are depending on one or both of these techniques for solutions to their decision analytic problems. TIS and TIG will be measured in months. results in a rating score which is averaged over several recent ratings. there are no replications and no interaction terms. policy specifying. because it represents a hierarchical weighting technique. Each of the methodologies to be evaluated in this study has received significant applied use. Unlike policy capturing.the product of w(i) and the single-attribute value of an intermediate level on attribute A(i) is the difference between the average evaluation of alternatives at that intermediate level on attribute A(i) and the average evaluation of alternatives worst on attribute A(i). combat-related decorations receive higher value scores than do non-combat service awards. given by the airman's supervisor. For example. hence no way to estimate error terms in the linear model. III. this section provides a more detailed discussion of each technique. 0-100). The score for awards and decorations is assigned according to the order of precedence of the award or decoration. (b) scores from the general organizational knowledge test (GOK). SMART was chosen because it is a representative multiattribute utility/value assessment methodology. w or k can be estimated directly from the w(i) or indirectly from the estimates of the overall value of the complementary alternatives. the number of judgments (hence independent equations) will equal (or only slightly outnumber) the number of unknown parameters. respectively. different practitioners will be more or less familiar with the specific details of alternative approaches. but disagreement exists. SMART. The JKT and GOK would be tests of the airmen's knowledge of their area of specialization and of general military subjects and management practices at their level. and HAWM. 13 . as to flie best form in which to apply them. even among experts. When the value model is determined to be multiplicative. (1979).
Elicitation of Sinple-Attribute Value Functions
The first step in SMART involves development of single-attribute value functions which are constructed by
arbitrarily assigning the "worst" level of a single-attribute scale a value of 0 and the "best" level a value of 100.
Levels in between are rated on a continuous scale between 0 and 100, with instructions to consider carefully the
difference in value between levels. If the underlying scale is numerical and continuous, curve drawing procedures
are often substituted for this rating technique.
In the context of this promotion example, consider the attribute AD with several levels ranging from "no
award or decoration" to the highest level consisting of numerous awards. As illustrated in Figure 2, the level "no
award or decoration" would receive a value of 0. The highest level, consisting of several examples of exemplary
award combinations, would receive a value of 100. Next, the analyst would pick any of the intermediate levels
on the scale, including individual awards and combinations of awards, and ask:
I---------I----------------------------------------------------------------------------------------------------------------- I
Combination 1. Medal of Honor
Combination 2. Distinguished
Service Cross,
Fiure 2. Example of a Rating Scale for Assessing a Single-Attribute Value Function.
"On a scale from 0 to 100, where would 'Purple Heart' fall between 'no decoration' and the exemplary
combination levels?" The decision maker may feel that a 'Medal of Honor/Purple Heart' combination is much
more valuable than the 'Purple Heart' alone and assign a value of 5 to 'Purple Heart' and an 80 to the 'Medal
of Honor/Purple Heart' combination. Similarly, other levels can be rated in between 0 and 100, thereby
providing the full underlying value functions.
To illustrate the curve drawing procedure, consider the attribute TIG, ranging from 0 months to 120 months.
A decision maker may be asked to draw a curve reflecting the relative value of different levels of TIG between
0 and 100. As the illustration in Figure 3 indicates, the relative value increments may initially be small, since to
consider promotion possibilities, an airman must at least have served a minimum length of time in the present
period. After a period of acceleration, the value of additional time in grade may level off. The nature and
implications of such curves are discussed in detail with the decision maker in order to arrive at a final shape.
3. Example of the Curve Drawing Technique to Assess a Single-Attribute Value Function.
Elicitation of Wgi2hts
Weights in SMART are assessed by the "swing weighting" method, in which the analyst presents the decision
maker with a profile of a hypothetical alternative that has the worst level on each attribute and another
hypothetical alternative that has the best level on each attribute. The decision maker is then asked to assume
that he or she is "stuck" with the worst alternative, but has an opportunity to move one (and only one) attribute
level from its worst to its best level. Which attribute would be most desirable to move? In other words, which
change from worst to best level would add the most overall value in terms of determining the promotability of
individuals? After identifying the attribute that provides this largest change or "swing," the decision maker
identifies the attribute with the second largest change, the third largest, etc. This process provides a rank order
of the weights in SMART.
Next, the decision maker is asked to consider the value difference created by stepping from the worst to the
best level in the most important attribute (i.e., the one that was chosen first), and to arbitrarily assign that value
difference a score of 100. Similarly, an attribute for which the swing would make no difference in value at all
is assigned a weight of 0. All other attribute swings are then given weights between 0 and 100. For example,
an attribute that has the potential of adding half the overall value of the highest ranked attribute would receive
a weight of 50. The resulting "raw" weights are summed up and each weight is divided by the total sum of the
weights to create normalized weights that sum to one. When attributes are hierarchically structured, weights are
assigned at each level of the hierarchy, and final attribute weights are obtained by multiplying the upper level
weights by the lower level weights.
The swing weight method in the promotion example would be accomplished by asking the decision maker
to rank order the desirability of moving an attribute from its worst to its best level. The decision maker might
likely rank IPR score as the number I attribute, as a low IPR score would essentially make the candidate
unpromotable. Following this change, the next most desired change may be in JKT, GOK, and AD. all of which
may be considered to add approximately equal value to the promotion decision model. Next comes TIS, and
TIG is last.
The swing in value in the IPR attribute would then be given a weight of 100 points. All other weights are
expressed in values between 0 and 100. Hypothetical results are shown in column 3. These raw weights are
highly skewed, because the IPR attribute produces an extreme swing in value (in practice one might worry
about the definition of the endpoints of that scale, or refine this attribute by breaking it down into subattributes).
Normalization of these weights is done mechanically. At the bottom of column 3 of Table 2 is the sum of the
raw weights and in column 4 are the normalized weights, which, of course, total 1.00.
Table 2. Illustration of the Swing Weighting Technique
Raw weigh,
sum: 136
sum: 1.00
To illustrate hierarchical weighting, consider the tree structure in Figure 4. In this case it might be logical
to first weight JKT versus GOK with respect to the knowledge (KNOW) objective only, then to weight TIS
versus TIG with respect to the time (TIME) objective only. This can be done with the swing weighting
procedure exactly as described above, and it would produce the results indicated in Table 3a. Next, weighting
of the relative swings of the four higher level objectives KNOW, TIME, AD, and IPR is done by asking the
Figure 4. Illustration of a Hierarchical Tree Structure with Hierarchical Weights.
decision maker to simultaneously consider swings of attributes under the objectives that are to be weighted.
A specific question might be: "Would you rather change both JKT and GOK from their worst levels to their best
levels or change both TIG and TIS from their worst to their best levels?" The answer to this question would
provide a rank order of the weights for KNOW and TIME. The questions regarding the other two attributes
(AD and IPR) would be identical to those illustrated in the non-hierarchical case. Together they might provide
a rank order as shown in Table 3b. Raw and normalized weights are also shown in that table. The final weights
for the lower level attributes JKT, GOK, TIS, and TIG are obtained by multiplying the upper normalized weight
with the respective lower level normalized weight (see Figure 4).
Table 3. Illustration of Hierarchical Swing Weighting
3a (Lower level)
The overall value of the ahcrnativc is then calculated 1)%thc Iornula v ( )j) n E Y: I v(X).2 Total saluc: 71. (Concluded Attribute Rank of swing Raw %eight Normalized weight 3b (Upper lcvcl) KNO)W JKT S21) . The X 's arc concrted into sinigle-attributc values v (X. For each altcrnati C () a profile of attribute lccvls X is Izeneratcd which indicates the degree to .75 . kiuhts and singlc-attribute values generates column 5.74 5.. a promotable candidate may have the profile described in column 2 of Table 4. Table 4. values 5(4 75 50 5 25 80( 17 W Weights of AtIr. The associated singlc-attributc values and weights might be as sho.50 5.2 2. Mlultiplving.khich tht alternative scott..) shich are simply read oilthe \ altL Cur'. on the attributes.95 for this candidate. Illustration of the Computation of .Table 3.(X ) Relative SingleAttr.Aggiregate Value for a Promotion Candidate Attributc Xu Candidate ) 's Scoring profi'lc JKT (JOK TIS TIU} AD IPR So points 75 points (4) months 12 months AF Commcnd. In the promotion example.07 A44 tI .0 1. and adding these cross-products produces the ovcrall saluc of 71.95 3.(7 .n in columns 3 and 4.14 (GOK TIM E TIS 4 6) TI6 AD 3 1)) IPR I I M) 1)7 74 Aggregation of Weights and Single-Attribute Values The aggrcgation of weights and singlc-atributc values is accomplished as follo s. W (X i) Cross-Products (17 . and graphs as shown in Figures 2 and 3. 1N) points V.
the additional assumiption is made that the w-eight ratios must be reciprocal. 19. are considered weight ratios.81).VM analog for the promotion example. In the 1IAWMI.sssd under each node. 9 meaning much more important)'? The numbers. at the bottom.. Here Promotable airmen aire the iltcrnativces (o~ and are repeated at the bottom of the tree.itv ( Hwane & Yoon. how much more important is that attribute (I meaning equally important.aluation problem. Overall Value Time in service/grade Knoxk lcdie tNT (.The Hierarchical Additi~e Weighting Method tHAWNI) Likc SM ART.. it will be QIsCusse d In a separate section.Mbeins with a hierarchical structure of the ev. Analy-tic Hierarchy Process (AHP) has undergone several metamorphoses (Saatv. a set oif n( n-I )/2 wecight ratios hilL thle co m plte n x n miatrix that defines. Howexer. \&.()K TIS Awkardls and Decorations TICG AD Individlual Performance rating IPR 0.-ce.. weights are interpreted to reflect the 'reclative importance" of the attributes or objctives. Since that step is somewhat similar to the value function assessment in other procedure.. 1977. presecnted wkith one pair and asked: 1. Figure 5 presents the H-A\. Weights are a. Which attribute do you think is more important? 2. with top values that are very much like a SMART structure. Elicitation of Weiihts The HAWMI process.. Weigzhts are also elicited for the bottom level (the alternatives) to indicate their relative desirability in achievingi bottom level objectives or tttr1Ibute. Illustration of an Ana[ltic Hfiera rchy.. with pairwise we-ight judgments. On a scale from I to 9). P-10. Method (l-AWNM) softwxare that w&as devecloped for the IBM PC/XT by Kansas State L nI~vr. I1S .ight ratios at each node. and entered into an n x n (attributes by attributcet matrix oIf weir~ght ratios in wkhich the diagonals are set to 1. Saats>. the alternatives fan out under each attribute as vet another 10e) of evaluation In 1he tree. HAWN \\. In the upper part of the t. is th candidate Figure 5. obtained from these %kcithtingjudgiments. i-he dcisio](n maker is.. Thus.) The %crsion of AHP discussed below is tbased on the techniques implemented in the Hierarchical Additise %VeivhtinL. comparing posil attributes. begins hw eliciting weights in the upper part of the tre.
