Technical Report 67,
Department of Civil Engineering,Tokyo Institute of Technology, 51-67.

Contingent focus model of Decision Framing under Risk
Satoshi Fujii1 & Kazuhisa Takemura2
1

Tokyo Institute of Technology, Japan
2
University of Tsukuba, Japan

Abstract
Decision problems which are identical in form may give rise to different decisions due tosubjective decision framing, in which the decision-making process can be altered depending
on how the situation is described. This is called the framing effect. We applied the Contingent
focus model (Takemura, 1994a) to an explanation of the framing effect. The model
hypothesizes that a risk attitude depends on the extent to which a subject focuses on possible
outcomes and probabilities, that is the focusing hypothesis, and focusing on possible outcomesand probabilities are, in turn, contingent on contextual factors including positive/negative
frame condition, that is the contingent focus hypothesis. In order to test these hypotheses, we
implemented two experiments (n = 180 for both experiments), which manipulated size ofletters describing outcomes and probabilities. The results were compatible with predictions
derived from the hypotheses, that is, the subjects more frequently selected risky options whenoutcomes were emphasized. We also applied the model to a psychometric meta-analysis ofsubjects' responses in experiments of Asian disease problem (Tversky & Kahaneman, 1981;
Takemura, 1994b) and one of the experiments of this study (4 experiments; n = 831). The
results were also compatible with predictions derived from the hypotheses.


1

Corresponding author: Tokyo Institute of Technology, Department of Civil Engineering,
2-12-1, Ookayama, Meguro-ku, Tokyo, 152-8552, tel & fax: +81-3-5734-2590
fujii@plan.cv.titech.ac.jp

e-mail:1

Introduction
Decision problems which are identical in form may give rise to different decisions due tosubjective decision framing, in which the decision-making process can be altered depending
on how the situation is described. This is called the framing effect (Tversky & Kahneman,
1981). For instance, when a decision needs to be made concerning whether or not one agrees
to undergo an operation, the decision arrived at may be different when a doctor tells one that
there is a 95% probability of living, compared to that when a doctor advises that there is 5%
probability of dying. The existence of this effect violates description invariance in which
different representations of the same choice problem should yield the same preference(Tversky & Kahneman, 1986).
Tversky and Kahneman (1981) posed a question under the following two frame conditions,which is a typical yet famous example called the Asian disease problem which gives rise to
the framing effect, and let subjects make a choice under each condition.
[Problem 1]
Positive frame condition:
Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill
600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact
scientific estimates of the consequences of programs are as follows. Which of the two programs would you
favor?
If program A is adopted, 200 people will be saved.
If program B is adopted, there is 1/3 probability that 600 people will be saved, and 2/3 probability that nopeople will be saved. (p.193.)”
Negative frame condition:
The question is the same except for the description of programs , which were changed as below:
If program C is adopted, 400 people will die.
If program D is adopted, there is 1/3 probability that nobody will die, and 2/3 probability that 600 people
will die. (p.193)”

Here, although the ways of describing the programs are different, it is clear that programs A
and C, and programs B and D are the same in extensively confirmed meaning, respectively.
Namely, “be saved” equals “not die”, and “not be saved” equals “die”. Tversky and
Kahneman (1981) reported that in the case that a profitable side was emphasized in thedescription of a positive frame condition most subjects chose risk aversive programs, i.e.
program A. On the other hand, in the case that a losing side was emphasized in thedescription of a negative frame condition most subjects chose the risk taking program, i.e.,
program D.
Tversky and Kahneman (1981, 1986) reported that the framing effect in decision making is arobust phenomenon. They suggested that, similarly to a visual illusion phenomenon insensation, the framing effect leads to a paradoxical judgment in its process, even though theparadox may be recognized afterwards. Framing effects have been reported to occur inrelation to medical judgments made by doctors (McNeil, Pauker, Sox, & Tversky, 1982), in
managerial decision making (Qualls & Puto, 1989) and in many other decision making
situations (see Kühberger, 1998).
Prospect theory
Tversky and Kahneman (1979) proposed Prospect theory as a theoretical explanation for2

framing effects. They highlighted a difference between subjective values for gains and losses
associated with choice behavior. As shown in Figure 1, the (hypothetical?) value function inprospect theory is concave in the gain area and is convex in the loss area, which implies that adecision maker is risk averse in the gain area and takes risks in the loss area. In addition, theslope of the value function is steeper in the loss area than in the gain area.