For example. repeating the process described above. Which of the two altcrnatives do you prefer with respect to the attribute under conidcration: 2.t) .72 . those weights that can best reproduce the (possibly inconsistent) assessed weight ratios. In the promotion example. the assessed weight ratio for TIS vs.25 for TIRY.33 for GOK. with no possibility for inconsistencies.. In the example.l nodes: JKT \crsu. hok much do0 you prefer this alternative on the attribute under consideration? As in the importance weight assessment. On a scale from I to 9 (1 meaning indifference.e. the assessed weight ratio ol JKT versus GOK might be 2.. the decision maker has tsmo choices in [LA\\ I: Lither continue the judgments of relative importance or produce judgments of the relativc preference of the ahcrnati~c. The diagonals are simply assumed. Since in the context discussed here. The decision maker is asked to provide relative weight ratios for each of the'se pair. In addition to providing the best-fitting x.. Illustrative Weight Ratio Assessment Normalized KNOW KNOW TIM E AD IPR 1 1/3 1/2 9 TIME 3 I 2 9 A) IPR 2 1/2 1 1/9 1/9 1/ 1 9 Inconsistency score: "eights . (iOK and TIS versus TIG.iprocal. there are only two lower le. The final scores for each alternative arc again the cigenvector of that matrix that best matches the relative preference ratios. Preference Scores Once the bottom level of alternatives is reached. Qtmeaning extreme preference). The circled numbers are the assessed ones.nc\) to I (highly inconsistent weight ratio assessments).67 for JKT and . The last column of Table 5 shows the \weight. derived from the HAWM program (as run in the HAWM software) and indicates that there is moderatc consistency in the weight ratio assessments. the decision maker is askcd& 1. Since there exists no possibility for inconsistency. considering the contribution to achieving the next higher objective (KNOW or TIME). Similarly. The others are inferred from the reciprocity assumption..Having obtained n(n-l)/2 weight ratios.olvC these weights as the cigenvcctor of the weight ratio matrix.054 If satisfied with the current assessment.resulting in relative weights of . so that n(n-1)/2 assessments are sufficient to fill out the complete n x n matrix. TIti might be 3.eight solution. After such an initial assessment. the HAWNI also provides an index of (in)consistencv which ranges from 0 (perfect coi. only this variant of the HAWNI will bc discussed.ntcns would generate 2 x 2 matrices. with respect to achieving the lowest level attribute. the latter intcrprctation is more intuitive. the relative preference assessments are assumed to be rc. The HAW\M . the upper level weight ratio assessment might produce a "eight ratio matrix such as the one shown in Table 5.13 . and for each pair of alternatixes. Both weight asses. the HAWM solves for the "best-fitting" set of normalicd ekights: i. Table 5. Under each lowest level node. resulting in relative weights of .75 for TS and . the results arc identical to those obtained by simply normali./in the raw weight ratios. the decision maker goes on to lower level nodes of the :ilue tree.. the decision maker is asked it' the ratios should be revised or kept unchanged. .. 1 19 .
14 04 ( 1.33) from Table 6. I. haxe differing levels of that attribute. The last column in that table indicates the rcnormaljicd scores that each of the candidates rccei'.034 AUIregation Rule The results of vcighting and preference assessments are aggregated in a form that is very similar to the .14 .. The overall values of the other alcrnativcs are calculated in a similar way. the \wcight on KNOW (. a I I I I 2i) . the analyst then . A preference comparison of these fi%c airmen mighi look like the one in Table (.es as a result of the relative preference judgments.traic this process in the promotion context.cs s wcrc onlckhat inconsistent. adds these cro. Table 6. Illustration of Relative Preference Assessments for Five Promotion Candidates on the JKT Attribute Candidate 01 01 01 04 05 Relative Score () 0 0 1 I1h 1/3 0 1 2 3 1. which in turn would be multiplied b\ the preference score of candidate 0 1 on attribute JKT (. The overall value of alternative 0 1 would be calculated by multiplying down all the normalized scale values for that alternative.S"MART rule by multiplying down the tree and adding the multiplicative elements for each aitcrnative.33 o05 ..To illu.s-products to generate the overall evaluation of alternative 01.. • .2 1 3 1/2 3 1 2 1/2 1 . Having done similar calculations for each of the paths connecting the top of the tree with alternative 9j at the bottom. consider the attribute JKT and assume that five promotable candidate..impl..I en.5). for example.3 2 1 1/' I/3 . Consider the cxample set of relative weights and preference judgments in Figure 6.13) from Table 5 would be multiplied by the weight on JKT (. The consistency index showAs that the ven.33 Inconsistency score: .2 1 2 1. Thus.
nor single category for discrete variables. Generally. can be nonlinear. This more limited view is taken in order to remain consistent with the manner in which the technique is most often applied. some arbitrary scale (for example. however. Neither are new model fitting approaches such as nonlinear regression parameter estimation or ridge regression.13 x. for example). Thcreforc.50 x a. O5 /I I / /I A\/ (. 1979).80) (.72 x 1.05) O r. the set of profiles should be comprehensive.0 x el) Fig= 6.... either in naturally occurring units (dollars..05) r. O 0 1. seven or fewer 21 . using experimental design considerations which seek to limit the number of judgments required (for example. Barron & Person.. the decision maker(s) is (are) presented with a number of "profiles. from some number of holistic judgments of attribute profiles. no single area of the scale for a continuous attribute.72) GK TIS TG AD IPR (.33) (. Illustration of the HAWM Aggregation Process. The decision maker is likely to have difficulty making judgments about unrealistic profiles..13) (. 05 O 1 . 0 to 100). that is. The decision maker is asked to provide a judgment of the value for the option.. Policy Canturing The policy capturing approach discussed in this report utilizes ordinary least squares (OLS) regression to derive a linear (in the unknown parameters) model of the relationship between attributes and a criterion.. Although there are several recent variations..) + (. it should reflect the full range of each attribute. (.) + .13 x.. r. unlikely or impossible combinations of attributes should occur infrequently or not at all.80 x b. 0O (.Overall Value JKT KNOW TIME AD IPR (." each of which describes an option in the decision problem. Selection of the profiles to be judged is one of the keys to proper utilization of the technique and takes several factors into account... Elicitation of Holistic Judgments In order to apply the policy capturing approach to the construction of a value model. First. The description is complete with regard to the attributes thought to be relevant. Second.. The predictor forms. O. Third.06) (. the set of profiles should be reflective of the real world of the decision maker. The number of attributes is closely related to the decision maker's ability to process information.06 x. The set should be selected to be balanced across the range of each of the attributes. should be allowed to dominate the set..50 x. such techniques are not considered here.. or a rank order within the option set.20) (1.09) (.33) + (..0) (1.) (bl) (el) (d1) (el ) V(0 1) = (. The option is described in terms of an exact value for each continuously measured attribute and a category level for discrete attributes.O 5 (a.0) 01 .
.. Example: Judgment Profile for Policy Capturing in Promotion Application.. a rank ordering....... some of these criteria for selection of an option set will be in conflict in many cases.... The decision maker would then be asked to respond with a score for each individual........ Finally.. or even categories (1 ...000).... While almost any statistical package provides the means to analyze the 22 . In addition.. 77 81 Figure 7.......... and the dependent variable is the decision maker's judgment of the promotability value of that profile. Clearly.. but only 1 month TIS)...... would be presented to the decision maker (or panel of decision makers) in a form similar to that shown in Figure 7..attributes are the maximum number that are considered in applications of policy capturing." The score can be expressed on some arbitrary scale (for example.............. the rule of thumb may apply that there should be a minimum of 10 cases (options) per variable (attribute) for which a weight parameter is to be estimated..... There may also need to be additional cases when the stability of the parameter estimates is in question such as would be caused by a strong multicolinearity problem among the attributes.... in resource allocation decisions cost is usually highly and positively correlated with some measure of time.. Purple Heart (3 awards) 133 .. The independent or predictor variables are the attributes... representing the individual's relative "promotability... There is no definitive guidance as to the number of options that need to be included in the option set.. the set would be screened to eliminate unlikely or impossible applicants (for example. the analyst must balance the criteria against one another in order to arrive at a usable set of options for judgment. In the context of the promotion example.. Job Knowledge Test Score General Organizational Knowledge Score Time In Service Time In Grade Awards and Decorations Individual Iliiaxr Ratings 86 62 47 months 18 months Air Force Achievement Medal... long time options in the option set..... in terms of the point scales used to measure each attribute. a set of profiles. Some options may be so unlikely as to appear ridiculous (e.... 0-100). an applicant who has the Congressional Medal of Honor and three Purple Hearts.... In application...... The profile set would also be constructed to minimize the intercorrelations among attributes in the set.. The profiles would have been chosen to ensure that the entire set is both representative of the pool of applicants who would normally come before a promotion board and that it adequately covers the range of each attribute. full-time training course costing $1................ a 1 year..... Purple Heart 135 106 8 Airman's Medal. Since OLS regression is the method of analysis...- 2... It would thus be unrealistic to have a large number of low cost...... Attributes Applicant 1.5 categories receiving 1 to 5 points each)........ each representing a candidate for promotion.. the set of profiles should be selected such that a variety of combinations of attributes are represented...... Model Development The value model is developed by performing a regression analysis on the judged profiles......... For example.g.
or feedback techniques can be used to eliminate group differences. where a single attribute is removed or the profile set changed. For example. the decision maker moves up a level. provide several descriptive features that are unavailable to most other approaches. policy specifying is a decision analysis tool that has been used primarily by the United States Air Force within the personnel utilization decision context. it is usually unclear whether the significance can be taken as exact. the squared multiple correlation coefficient (R2 ) provides an estimate of the completeness of the attribute set. and completely new analysis performed to evaluate impact. which have seen extensive and widespread use. Hierarchical Structure The decision maker. & Albert. The decision maker then continues through the set of decision variables. decides upon a decision objective and a set of decision variables (attributes). The regression equations are clustered using a clustering routine such as the Hier-Grp software (Ward. 1977) by researchers at the Air Force Human Resources Laboratory to provide a preference modeling tool which explicitly considers the interaction of decision variables. the decision hierarchy as shown in Figure 8 could be derived from the problem. On the other hand. such an arrangement is somewhat arbitrary in this decision context. perhaps. this tree will be used for the rest of the discussion of policy specifying. given the independence assumptions of the sample statistic. Although it may be seen that there are three pairs of decision variables producing three separate functions which are later combined into two additional functions. sequential analysis. 1985). Policy specifying provides the decision maker with a decision model within a hierarchical decision structure which does permit the decision maker's preference function to include variable interaction terms. little or no software exists that facilitates other aspects of the use of this form of analysis for building value models.. For example. combining EXPERIENCE with POTENTIAL or IPR with JKT. Once all the logical pairs are formed. At any rate. forming interacting pairs when appropriate. together with the assistance of a decision analyst.judgments in this manner. to consider the interaction of decision variables with functional relationships (i. the standard statistical packages. 23 . The resulting clusters of equations are then examined to determine how many different rating patterns were evidenced by the rating panel. most packages provide a significance test fGr the model but. One might argue that some other order of combination is just as logical. when applied in this context. Policy SpeciVying Unlike SMART and HAWM. In a group situation. previously paired decision variables) or functional relationships with other functional relationships. Each requires multiple. the individual decision maker's equations are clustered using a mathematical clustering routine. Using the promotion decision context as the example. The decision analysis process of policy specifying begins by having the decision maker decide which pairs of variables should logically interact. in hierarchical fashion. The variables themselves may be either quantitative or qualitative.e. in order to arrive at a single equation of promotability. problem structuring and sensitivity analysis are either not addressed in existing software. Aberrant raters can be removed so that the individual equations can be aggregated inte a single equation. In addition. The technique was developed in the mid-1970's (see Ward. Treat. or are difficult and cumbersome to perform. Descriptive names are usually given to specific pairs at each level of the hierarchy until the overall decision objective is reached.
In order to simplify the choice from among a myriad of possible starting functional forms. are known but the b. X 2 combinations. p p = number of terms in the function b0 = an unknown constant X1.. Specification is completed when p + I independent restrictions are imposed. This model is defined in Ward (1977) as the following: Y = b0 + blXla + b2X 2b + b3XlaX2) (2) 24 . These policy statements result in a set of equations (restrictions) in terms of bi and b0 so that the numerical values of the weights can be determined. 1977).. and X2. In the current version of policy specifying.. Promotion Policy Specifying Hierarchy. (1) Prior to the policy specifying process.. = the unknown weights to be determined by the policy specifying procedure j=1. X2 = variables which are not vectors of data but are variables or combinations of variables which. the decision maker/decision analyst team must form the interactive functions for each of the pairs.PROMOTABILITY (FOS) CAPABILITY (F04) PERFORMANCE (F02) POTENTIAL (F01) II GOK JKT F 1 AD IPR EXPERIENCE (W03) 1 TIS 7 TIG Figire 8. the range of possible values for X1 and X. For this example. Once the hierarchical decision tree is formed. this is done by using the following general procedure: Specifically let b. Policy specifying proceeds by constructing the pairwise functional relationships between the decision variables which are the consequence of specifying Y values for stated X. when given a set of weights bj and b0 and a set of values for X1 and X2 will yield a composite value Y.... The general starting function is: Y = b0 + b1 X1 + b2X 2 + b3XIX 2 + b4X1 2 + b5X 22 + . Once the values of bj and b0 are known.bpXmIXn2. Each of these models attempts to capture the interaction between and among the decision variables.. the decision analyst has two starting models to work with (Ward. then predicted values Y can be calculated for any values of X. and b0 values are not known. the following model will be selected as the starting model.
bl. b3 are as defined previously. 90 so 70 O=0 60 (100.where: bo. JKT-GOK Worst/Best Payoff Table. The decisions concerning the extreme points given the worst/best value of the other variable result in the payoff table in Figure 10. b3). GOK JKT 0 100 100 50 100 0 0 20 Figur 10. bl. The decision maker begins by deciding the extreme points of the relationship between JKT and Y (Payoff) or GOK and Y. JKT and GOK).0) 0 10 20 30 40 50 60 70 80 90 100 JKT fW= 9. there are four unknown parameters to solve (b0. Note that the decision maker has also decided that the relationships are linear (ab = 1) but that there is interaction between JKT and GOK since the payoff function for one of the variables changes depending on the level of the other variable. The decision maker has also scaled the decision variables and payoffs between 0 and 100. a and b are set to 1. Since the decision maker has decided that JKT and GOK are linearly related. Figure 9 depicts what a decision maker might have decided about the JKT-GOK relationship. b2.0. Y is a composite measure of the strength (payoff) of the relationship between X1 and X2 (in this case. 25 . at points where the other variable is at its worst or best.50) 40 30 10 (0. JKT-GOK Relationship For this starting model. b2.
the decision maker is given feedback about what impact his.Using the promotion example translated into this starting model. the decision maker might be given the payoff table in Table 7 as a result of applying the current functional relationship (Equation 4) for JKT and GOK.003 10. a surface is fit to the points and a function formed which represents the decision policy. (3) Now there are four points (restrictions) for the payoff (Y) which are sufficient to allow the computation of the weights: Y(0.5 b. A variation on this approach is to allow the user to expand the model (number of terms and degree of interaction) and to evaluate the goodness of fit at each expansion. this function has some statistical error of fit which should improve with more points. Surface Fitting Procdure An alternative to the use of specified starting models has also been developed.000 Since each weight is now known. With a sufficient number of points.003 (JKT)(GOK) (4) The process continues for each of the other pairs of decision variables or functions until function F05 (PROMOTABILITY) is formed.2 100 Y(100. = 100 Y(0. The decision maker could decide that the relationships depicted in the table do not adequately represent his/her policy and make changes in one or more of the parameters of the starting model and repeat the computation of F01.100) = 0 + bj(0) + b2(100) + b 3 (0)(100) = 20 b2 =20 = . function F01 can be stated as: F1 = .2(100) + b 3 (100)(100) = 100 b3 = 30 = .0) = b0 + b 1(0) + b 2 (0) + b3(0)(0) = 0 b= Y(100.'her interaction decisions have on the payoff at each point in the tree. At each stage of the model formulation. Fortunately. 26 .5JKT + .2GOK + . These alternative fitting procedures allow for more flexibility in function development. GOK) = b0 + b 1JKT + b 2 GOK + b 3 (JKT)(GOK). For example. these computations are handled by the policy specifying software package.0) = 0 0 + bl(100) + b 2 (0) + b3(100)(0) = 50 = . This alternative procedure allows the decision maker to supply various points in the payoff table. Of course. with function FO1 (POTENTIAL).100) = 0 + . Equation 2 becomes: Y(JKT.5(100) + .
At the same time.Table 7. 27 . that is. they could be used to evaluate other techniques than those considered in this study. Thus. Attributes were designed to be generalizable. The attributes roughly divide into two categories: those related to scientific issues. and those related to empirical or elicitation issues. most criteria reflect concerns that are relevant to deciding in a particular context which technique to use. although specific comparisons between the four approaches to be evaluated in this study suggested some criteria. the evaluation conducted for this study required attributes suitable for comparing all four techniques within a specific context. JKT-GOK Payoff Tab'e GOK JKT 0 10 20 30 40 50 60 70 80 90 100 100 50 55 60 65 70 75 80 85 90 95 100 90 45 50 54 59 64 69 73 78 83 87 92 80 40 44 49 53 58 62 66 71 75 80 84 70 35 39 43 47 51 56 60 64 68 72 76 60 30 34 38 41 45 49 53 57 60 64 68 50 25 29 32 36 39 43 46 50 53 57 60 40 20 23 26 30 33 36 39 42 46 49 52 30 15 18 21 24 27 30 32 35 38 41 44 20 10 13 15 18 20 23 26 28 31 33 36 10 5 7 10 12 14 16 19 21 23 26 28 0 0 2 4 6 8 10 12 14 16 18 20 Evaluation ADnroach The framework for assessing the methodologies included specification of evaluation attributes that were context dependent and a scale on which to score the techniques being evaluated. A total of 15 attributes were defined and included in the technique scoring device and are described in detail in Figure 11.