value

reference point•

outcomeFigure 1. Value function assumed in Prospect theory
weightprobability

Figure 2. Probability weighting function assumed in Cumulative Prospect theory
Tversky and Kahneman (1992) extended Prospect theory by formulating a value function
using a Choquet integral and labeled it Cumulative prospect theory. With respect tomathematical descriptions of a value function, Cumulative prospect theory can be categorized
as a nonlinear utility theory (Fishburn, 1988), which is an extended version of subjective
expected utility theory (Von Neumann and Morgenstern, 1944; Savage, 1954). However,
Prospect theory is substantially different from the utility theory because the latter assumes
that original points of utility functions never shift, whereas the former assumes that original
points of the value functions, i.e. reference points, shift depending on the description of adecision problem. Prospect theory explains framing effects by a shift of the reference point.
3

When a reference point is greater than an outcome, the outcome is interpreted as a gain.
However, if the reference point shifts to be less than the outcome, it then comes to be
regarded as a loss. Since Prospect theory assumes that subjects avoid risks when outcomes areframed as gains (i.e. positive frame), and that subjects take risks when outcomes are framed as
losses (i.e. negative frame), Prospect theory predicts that risk attitudes change depending on
the frame condition. Another cause of framing effects indicated by Tversky and Kahneman(1981) is that, as shown in Figure 2, the weighting function of probabilities is nonlinear. Thisimplies that framing effects become more prominent as the value of gain or loss for a certain
alternative becomes larger.
Reference PointFor Prospect theory, a reference point is a key concept necessary to explain decision making
under risk, because risk attitude, which determines a decision, depends on the relation
between a reference point and an outcome. This implies that it is indispensable to be able topredict the position of a reference point and its shift due to contextual factors, including
positive/negative frame conditions, for a theoretical understanding and prediction of decision
making under risk in the actual environment in which numerous contextual factors areembedded.
Does Prospect theory, then, provide a theoretical and quantitative explanation as to the shift ofa reference point per se? With respect to this question, Tversky and Kahneman (1981) stated
the following:"The frame that a decision maker adopts is controlled partly by the formulation of the problem and partly
by the norms, habits, and personal characteristics of the decision maker" (p. 453)

In line with this conjecture, Fischhoff (1983) reported the experiment that investigatedreference point positions while postulating the validity of Prospect theory. However, he foundthat it was difficult, or even impossible, to identify a reference point position from external
observations, i.e. actual choices. In addition, he found an inconsistency between a reference
point that is derived from actual choice based on Prospect theory, and a self-reported
reference point. To the present time, a methodology to identify reference point position does
not seem to have been proposed.
While Prospect theory postulates one reference point, a decision maker may, however, havemultiple reference points. For instance, Takemura (in press.) proposed the Mental ruler theory
that postulates two reference points to explain numerical judgements. He confirmed that thetheory provides a better fit to judgmental data than other theories. In addition, Maule (1989)
collected verbal protocol data of decisions involving the Asian disease problem and foundthat 5 subjects out of 12 made their decisions while adopting two different reference points.

Contingent focus model
Basic idea
A reference point is a useful concept used to explain the framing effect. However, as is argued
above, it is difficult to define a reference point, to theoretically predict its position and its shift.
Furthermore, Prospect theory can not explain decision making when a decision maker has
multiple reference points. For these reasons, one of the authors of the present study proposed
the Contingent focus model, while abandoning the concept of reference point to explain theframing effect (Takemura, 1994a).
4

The basic assumption of the Contingent focus model is that framing effects emerge, not whena reference point shifts, but when a decision maker changes focus on possible outcomes andprobabilities depending on frame conditions of decision problems. As shown in Figure 3,
under positive frame conditions, a decision maker is assumed to pay more attention toprobabilities than to possible outcomes, which results in the decision maker being risk averse.
On the other hand, under negative frame conditions, a decision maker is assumed to pay more
attention to possible outcomes than to probabilities, which results in risk taking. In otherwords, a decision maker is assumed to attend to negative outcomes (i.e. loss) more intensely
than to positive outcomes (i.e. gain).
This hypothesis is in line with the loss sensitivity principle (Gärling, et al., 1997; Romanus &Gärling, 1999) which presumes that a decision maker is more sensitive to a negatively-framed
outcome (i.e. loss) than to a positively-framed outcome (i.e. gain). Prospect theory
hypothesizes that the value function of outcomes is steeper for losses than for gain, which isalso in line with the hypothesis, since curvature of the value function implies the decision
maker's sensitivity to outcome. Furthermore, Kahaneman & Tversky (1984) directly argued
that "losses loom larger than gains (p. 348)". These arguments imply that a decision makerpays more attention to outcomes under negative frame conditions than under positive frame
conditions, as is assumed in the Contingent focus model.