Ability to use method with little or no training. while others have been less widely used and not much has been published about their use. or higher order polynomial relationships. Figure 11. and then wants to test how the introduction of new problem attributes would affect the decision model. and the decision maker's preferences and decision logic. Ability to communicate the technical aspects of the problem. the analyst wants a decision modeling technique that will encourage detailed understanding of the substantive features of the problem. This ability is concerned with how easy the method is to use. There are contexts in which the user has no experience using decision modeling techniques and therefore it would be important for the technique to be easily understood and require little experience or training for use.Ability to model judgmental dependence. the problem attributes cannot be judged independently. Ability to expand model to incorporate new problem information. The analyst might want to find a technique that provides easily communicable attribute scales and facilitates their understanding. multilinear. the analyst wants to use a technique that facilitates communication. Another area in which a technique might excel would be that it easily lends itself to displaying key problem components and their linkage to the decision recommendations. In some decision contexts. and is asked to evaluate each decision option separately. Some techniques will have well-founded axiom systems. It may be that there is an interaction among the attributes that must be considered. For some decision problem areas. Decision Attributes. 28 . the analyst uses a decision modeling technique to model and replicate the decision maker's decisions. this becomes important because the decision models will be scrutinized closely for accuracy and repeatability. the decision maker's value structure. so that they are not usable by the non-expert. the analyst may need to adopt a role to help the decision maker understand more about the problem. rather than sequentially. is also desired. rather than to study his decision process. Some methods are very complex and difficult to understand. and the sensitivity of the problem to the modeling approach. Others will have been developed using an ad hoc approach without much thought given to utility measurement theory. This ability concerns the ease with which a decision model developed using a decision modeling technique can be changed when new problem information is added. In the most general case. In these contexts. Others are more usable by the non-expert who has some experience or training. since the decision maker is shown all the decision attributes for each decision option simultaneously. the decision modeling technique is used to model the decision maker's decision holistically. In some contexts. Some decision modeling techniques have been well researched and have a great deal of empirical and psychophysical support in the published literature. In some contexts. In some contexts. Some techniques can handle the introduction of new information easily. or that combinations of the attributes are more important than single attributes. The analyst might also require the technique to facilitate an understanding of how the decision problem might be sensitive to the modeling technique used and the attributes of the problem. rather than to provide the decision maker with a model that can be applied to solving the problem. In these cases. and published and defended in well-known journals. Ability to model judgments holistically. The analyst might also want to use a method that requires explicit definition of the decision maker's values and preferences in an easily communicable form. founded in utility measurement theory. the analyst uses a set of problem attributes and decision options to develop the decision model. Ability to develop a decision model that is theoretically defensible and scientifically well founded. A technique that produces a detailed understanding of the decision maker's value structure. some contexts require techniques that have the ability to model more complex forms of judgmental dependence among attributes. In some decision contexts. Ability to aid understanding of the features of the problem. This ability concerns how well researched the decision modeling technique is and how well it can be explained. This judgmental dependence can be modeled by techniques that allow the use of multiplicative. and others require the process to be reaccomplished to incorporate new information. to aid the decision maker in this understanding.
An acceptable technique will be essentially straightforward to use. Some decision modeling techniques will be more amenable to this form of analysis than will others. and this single person will develop the decision model. Ability to develop model with little decision maker involvement. In some contexts.Ability to perform sensitivity analysis. there arises the need in some decision contexts to perform a sensitivity analysis on the decision model. In these contexts. for problem structuring. the final product of the decision modeling exercise. there will be only a few options to choose from. Other techniques are not equipped for this type of application. Some techniques handle this relatively easily because they develop mathematically based models that take the form of an equation. After an analyst has developed a decision model. and some techniques can be used only with a single decision maker. or for problem evaluation. Techniques vary in their ability to be used by an analyst who has limited availability to a decision maker during the decision modeling process. computer resources are abundant and this will not be an issue. will be delivered to a customer who must implement and use it operationally to make decisions. Ability to model a group decision making process. Ability to develop model with little analyst involvement. the decision maker's time is limited or very expensive. This equation can be applied to a new decision option by simply plugging in the new attribute values and determining the results. and this will affect the choice of decision modeling technique. Acceptability to the users of the final product. Techniques will vary on their ability to handle different sizes of option sets. In some decision contexts. Some decision modeling techniques require many decision options in order to develop a reliable model (such as regression-based holistic modeling techniques) and might not produce reliable decision models with a small number of options. the decision model developed. which becomes more tedious as the number of options increases. Ability to develop decision model without using a computer. Some techniques have been explicitly developed to meet the problem of developing a group decision model. The analyst may wish to modify the weights on particular attributes or the form of the model or the way in which the value hierarchy was constructed. The number of decision options to be considered in developing a decision model will vary from one decision context to another. Ability to model decision environment with many decision options. or there is a single decision maker who will be responsible for the decision problem. Decision modeling techniques vary in their capability to be used without an analyst to aid the decision maker. Other techniques might be able to be used with or without a computer. In some contexts. either the group appoints one person to be spokesperson for the group. several features of the decision modeling technique will affect how well the decision model is accepted. In some contexts. the decision maker is actually a group of people who must make the decision and therefore the group itself develops the decision model. still others might have to be used without a computer because no software exists that supports the methodological approach. Some decision modeling techniques require extensive computer support. In some decision contexts. whereas in others the number of options may be large. In some contexts. and the analyst desires after the fact to apply this model to new options that were not considered in developing the decision model. In some contexts. the decision model is developed using one set of decision options. the decision maker may have to develop the decision model using no or little analyst involvement. but in other contexts computer resources may be scarce or non-existent. and produce models that are easily understood. or the technique requires all decision options to be known beforehand in order to develop a model. the decision model. Others require pair-wise comparisons between all options. there are no analysts available to aid the decision maker in using the decision modeling technique. the analyst will modify some part of the model to determine how sensitive the results of applying the decision model to a set of options are to changes in that part of the model. Figure 11 (concluded) 29 . or the only analysts available are too expensive to use. for parameter elicitation. and will require judgments that are easily made by the decision maker. These techniques will produce a logical structure that is substantially acceptable. In other contexts. In a sensitivity analysis. to determine if these changes impact the decision recommendations for a particular decision option set. because the model lorm is a hierarchy rather than an equation. In these contexts. others can be adapted to meet this condition. and the analyst will have to develop the decision model with very little input from the decision maker. Ability to apply decision model to new options.
1976). 30 . whereas policy capturing scored highest on 3 of the attributes. Each expert rated the technique they knew across each attribute and a single rating for each attribute for each technique was calculated using an average of all ratings. The scale used to judge the techniques is shown at the top of Figure 12. and ranges from "extremely capable" to "extremely incapable" of providing each of the 15 attributes. The judgment to be made in each case was whether the technique was able to provide the user with that capability and then to what degree it was able to do soEvaluation Results The matrix was provided to 18 experts familiar with one or more of the four techniques. The agreement among experts was tested by calculating an interrater reliability for the expert's rating on each technique (see Christal & Weissmuller.These attributes were then used to develop the Technique Scoring Matrix shown in Figure 12. These scores reflect that SMART was considered to be best on 8 of the 15 attributes. The scores given for each of the techniques are shown in Table 8. corroborating the accuracy of using the averaging technique to smooth differences. The interrater reliabilities (Rkk) ranged from .90 for the policy specifying ratings.70 for the SMART ratings to .
and the decision maker's preferences and decision logic Capable of being used with little or no training Capable of developing a decision model that Is theoretically defensible and well founded scientifically Capable of expanding model to Incorporate new problem information Capable of performing sensitivity analysis Capable of producing a final product that Is acceptable to the user Capable of being used without a computer Capable of modeling decision environment with many decision options Capable of being applied to a new decision option set Capable of being used to develop model with little analyst involvement I Capable of being used to develop model with little decision maker involvement I j I I I Capable of being uised to model a group I decision making process I Fizur 12. 2.I this technique is: 8. and the sensitivity of the problem to the modeling approach Capable of communicating the technical aspects of the problem. 31 . 5 4. 6. 3. 7. I Extremely Capable Very Capable Moderately Capable Slightly Capable Slightly Incapable Moderately Incapable Very Incapable Extremely Incapable Capable of modeling Judgmental dependence Capable of modeling decisions holistically Capable of aiding understanding of the problem. 1. the decision maker's value structure. Technique Scoring Katrix.
3 6.4 1.4 _ I I I I POLICY CAPT _ _ _ _I 7.0 4.0 1.8 5.3 linvolvement I lAbility to model Igroup process 32 7.4 -_ _ I 5.0 3.0 3.8 7.8 6.3 5.4 I 1 I I 4.6 5.0 3.7 1 I 2.6 .9 1 6.4 5. I I _ _ _ _ _ I jAbility to model I lJudgmental 1 Idependencies I I _ _ _ _ jAbility to model 1judgments 1holistically I _ SMART _ _ _ 3.6 7.9 _ I I I aid lunderstanding I lAbility to lAbility to I 1 Icommunicate the Idecision logic I I I lAbility to use I Itechnique with no 1 Itraining I I I lAbility to developl Itheoretically 1 Idefensible model I I lAbility to expend Imodel with new 1 linforuation I I JAbility to perIform sensitivity lanalysis I 4.1 3.7 1.Technique Scoring Results Table 8.6 7.9 7.4 6.0 5.6 7.8 7.3 _ _ _ I 1 _ HAWM _ _ _ I I POLICY SPEC _ _ _ _ 3.1 I lAbility to JAbility to model jw/ little analyst linvolvement I jAbility to model 1with little DM 2.6 I 4.7 5.3 5.8 I 5.0 3.7 3.0 I I 6.6 7.0 5.6 3.7 I I I 4.8 I 6.2 I lAbility apply Idecision model to Inow option set 1 I 1 3.1 I I I 6.7 3.8 I jAcceptability of Ifinal product I lAbility to model Idecisions without I& computer I I to model I Idecision with manyl Idecision options 1 6.3 1 I 5.8 I I I 7.8 6.4 4 7 3.0 6.8 1 5.0 4.8 5.8 6.0 3.0 _ I _ _ 1.
The categories in which SMART scored lowest pinpoint its weaknesses: its inability to model judgmental dependencies and its inability to model judgments holistically. SMART has a computer implementation that works well and does not require much involvement on the part of a decision analyst. ability to apply model to new decision option set. and ability to model with little decision maker involvement. It scores well on the group attribute since it was developed to systematically handle group decision making situations. Even with its lack of complexity. The technique also has the weakness of involving many resources. and therefore cannot take advantage of advancements or variations which have been described by others but not implemented in these particular software packages. even though it was rated lowest on only one of the attributes: ability to aid understanding. acceptability of the final product. The other techniques have also been judged in this report as single implementations of a body of literature. primarily because of the lack of complexity in the method. and a statistical software package to determine the regression equations. offers little insight into decision problems. Policy capturing also has the advantage of being considered in this study as a class of techniques which have been in the literature for over 25 years. It is a hierarchial procedure by design. Because of its descriptive nature and the fact that the final output is a policy equation. A great deal of time and resources are required before and after a policy capturing session. It naturally also has the most empirical literature published. ability to communicate decision logic. SMART Evaluation The strengths of SMART are reflected in the 8 attributes on which it ranked first: ability to aid understanding. all models in SMART must be additive and linear in all attributes. In addition. ability to model decisions without a computer. but only on mainframes which lack the flexibility of traveling to where the user is located. ability to communicate the decision logic. ability to use with no training. On the negative side. because of its age and the fact that it is a class of techniques. The other three techniques are primarily prescriptive techniques. policy capturing rates highest in its ability to be applied to a new decision option set. and has no capability for modeling judgments holistically. SMART is well founded axiomatically.In contrast. easy to use and easy to understand. based on decomposition techniques developed to be used by single decision makers. and was developed to be used in a group setting. HAWM was ranked last in nine categories: ability to aid understanding. and because of its descriptive nature. ability to expand with new information. ability to perform sensitivity analysis. It is a fairly straightforward technique. ability to develop a theoretically defensible model. Policy capturing. by its design and use. policy specifying was ranked first on only 3 attributes but last on 4 attributes. 33 . Most applications of the technique use hard copy records to elicit judgments. paper and pencil to record them. so that judgmental dependencies cannot be addressed. because the only outputs available for examination are the regression weights. Policy capturing has some weaknesses. or the rationale for a particular decision. Some implementations have automated portions of this procedure. in setting up judgment samples. Policy capturing is strong in these areas primarily because it is a descriptive technique based on holistic judgments. and have been implemented in many different forms. Policy Capturing Evaluation Policy capturing has some strengths also. has no facility to incorporate a hierarchy. Decision makers believe the results and trust in its use. ability to perform sensitivity analysis. HAWM Evaluation HAWM was ranked first on only one attribute: ability to model decision with little analyst involvement. There is no one computer implementation of the class of techniques known as policy capturing. HAWM was ranked first only once and was last on 8 attributes. SMART has no built-in procedure for handling functional dependencies or correlations. The judgments made in the hierarchy are naturally made and readily communicated. and ability to model group processes. with the difference judgments that are required based on axioms from measurement theory. and in analyzing the results. as evidenced by the categories in which it rated highest: ability to model judgments holistically.
However. ability to use without a computer. There are six decision attributes used in this context: Individual Preference (IP). ability to model with little decision maker involvement. The addition of new alternatives can upset the rational prescriptions of the technique primarily because the alternatives in HAWM are introduced as part of the hierarchy. Time Remaining to fill job (TR). The ranking of policy specifying as highest on the judgmental dependency attribute is significant. and ability to model decisions with many decision options. 1985). The introduction of new alternatives can cause rank reversals for alternatives that had been previously judged.acceptability of final product. unlike the other two techniques. Technical School predicted Success (TSS). and then participates with the individual in deciding what job he/she should fill in the Air Force. and could not handle any functional forms except linear additive models. an enlisted person-job-match system. Policy specifying was developed to meet a perceived void in the decision modeling field--the inability to handle judgmental dependencies (sometimes called interactions). The contexts studied were: an Air Force promotion board. The Air Force promotion board decision context has already been discussed in detail as the common example in Section III. The nature of this decision context is that it is a sequential process: as one job is filled another person with unknown characteristics arrives requesting a job. Before a discussion of the evaluation methods is carried out. and the ability to model a decision with many decision options. Its low ranking in terms of analyst involvement reflects the amount of time required by the decision analyst and the decision maker to arrive at a pairwise hierarchy and a pairwise function for each element in the hierarchy. This implementation of the technique was not equipped to handle a group decision process. Policy Soecifyine Evaluation Policy specifying was ranked highest on three attributes: ability to model judgmental dependencies. policy specifying in this implementation is a very complex procedure that is difficult to communicate to users. Policy specifying was ranked lowest on four attributes: ability to use technique with no training. Saaty & Takizawa. Decision Contexts In the Air Force enlisted person-job match (PJM) decision context. the Air Force is faced with making a classification decision about each individual entering the Air Force. Like the other two prescriptive techniques. IV. and ability to model with little analyst involvement. the literature discusses versions of Saaty's AHP process which theoretically could handle non-additive and nonlinear models of the decision process (Harker & Vargas. namely. it suffers from the lack of features to handle functional dependencies or group decision processes. ability to develop a theoretically defensible model. the technique is extremely sensitive to the introduction of new information. as the decision maker is formulating a decision model. ability to expand model with new information. and the prioritization of R&D projects. Policy specifying was the only technique of the four studied which allowed for this ability to specify more complex models through the introduction of curvilinearity and interaction. and ability to model a group process. HAWM was rated last in ability to model decisions with many options and ability to be applied to a new option set. The classification decision is two-tiered in that the Air Force first decides whether or not to allow the individual to enlist. HAWM ranked last in the attribute of modeling a group process and low in the ability to model judgmental dependencies for nearly the same reason. 1985. two of the three decision contexts will be discussed in more detail. However. policy specifying was also ranked first on the ability to expand with new information. Thus the decision options (each person-job match) are unknown and many. ability to apply decision model to a new option set. The introduction of any new information requires that the judgment process be reaccomplished since every member of the hierarchy must be pairwise compared to every other member of the next level in the hierarchy. Fraction of jobs Filled (FF). ability to model decision with many options. it has the smallest body of published literature of the four techniques. EVALUATION OF CONTEXT/TECHNIQUE MATCH In this section discussion will focus on the evaluation of these four techniques as applied to three Air Force decision contexts. for very nearly the same reason. Because it is a technique used almost exclusively by the Air Force Human Resources Laboratory. Job 34 . Because it is built using a very flexible pairwise hierarchy.
In the R&D project context. as reflected by the minimum score required on the ASVAB in order to qualify for each particular job. but here the reference is to the formulation by DeWispelare (1983). Each job will have its own requirement score in one of the four aptitude areas. since it is the result of predicting a person's success in a technical school using demographic data about the individual. the Air Force is faced with making a decision about how R&D funds should be programmed over a fiscal year. In this context. and a scheme is necessary for determining how to best allocate the funds. A regression equation is developed using actual technical school results for each technical school as the dependent variable. Administrative (A). The SP attribute is an estimate of the number of potential sponsors for the project. There are more projects requiring funding than funds available to pay for them. and Applicant Aptitude (AA). the intention of this variable is to reflect the impact on the job assignment system of leaving a job empty. JR is the aptitude requirement of each job. and Time to Project Fruition (TPF). The TB attribute is measured using a 10-point scale that reflects how much of the R&D effort has already been expended on any particular project area. as determined through survey or telephone interview. G.Requirement (JR). Many different formulations have been tried for this problem.75 for the promotion board context to . This attribute is estimated using expert opinion and past history. and a payoff (utility) table was generated using the policy specifying technique. As with the technique ratings. FF. The attribute C reflects an estimate of the cost to complete the project within a 5-year planning horizon. and reflects the utility. using the same 15 attributes to form the rating form shown in Figure 13. A. For more information on this decision context. Cost (C). Evaluation Aproach The framework for evaluating the methodologies in specific contexts starts with the 15 attributes that were developed for the technique evaluation in Section II of this report (shown in Figure 12). General (G). the reader is referred to Ward. Hendrix. there are four attributes to be considered in making the decision: Technology Base (TB). In this decision context. The eight-point scale on this form reflects the need for the technique used to have the 15 abilities shown on the form. and in many cases will have a combination of scores required. the options are few and known before the decision has to be made. The job characteristics ae the JR. and E aptitude areas of the Armed Services Vocational Aptitude Battery (ASVAB). Haney. Sponsorship Potential (SP). These scores were then matched with the technique scores from the first group of experts. the interreliability for each set of raters' ratings was calculated. of each combination of context need and technique capability. A second group of 13 experts were sent these forms (a group of experts distinct from those who evaluated the techniques in Section III). The TR attribute is related to the FF attribute in that TR reflects the length of time remaining to fill the particular job. The rater first decides on whether or not the ability is important to the decision context and then to what degree it is or is not important. corroborating the accuracy of using average ratings for the group of experts. The results were collected and then averaged to form an average context need for each ability. and person characteristics. As soon as a technique falls below the minimum needs of a context. Of course. the payoff is reduced substantially until the curve flattens out at the lower scores. The FF attribute reflects the number of jobs of any one kind that are presently available divided by the number initially available during a specific period of time. The payoff table generated here reflects the opinion of the experts that the technique that meets or exceeds the needs of the context will always receive the maximum payoff of 100. 35 . and Pina (1977). The four aptitude areas in this context are: Mechanical (M).85 for the PJM context. to the context. A similar evaluation tool was developed for each context. indicating the fraction of jobs currently filled. These attributes are divided into two categories: job characteristics. The TSS attribute is both a person and job attribute. This table is shown as Table 9. and Electronics (E). with a Delphi procedure used to achieve consensus among the judges. The attribute TPF is an estimate of the actual time required to achieve the research objective. Among the person characteristics are the IP and AA attributes. and the decision is typically made by a team of experts within the research organization. and TR attributes. These reliabilities ranged from . These judges were asked to score the need for these abilities within a context with which they were familiar. The IP attribute is collected from the individual using a crude measuring instrument which allows the individual to express interest in the four aptitude areas on a scale from 0 to 10. The AA attribute is the person's scores in each of the M.
In this context this ability is: S. I I Context Scoring Matrix. the decision maker's value structure. 7. Extremely Important Very Important Moderately Important Slightly Important Slightly Unimportant Moderately Unimportanti Very Unimportant Extremely Unimportant Ability to model Judgmental dependence Ability to model Judgments holistically Ability to aid understanding of the features of the problem. 5. 1. the decision model developed Ability to develop decision model without using a computer Ability to model decision environment with many decision options Ability to apply decision model developed to a new decision option set Ability to develop model with little analyst involvement Ability to develop model with little decision maker involvement I I Ability to model a group decision making process Figure 13. 36 I . 4. and the decision maker's preferences and decision logic Ability to use method with little or no training Ability to develop a decison model that is theoretically defensible and scientifically well founded Ability to expand model to incorporate new problem information Ability to perform sensitivity analysis Acceptability to the users of the final product. 3. 2. and the sensitivity of the probleml to the the modeling approach Ability to communicate the technical aspects of the problem. 6.