Decision Maker

Decision Maker(under positive frame condition)(under negative frame condition)

Figure 3. Basic idea of Contingent focus model (Takemura, 1994a)

Numerical Representation
Similarly to Prospect theory (Kahneman & Tversky, 1979) and the subjective expected utility
theory (Von Neumann and Morgenstern, 1944; Savage, 1954), the Contingent focus model
also describes decision making under risk. In the Contingent focus model, it is hypothesizedthat a decision maker chooses an alternative whose subjective decisional value is maximum
from among possible alternatives. The value is formulated as follows.
U(X, P) = F(X)aG(P) (1-a)(1)

where, X denotes possible outcome, P denotes the probability that a decision maker gets X,
U(X, P) denotes a subjective decisional value of an alternative of X and P, F(X) denotes the
subjective value of a possible outcome X (F(X) > 0), G(P) denotes the subjective value of P
(G(P) > 0), and a denotes a parameter (0 ≤ a ≤ 1) indicating the degree of focus on outcome X.
We label this parameter as the focal parameter. As the focal parameter, a approaches 1 from 0,
for a decision maker making riskier decisions. When a equals 1, only outcomes influence thedecision making and a decision maker is extremely risky. On the other hand, as a approaches
0 from 1, a decision maker becomes risk averse. When a equals 0, only probabilities influence
the decision making, and a decision maker is extremely risk averse. This hypothesis, which
5shows how focusing on possible outcomes and probabilities determines a risk attitude, islabeled as the focusing hypothesis.
The focal parameter a can be hypothesized to change depending on contextual factors,
including frame condition. This hypothesis is labeled as the contingent focus hypothesis. Thus,in the Contingent focus model, framing effects are ascribed to changes of the focal parametera, and not to a shift of reference point. This contingency of the focal parameter is formulated
as follows:a = Ψ(θ)(2)

where, θ denotes a vector of contextual factors and Ψ( ) denotes a function indicating thecontingency of the focal parameter a on θ. Contextual factors (θ) include positive/negative
frame conditions. A basic idea of the Contingent focus model to explain a framing effect, that
is, a decision maker attends to negative outcomes more intensely than positive outcomes,
indicates that the focal parameter a is supposed to be larger under negative frame conditions
than under positive frame conditions.
Elaboration condition, which refers to how well a decision is elaborated, is a possible
contextual factor included in θ. When a decision is elaborated by virtue of a long decisiontime or a self-justification of a decision, a decision maker may frequently discover covert
aspects of a decision problem which are not explicitly described compared to when thedecision problem is not elaborated. For example, when decision making is elaborated, adecision maker might discover the fact that 200 survivals implies 400 deaths although 400
deaths were not explicitly described under the positive frame condition in the Asian diseaseproblem. Accordingly, the Contingent focus model predicts that differences in the value of the
focal parameter a for positive and negative frame conditions are less when decision making iselaborated than when it is not elaborated. This decrease in the difference of the focal
parameters for positive and negative frame conditions is, in turn, conjectured to eliminate theframing effect. A series of experiments by one of the authors of the present study, whereupon
the extent of the elaboration was manipulated, confirmed this prediction; that is, framing
effects were not observed when decisions were elaborated (Takemura, 1992, 1993, 1994b).
These results cannot be adequately explained by Prospect theory.

Empirical Tests
The focusing hypothesis, which states that the extent of focusing on possible outcomes andprobabilities determines risk attitudes, is a key to explaining framing effects by Contingent
focus. However, this hypothesis has not been sufficiently tested by experimental data. In order
to confirm whether risk attitudes change in line with the prediction of the focusing hypothesis,
we implemented two experiments in which the relative sizes of letters of possible outcomesand probabilities were manipulated compared to the other letters in described decision
problems.
Experiment 1
The first experiment was a 3 (control-emphasis condition, outcome-emphasis condition, andprobability-emphasis condition) by 2 (positive/negative frame conditions) factorial
experiment. The subjects for this experiment were 180 students and staff members at Kyoto
University, Japan. They were randomly assigned to one of the 6 conditions, with 30 subjects
in each condition.
6

For the positive frame condition, the following decision problems were used. Decision
problems for negative frame conditions were identical with those under positive conditions
except that the word "loss" was used in stead of "gain".
(control-emphasis condition)
Which do you choose?
A: certainly gain 20,000 yen
B: a lottery with a 50 % chance to gain 40,000 yen and a 50 % chance for no gain.

(outcome-emphasis condition)
Which do you choose?
A: certainly gain 20,000 yen
B: a lottery with a 50 % chance to gain 40,000 yen and a 50 % chance for no gain.

(probability-emphasis condition)
Which do you choose?