Table 9. 37 • I' I I' ' . Weighting was accomplished using the Context Weighting Matrix. until the eight twigs of the scientific portion of the hierarchy were rated. examining the quality of a technique's axiomatic foundation. This hierarchy is shown in Figure 14. These weights were then normalized for use in the SMART procedure. reflecting how much less important they were than the top ranked match. There are two main branches in the structure representing scientific issues versus issues that reflect empirical and/or applied considerations. Payoff of Context/Technique Match Technique Capability 1 1 2 3 4 5 6 7 8 100 100 100 100 100 100 100 100 2 64 100 100 100 100 100 100 100 3 53 62 100 100 100 100 100 100 e x t 4 42 52 62 100 100 100 100 100 5 32 42 52 63 100 100 100 100 N 6 21 32 43 54 65 100 100 100 7 11 22 34 45 57 69 100 100 8 0 12 24 37 49 61 73 100 C 0 n t e e d A hierarchical set of evaluation criteria was developed. then relative weights were assigned to the other matches. The structure was designed to be comprehensive while ensuring independence between criteria whenever possible. and issues involved with model elicitation. For each of the "twigs" shown at the far right of the value structure--labeled context/technique match--the same group of experts who scored the contexts were asked to use the SMART procedure with the swing weighting methodology described earlier to generate the relative weights for each alternative technique context match. First the expert assigned a rank of 1 to the most important context/technique match and 2 to the second most important. based on the same 15 abilities measured in the context and technique scoring matrices. Empirical considerations are broken into issues such as acceptability to users. understandability of methods and results. a percentage of 100 was assigned to the highest ranked match. and the technique's complexity and/or difficulty of understanding. shown in Figure 15. The purpose of the hierarchy was to allow the decision maker to give relative weights to the 15 abilities for each context. II IA . The scientific branch focuses primarily on validity and versatility issues. the technique's ability to model complex value structures. including a technique's usefulness in group decision making. and its requirements for resources and decision maker involvement. Once all eight were ranked.
Hierarchical Structure.Ability to model Judgmental dependencies context technique match - Ability to model judgment* context - technique match holistically Ability to aid understanding Scientific Issues - context technique match - Ability to communicate the decision logic - Ability to use technique with no training - Ability to develop theoretically defensible model - context technique match context technique match context technique match Ability to expand model with new information Ability to perform sensitivity analysis Technique Utility in This Context Acceptability of final product Empirical Issues context technique match context technique match - context technique match - Ability to model decisions without a computer - Ability to model decision with few known options - Ability to model decision with many unknown options - context technique match context technique match context technique match Ability to model with little analyst involvement context technique match Ability to model with little D1K involvement context technique match Ability to model group process context technique match Ea14. 38 .
39 I . lAbility to model Idecision with Imany options I Poor context technique match I I I I I I I Good context I technique match Poor context technique match I 1- Good context technique match I _ jAbility to apply Idecision model to Inew option set I _ _ _ _ _ Poor context technique match I I I I Good context technique match _ _ _ _ _ I I I I Poor context technique match lAbility to model Iwith little DH lnvolvement I I Poor context technique match I Good context technique match I I _ I _ I I I Poor context technique match II lAbility to model Igroup process _ _ _ _ _ _ _ _ _ _ _ Good context technique match jw/ little analyst lInvolvement I _ I lAbility to model _ I I I I _ I I I Idocisions without Is computer _ _ _ I Itheoretically Idefonuiblo model I lAbility to expand loodel with new linformation _ _ I I lAbility to develops I Weight I II _ II_ I I I I Iholistically _ _ _ technique match Poor context technique match Ijudgments _ _ Good context technique match II _ Rank I I Idepandencies I I _ I Good context technique match I _ _ _ _ I I _ _ _ _ Good context technique match I I I Figur= 15.CONTEXT I I II _ _ _ _ _I lAbility to model 1judpantal I Worst _ _ _ _ _ I I_ _ Bet _ _ _ I_ Poor context I lAbility to model I Good context technique match I Poor context technique match I Good context technique match I I Poor context technique match I I Good context technique match I jAbility to use I Itechnique with no Poor context Itraining I technique match I Good context technique match II I I lAbility to aid lunderstanding I I !Ability to ]communicate the Idecision logic I I I Poor context technique match Good context I technique match I I I I Poor context technique match Good context I technique match I lAbility to per- I Iform sensitivity janalysie I I Poor context technique match Good context I technique match I I I II II I ]Acceptability of Ifinal product I I lAbility to model I I Poor context technique match I 1. Context WeigbUng Matrix.
The resulting payoffs are shown in Table 11. and ability to apply the decision model to a n:w decision option set.V. This group of experts also gave relative weights to the 15 abilities using the swing weighting method described in Section III. ability to model in a decision environment with many decision options. The average relative weights used in the utility determination are shown in Table 12. using the payoff matrix of Table 9. Table 13 reflect. In the analysis process. These weights were used as the twig weights in SMART. the final results of the utility determination procedure. with the assumption that the scientific and empirical sides of the hierarchy would receive equal weight in the utility determination. but combinations of techniques were not studied in this evaluation. CONTEXT EVALUATION RESULTS Person-Job-Match Context The results from employing the context scoring matrix for the PJM context are shown in Table 10. This table shows the average rating for each ability given by the group of experts that participated in the study. with policy specifying a close second choice. the experts believed that the three most important abilities a technique should have were acceptability of the final product to the users. In the actual decision context. Policy capturing was ranked highest in the PJM context. the Air Force has used a mixture of policy specifying and a utility weighting procedure similar to SMART. These payoffs were then used as the scores for the matches in the SMART procedure. Multiplying by the payoff scores determined above resulted in the relative utilities for the four techniques shown in Table 13. the average scores were then combined with the average scores for the techniques previously collected. Within this context. 40 . These last two abilities reflect the sequential nature of the PJM decision context.
Extremely important Very Important Moderately Important 5. the decision maker's value structure. Slightly Important 4. the decision model developed Ability to develop decision model without uiing a computer 2. Extremely Unimportant 2.9 product. Slightly Unimportant Moderately Unimportantl 1. 7.1 Ability to model a group decision making process 6.3 Acceptability to the users of the final 7.4 Ability to perform sensitivity analysis 5. and the sensitivity of the probleml .lahkI 10.7 41 .4 Ability to model JudL-eents holistically 4.. 3.4 many decision options Ability to apply decision model to new 7. 6. Very Unimportant Ability to model Judgmental dependence 6.4 Ability to develop a decison model that is theoretically defensible and scientifically 5.4 well founded Ability to expand model to incorporate new problem information 6. and the decision maker's preferences and decision logic 6.7 Ability to develop model with little decision maker involvement 5.9 Ability to model decision environment with 7..4 Ability to use method with little or no training 5.3 decision option set Ability to develop model with little analyst involvement 3. 9 to the modeling approach Ability to communicate the technical aspects of the problem. PJM CoKtaIt In this context this ability is: 8.7 Ability to aid understanding of the features of the problem.
JaWM 11. Payoffs for PJM Context I I __ _ PJK _ IPOLICY SPECIFYING _ _I __ jAbilty to model Ijudsmental Idependencies _ 1 _ _ POLICY I__ _ SI4ART CAPTURING _ 100 _ _I _ _ 61 I HAWK( I __ __ _ 42 43 II lAbility to modal I 1 [judgments I 61 I III _ _ _ I_ _ 1 junderstanding I _ _ I_ _ 100 55 _ I _ I 1 I_ _ 72 1 Idecision logic I _ 70 _ _ _ _ I _ _ _ 74 100 I 1 68 1 I _ _I _ I I icommunicate the _ 1 I lAbility to _ 35 I IAbility to aid _ 1 100 Jholistically 100 1 I I_ _ _ _ _ 65 I I_ _ _ I_ _ _ _ jAbility to use I Itechnique with no 1 !training 58 lAbility to developi ItheoretIcally 1 Idefensible model I 7 1 100 100 100 100 1 51 58 37 100 1 100 100 60 I jAbility to perIform sensitivity I [analysis I_ _ I _ _ I _ 1 I I I lAbility to model Idecisions without Ia computer I I I___ _ _ I I _ _ _ _ _ I___ I___ jAbility to model Iwith little analyst involvment I I lAbility to 1 100 I 1 I I_ I _ _ 1 I _ _ I_ _ I 70 _ _ I _ _ _ I 76 58 100 100 I I I 61 _ 1 I _ _ _ 65 I I_ _ _ I_ _ _ _ _ I 76 74 1 I _ _ _ I 61 _ _ _ _ _ _ I I _ _ I _ _ _ _ _ _ I_ _ _ I_ _ _I 60 I I 42 I 12 I _ _ _I_ I 1 _ I 65 I _ 13 I I _ _ I 77 74 _ _ 1 I I _ I_ I 1 55 I 1 I 65 Jwith little DM14 linvolvement 100 I I lAbility to model model Igroup process II _ 71 jAbility to apply I Idecision model to Inew decision set I _ I imany options I _ 1 Idecision with 67 I jAcceptability of Ifinal product lAbility to model 1 _ I I 1 _I I I lAbility to expand I moodel with new linformation I _I I I I_ T I I _ I 100 100 1 100 54 58 1 51 100 55 45 .
the decision model developed .039 .048 Ability to develop model with little decision maker involvement .095 Ability to develop model with little analyst involvement .061 .077 Ability to perform sensitivity analysis .059 Ability to aid understanding of the features of the problem.053 Acceptability to the users of the final product.Tahk 12. and the sensitivity of the probleml to the modeling approach Ability to communicate the technical aspects of the problem.032 Ability to model decision environment with many decision options . the decision maker's value structure. and the decision maker's preferences and decision logic Ability to use method with little or no training Ability to develop a decison model that is theoretically defensible and scientifically well founded .051 Ability to expand model rn incorporate new problem information .088 Ability to apply decision model to new decision option set . PJM Context Weghts Ability to modal judgmental dependence .054 .053 Ability to model a group decision making process .099 Ability to model judgments holistically .105 Ability to develop decision model without using a computer .075 43 .
These payoffs were then used in the SMART procedure using the context weights shown in Table 16. Policy capturing procedures were found to be most appropriate for the Air Force promotion system context. Table 17 reflects the final result of the utility ranking procedure. the ability to apply the model to a new option set. These weights.9 SMART 72.1 HAWM 53.7 Promotion Board Context The same procedure was then applied to the promotion board context. the ability to model an environment in which there are many decision options. These ratings resulted in the payoffs shown in Table 15.Table 13. The experts' ratings show that the highest rated attributes for this context were the ability to model judges holistically. Even though PJM and this context have two attributes rated highest in common. and the ability to model a group process. the acceptability of the final product to the user. Based on this. thus providing some support for the utility procedure used in this analysis. resulted in the relative utilities for the four techniques shown in Table 17. the Air Force has used the policy capturing technique for promotion board work.2 POLICY SPECIFYING 75. it would be expected that the rank ordering of the four techniqucs should be different. the total ratings are quite different from the ratings given in the PJM context. when combined with the technique ratings. In the actual decision context. when multiplied by the payoffs. 44 . Table 14 contains the average expert opinions as to the importance of the 15 attributes in this context. Overall Utilities: PJM Context POLICY CAPTURING 76.
6 Ability to use method with little or no training 5.Ium 14.2 I Ability to model judgments holistically I I I 7.0 Ability to model a group decision making 7.6 process 45 .0 well founded Ability to expand model to incorporate now problem information 5.8 using a computer Ability to model decision environment with 7.2 I I Ability to develop a decison model that is theoretically defensible and scientifically 6.0 Ability to perform sensitivity analysis 4. the decision model developed Ability to develop decision model without 2. Moderately Unimportantj Very Unimportant I. 4. Very Important 6. 2.8 Acceptability to the users of the final 7.0 analyst involvement Ability to develop model with littlc decision maker involvement 5.2 many decision options Ability to apply decision model to new 7. Slightly Important Slight4v Unimnortant 3. and the sensitivity of the probleml to tne modeling approach Ability to communicate the technical aspects of the problem.4 decision option set Ability to develop model with little 4. Prom In this context this ability is: In Be"d Conteit 8. the decision maker's value 6.0 structure. Extremely Important 7.4 I I Ability to aid understanding of the features of the problem. Extremely Unimportant Ability to model Judgmental dependence I 4.6 product. Moderately Important 5. and the decision maker's preferences and decision logic 5.
Payoffs for Promodon Board Context SII I PROHOTION BARD I IPOLICY SPECIFYINCI POLICY CAPTURINGI I I I jAbility to model lJudgmental Idepandencies 1 I _ _ _ _ I 1 I _ [Ability to model Ijudgments Iholistically 100 I _ _ _ _ I I I I 63 64 I _ _ _ _ _ I I _ _ _ _ _ _ II 37 1 100 6 30 I I III jAbility to aid junderstanding 1 II I lAbility to 1communicate the Idecision logic I I 100 71 100 73 100 100 100 72 69 100 II jAbility to use I Itechnique with no Itraining 59 I I lAbility to developj Itheoretically 1 Idefensible model I _ I HAN I I II I I 100 I _ I SHART _ _ _ I jAbility to expand lmodel with new linformation I 100 I I 54 I 100 I 1 100 I _ _ I I _ _ _ _ I I 71 I _ _ _ _ I I_ _ _ _ I 100 63 69 50 100 100 100 64 73 72 78 61 62 66 100 100 78 75 62 15 73 76 64 11 63 68 I100 56 55 59 52 47 37 II jAbility to perIform sensitivity lanalysis II I I I I jAcceptability of Ifinal product I lAbility to model I jdecisions without 1 I computer I II lAbility to model I Idecision with lmany options II I lAbility to apply I Idecision model to Inew option set I II lAbility to model I Iw/ little analyst 1 involvement I to model Iwith little DM linvolvement lAbility I lAbility to model Igroup process I _ _ _ _ I100 I 1 I I1 53 100 I I I _ _ I I___ _ 46 _ _ I _ _ _ _ _ _ I .Tabl 15.
077 Ability to apply decision model to new decision option set .036 Ability to model decision environment with many decision options .Tmj 16. and the decision maker's preferences and decision logic .069 .056 Ability to perform sensitivity analysis .068 I I Ability to expand model to incorporate new problem information .079 Ability to aid understanding of the features of the problem.069 Ability to use method with little or no training .-led I .050 Ability to develop a decison model that is theoretically defensible and scientifically well fo.087 47 . the decision maker's value structure. Promotion Board Context Weights I 1 Ability to model judgmental dependence .089 Ability to develop model with little analyst involvement . the decision model developed . end the sensitivity of the probleml to the modeling approach Ability to communicate the technical aspects of the problem.044 I I Ability to model judgments holistically .057 Ability to develop model with little decision maker involvement .055 Ability to model a group decision making process .062 Acceptability to the users of the final product.094 Ability to develop decision model without using a computer .
the Air Force uses many different procedures since this prioritization occurs at every R&D organization within the Air Force. In the actual decision context.0 POLICY SPECIFYING 73. Multiplying by the payoffs gave the relative utilities shown in Table 21. using the same procedures as were used on the other two contexts. The two attributes rated highest by the experts as being most important to this context were: ability to aid understanding and acceptability of the final product. The AFHRL has used policy specifying with some success. This combination of attributes is different from the two decision contexts previously studied and should have resulted in a different rank ordering of the four techniques.6 74. Table 18 contains the average expert opinions as to the importance of the 15 attributes in this context. 48 . Table 21 shows the final results of the assessment. These ratings resulted in the payoffs shown in Table 19. resulting in the twig weights shown in Table 20. Overall Utilities: Promotion Board Context POLICY CAPTURING SMART 80. and DeWispelare (1983) has suggested a more intricate form of multiattribute utility function development than the SMART procedure studied in this report.Tabl 17.0 HAWM 55. The experts also rated the relative weights for the 15 attributes in this context. The SMART procedure was found to be most appropriate for use in the R&D project context. when combined with the technique ratings.5 Research and Development Prolect Context The last context studied was the R&D project context.
Ixtremely Unimportant Ability to model Judgmental dependence 6. the decision maker's value structure. Slightly Unimportant 3.8 using a computer Ability to model decision environment with 5.4 Ability to develop model with little analyst involvement 3.6 Ability to use method with little or no training 5. Moderately Unimportantl 2. Very Unimportant 1.0 6. Very Important 6.2 Ability to model a group decision making process 6.0 many decision options Ability to apply decision model to new decision option set 6. the decision model developed 7.0 Ability to aid understanding of the features of the problem. Extremely Important 7. Moderately Important 5. and the decision maker's preferences and decision logic 7.6 Acceptability to the users of the final product. and the sensitivity of the probleml to the modeling approach Ability to communicate the technical aspects of the problem.6 Ability to model Judgments holistically 3.0 Ability to develop decision model without 2.0 Ability to perform sensitivity analysis 6.0 Ability to develop a decison model that is theoretically defensible and scientifically 6. Slightly Important 4.4 III well founded Ability to expand model to incorporate new problem information 6.Abk I& R&D Pired Citint In this context this ability is: B.2 49 .2 Ability to develop model with little decision maker involvement 3.
Payoffs for R&D Project Coatet I R& II OJ ECT IPOLICY SPECIFYINGI POLICY CAF U I lAbility to modal I Ijudgmental Idependencles 1 II I lAbility to model Ijudgments 1holistically I II. I GI I I SMRT I "Mi I I I I I 100 59 41 42 100 100 53 100 75 63 i100 65 68 66 lO0 64 61 70 i100 I100 100 I100 66 55 61 41 I lAbility to aid 1 Iunderstanding II I lAbility to Icoumunicate the Idecision logic I lAbility to use I 1 I Itechnique with no Itraining I I 1 lAbility to developi Itheorsticolly Idefensible model I I I I 50 I lAbility to expand I Imodel with new 1 lInformation I lAbility to perIform sensitivity lanalysis I 1 I I I 1 68 1 _ 78 I___ I Idecision with Imany options 1 I _ _ _ _ I I Jw/ little analyst 1 linvolvement I I I 1with little DM linvolvement I 1 I I lAbility to model Igroup process I I100 65 _ _ _ _ I _ _ I I_ _ _ _ _ I 62 66 100 100 I i _ 100 I100 100 38 72 21 _ I 100 _ _ _ I 100 _ _ _ _ 70 _ 1 _ _ I I I 100 _ _ _ _ _ I 100 I100 I 100 69 59 50 I I I lAbility to model I 77 48 I JAbility to apply I Idecision model to )new option set I _ 71 I lAbility to model I 69 I JAbility to model tdecisions without 1 (a computer I lAbility to model I I JAcceptability of Ifinal product _ I 100 I II I I I I 100 100 I 64 100 I I 50 _ .Iahk 19.
059 Ability to perform sensitivity analysis .086 Ability to develop model with little analyst involvement .069 .072 Ability to model judgments holistically .068 Ability to expand model to incorporate new problem information . and the decision maker's preferences and decision logic Ability to use method with little or no training .069 Acceptability to the users of the final product. and the sensitivity of the problemj to the the modeling approach Ability to communicate the technical aspects of the problem.041 Ability to aid understanding of the features of the problem. the decision model developed .035 Ability to model decision environment with many decision options . the decision maker's value structure.081 51 .104 Ability to develop decision model without using a computer .082 Ability to apply decision model to new decision option set .ITbn 20.057 Ability to model a group decision making process .055 Ability to develop model with little decision maker involvement .080 .041 Ability to develop a decision model that is theoretically defensible and scientifically well founded . R&D Project Cotuui Weights Ability to model judgmental dependence .
but the current implementation should be modified and enhanced. would feed the information back to the analyst and the decision makers. This modeling component should allow for a form of curve fitting. lilrovements to Policy Canturin The suggested improvements to the policy capturing implementation are directed toward strengthening the weaknesses described in Section I1. Overall Utilities: R&D Project Context SMART 83. Results of the analysis clearly show that the group of experts believed that a policy specifying capability serves a purpose not fulfilled by the other three techniques. This would include: a userfriendly interface. similar in a sense to the R 2 measure in policy capturing.0 POLICY SPECIFYING 80. Policy capturing as a tool also serves a purpose not met by the other three techniques. and store the resultant judgments. together with the reporting module. This would be done by allowing the analyst or decision maker to access through the software package a special modeling component which specifies the nature of the relationships among attributes. a profile generation module. using inputs from the decision analyst regarding attributes. but that the current implementation of the technique could be improved. More importantly.9 VI. It is suggested that a new version of policy specifying be developed which uses a SMART-like approach to define ordinary single-attribute utility functions and to aggregate the separate utility functions. IMPLICATIONS FOR POTENTIAL IMPROVEMENTS TO DECISION MODELING TECHNIQUES In this section suggestions are made for extensions and/or modifications to the policy specifying and policy capturing techniques and are directed toward improving the value of these techniques in terms of the evaluation criteria used in the present effort. Such a facility would have to be capable of analyzing parallel policies. With 52 . The clustering module would be available for performing clustering of decision makers' equations.7 POLICY CAPTURING 82. loirovements to Policy Sneciftngg Improvement of policy specifying as a decision modeling technique should be directed toward eliminating problems of user acceptance and understanding underscored in the evaluation. if desired.Table 21. and a reporting module. The policy specifying tool should also incorporate two additional major features. The judgment data collection module would provide the profiles to the decision makers in an automated form. The profile generation module would automatically generate profiles to be judged. a judgment data collection module. The ability to specify interaction terms in the utility functions should be retained when the decision maker feels the context warrants it.3 HAWM 59. the second is the capability for using the tool in a group decision making mode. The regression analysis module would be used to analyze the judgments and. a regression analysis module. A microcomputer version of the technique should be developed that allows for all steps of the technique to be accomplished within one software package. Implementation of such a software package on the microcomputer should directly address the problem of intensive decision maker and analyst time and computer resource demands from using policy capturing. The first would be some form of consistency determination or comparison of model results to a desired set of results. which would likely be more acceptable and easier to communicate than is the current practice of specifying corner points on a linear equation template. rather than merging the policies. a clustering module. and sample sizes. distributions.
speed. policy development.improved ease of use. neither do the SMART and HAWM techniques fill every need. sensitivity analysis. especially if context specific applications are considered. reporting. and batch profile generation and scoring. Sugested Imnrovements to the Overall AFHRL Plcy Modelin Ca~abilitv In the overall analysis. policy analysis. This framework would be developed in modular fashion. feedback. However. problem structuring. which makes available to the user all four techniques within an integrated framework. and feedback such a policy capturing model should be a great aid to problem understanding and problem solution. 53 . What is called for is development of a composite policy analysis/development tool. it is clear that neither policy specifying nor policy capturing answers all the needs of decision modeling. with modules for each of the functions required in a policy modeling tool: intelligent interface.
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for each tuple of pairs. They do not pose any problems for the formal application of difference measurement." Difference measurcn'rtt has been shown in several studies to be the appropriate formal basis for interval scale measurements like the oes required in policy specifying. c.. it is possible to vary one of the elements so that the strength of preference in one pai matches the strength of preference in the other. 1971) is an appropriate basis for providing justification for these judgments. assumptions 1-5 would have to be tested in each specific case Assuming that at all levels and places in the tree the relation ... these strength of preference judgments are transitive. These two-attribute ratings are then fitted by some polynomial. An Axiomatic Basis for Judgments Required in Policy Snecifvine Policy specifying procedures usually employ numerical rating scales of hypothetical objects varying on two attributes on a scale from 0 to 100. These assumptions are formally stated by Krantz et al. (c. has the same meaning is. and d into the real numbers such that (a. i. if the relation of strength of preference substantively changes as one moves from one part of the hierarchy to another. strengths of preferences "add". Thus. the hypothetical objects are chosen to array at the extreme points of a two-attribute plot of possible objects. 61 . 5. difference measurement theory (Krantz et al.d) is interpreted as "the strength of preference of a over b is greater than or equal to the strength of preference of c over d. if a is preferred over b and b is preferred over c.e. In simple terms. it h's strong implications for the resulting functional forms.much more convenient. b. as one compares two-dimensional objects in different parts of the tree. pairs of objects can be ordered in terms of the relative preference of one over the other. In particular. Typically. The rating task requires relative difference judgments. 4.e. it prohibits the possibility of polynomials that include different utility functions defined over the same attribute. in principle. then the strength of preference over c should be the "sum" of the strength of preference of a over b and the strength of preference of b over c. or different ratings are performed for one attribute at differing levels of the other attribute. who showed that the assumptions imply that a function must exist that maps objects a. where the rating reflects the strength of preference or relative degree of desirability or achievement. 3. thre are no infinitely desirable or undesirable objects in the set of alternatives that are to be evaluated. 2. A possible complication arises in policy specifying.d) if and only if v(a)-v(b) > v(c)-v(d) where (a.e.. judgiig the relative spacing in desirability (or some other value-relevant aspect) of the two-dimensional objects. (1971). of course. Such shifts should be spelled out clearly in the instructions for making these judgments. this theory requires that 1.b) j (c. except that. This issue will be discussed next. i.APPENDIX: AXIOMATIC BASIS FOR POLICY SPECIFYING There appear to be two theoretical areas in which the policy specifying technique could be improved substantially without major changes to the technique or loss of practicality: providing an axiomatic foundation for the judgments required in eliciting the utility functions and providing an axiomatic foundation for the polynomial model forms. i.b) .
Since the domain of the single-attribute utility functions is changed. (A-2) because in it x appears with two different power coefficients. The idea would be that t should be fairly easy to fit most judgments satisfying (A-3) with a polynomial of the form (A4). an important restriction occurs when an attempt is made to compare and integrate two higher level objectives 62 . For example. a polynomial aggregation rule has been assumed. Simple multilinear polynomials follow directly from two assumptions: (a) The relation . and there exist no necessary behavioral assumptions justifying it. It turns out that forms like (A-3) have a very straightforward axiomatic base in difference measurement. justifies form (A-3). for example. the three-attribute polynomial v(x. a simple polynomial form of (A-3) would be v(x l . the aggregation rule must be a simple multilinear form: V(Xl. Furthermore. X2 ) = V1 (X) + v 2 (X2) + w V1 (Xt) V2 (x 2 )- (A-3) The "polynomial" part of the model would further restrict the v's to be positive integral power functions of the x's. Examination of what happens to the terms of models (A-3) and (A-4) if one moves around in the hierarchy indicates that lateral movements do not affect the model. any power that is likely to fit the judgments that are provided can be selected. together with assumptions 1-5 described earlier. a typical polynomial for three attributes would be V (x. This assumption. thus in essence creating the possibility for different utility functions defined on the same attribute. x2 ) = (ax 1 +b)m + (cx 2 +d) n + w(ax l +b)m (cx2 + d)n (A-4) where m and n are positive integers. With n attributes.z) = x + y + z + x2 z. Each attribute can have only one power coefficient and is termed the simple multilinear polynomial model. However. The key assumption is multilinear difference independence (Dyer and Sarin call it "weak difference independence").y. It requires that the order of strengths of preferences made for pairs of objects that vary only in one attribute is unaffected by constant values of the other attribute. In this model.An Axiomatic Foundation for PolXnomial Model Forms In most applications of policy specifying. the same attribute domain can. integral powers.y. and (b) at each pair-wise comparison. occur with several different power coefficients. in Dyer and Sarin (1979) and Von Winterfeldt and Edwards (1986). which is described.z) =x 2 + y = 7 + x2 z 3 + yz 3 + x2 y +x2 y z3 (A-i) would be admissible. has the same meaning everywhere in the tree. The simple polynomial form (A-4) is somewhat more restrictive. but the following (seemingly simpler) polynomial would not be allowed: v(x. Providing an axiomatic basis for such polynomials within the framework of difference measurement theory requires that the aggregation rules be substantially more complicated than the additive or multiplicative forms usually developed in the literature.y. Specifically. in principle. rather than an explicit behavioral assumption. A "simple" version of a polynomial difference model will be considered first. However. or a power function of some positive linear transformation of the x's. a simple polynomial is a linear combination of products of the attribute variables raised to non-negative.z) = 2 X3 y 2 + Z4 Z + x y3 z . (A-4) could simply be incorporated into a policy sp'-cifying model as a form of "curve fitting" routine.
v(v.that are now expressed in terms of the v's. that contradiction is disallowed and thereby the possible polynomial forms for policy specifying substantially reduced. assume that in Figure A-i. the decision maker may think of the "importance of physical strength.. Y2) YI + Y2" V [ J vx v(xJ) xi Vy v(x 2) v(y) x2 YJ Figure A-i. 63 v(y 2) Y2 . j must mean something different at different places in the tree --a somewhat messy. e." When comparing the second pair. x2) = x1 + x2 and vy (YI. the assumption is that the aggregation rule is a simple multilinear polynomial. vY) = vXM + vyn + kvXm vyn . consider the simplified structure in Figure A-1. As before. (A-5) The problem is that by virtue of the assumption that the relation at the seccnd level of comparison must be identical to that of the lower level. x and x2 are two variables measuring an individual's knowledge about a subject. Tree Structure to Illustrate Hierarchical Utility Assessment." Both individual functional forms may be extremely simple. it is required that m = n = 1.. For example. In other words. and y2 are measures of physical strength.. a utility of a utility is a utility. When comparing the first pair.g. and y. To create the possibility for richer forms. To consider an example. i.e. the decision maker may think of the "importance of knowledge. but possibly justifiable assumption. Vx(x 1 . By assuming identical relations at all levels. The necessary implication of assuming m = 1 or n = 1 is that the strength of preference order at the higher level could be in contradiction with the strength of preference order at the lower level.
and there is no reason not to assume a functional form like V(Vx. Y1. + )2) b + W(x1 + x2 )a(y. + Y2 )b (A-7) which is a substantially more complex form than the proposed simple multilinear polynomials. and vy. To contrast these model forms. x2 . once this is accomplished. However. To construct an axiom system for the general multilinear polynomial model is not difficult in principle. any form of polynomials can be generated.When comparing the "aggregate" knowledge score and the "aggregate" physical strength score. but would theoretically require checks of axioms at each level of the tree. the model generated by (A-6) will be termed the general multilinear polynomial.GOVERNMEN PR:NTING OFFICE: 64 1988 . vy) = Vxa + b + kva v b (A-6) thus v(xl. the evaluator may think in terms of how desirable it is for a person seeking a job to have some combination of v. . Y2 ) = (xl + x2) a + (y. * .561048 / 80038 .
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