A: certainly gain 20,000 yen
B: a lottery with a 50 % chance to gain 40,000 yen and a 50 % chance for no gain.

As described above, under the outcome-emphasis condition, possible outcomes wereemphasized by larger bold fonts than the other letters. Emphasized letters were described bysize 18 fonts, while the other letters were described by fonts of size 10.5. In contrast, for the
probability-emphasis condition, probabilities were emphasized in the same way.
Due to the experimental manipulation of size of letters, it was supposed that subjects would
focus on possible outcomes more strongly under the outcome-emphasis condition than under
the probability-emphasis condition. Accordingly, the focusing hypothesis predicts that
subjects take risks more frequently under the outcome-emphasis condition than under the
probability-emphasis condition, regardless of the positive/negative frame conditions.
Manipulation of the positive/negative frame conditions in this experiment has been used toshow the reflection effect (Kahneman & Tversky, 1979), which denotes a decisional
phenomenon whereby a subject takes risks when a choice is between losses, whereas heavoids risk when a choice is between gains. This effect can be predicted by Prospect theory,
since the theory assumes that a value function for gains is concave while that for losses isconvex. The effect can also be predicted by the Contingent focus model, since the model
hypothesizes that a decision maker pays more attention to outcomes presented under negative
conditions than if they were presented under positive conditions. The net effect is for the
subject to take greater risks risk for negative frame conditions than for positive frame
conditions.
Table 1 shows results of these experiments, which indicate that subjects preferred risky
options more frequently under negative frame conditions than under positive frame conditions
for the respective emphasis conditions. Table 2 presents the results of a hierarchical log-linear
analysis. The hierarchical log-linear analysis yielded a significant main effect of apositive/negative frame conditions on risk attitudes (reject risk vs. accept risk), that is P * R.
This result may be similar to the reflection effect. However, the finding indicates that subjects
7were relatively more risky under negative frame conditions than under frame positive
conditions. As can be seen in Table 1, under the probability emphasis condition, subjects were
not risk takers at all, even under the negative frame condition. For the control-emphasis
condition, there is no clear tendency that subjects were risk takers under the negative frame
condition. Since the reflection effect denotes that a subject takes risks under negative frame
conditions and avoids, on the other hand, risk taking under positive frame conditions, theresults were not compatible with reflection effects. In contrast, for the Contingent focus
model, which hypothesizes that positive/negative frame conditions determine the extent ofrelative attention towards outcomes which in turn determines risk attitude, the model predicts
that subjects were relatively riskier under negative frame conditions than those under positive
frame conditions. Accordingly, the results presented here do not support Prospect theory, but
do support the Contingent focus model. The results may imply that the reflection effect is a
special case which is brought about by a difference of attentions towards outcomes between
positive and negative frame conditions.
Table 1 Outcome/uncertainty Emphasis Effect and Reflection Effect
positive frame
negative frame 
Emphasis
Reject risk Accept risk
Reject risk Accept risk
condition
% (N)
% (N)
% (N)
% (N)

Probability
90.0 (27)10.0 (3)50.0 (15) 50.0 (15)Control
83.3 (25)
16.7 (5)56.7 (17) 43.3 (13)Outcome63.3 (19)36.7 (11)30.0 (9) 70.0 (21)

Table 2 Results of Log-Linear Analysis


Model

χ2

df

p



(1) F*E*R, F*E, E*R, F*R, F, E, R .0
(2) F*E, E*R, F*R, F, E, R
0.85
∆1-2: F*E*R
0.85(3) F*E, F*R, F, E, R
11.85
∆2-3: E*R
11.00
(4) F*E, E*R, F, E, R
26.66
∆2-4: F*R
25.81

0
2
2
4
2
3
1

n.s.
p < 0.005
p < 0.001



F, frame condition (positive/negative); E, emphasis condition (uncertainty/outcome/control);R, risk attitude (reject risk/accept risk)

Table 1 shows that more subjects selected risky options under the outcome-emphasis
condition than for the probability-emphasis condition, regardless of the positive/negative
frame conditions. The hierarchical log-linear analysis reported in Table 2 yielded a significant
main effect of emphasis condition (control-emphasis condition, outcome-emphasis condition,and probability-emphasis condition) on risk attitudes (reject risk vs. accept risk), that is E * R.
This result is in line predictions derived from the focusing hypothesis and the contingent
focus hypothesis in the Contingent focus model.
8

Table 3 Outcome/uncertainty Emphasis Effect and Framing Effect
positive frame
negative frame 
Emphasis Effect Reject risk Accept risk
Reject risk Accept risk
% (N)
% (N)
% (N)
% (N)

Probability
70.0 (21)30.0 (9)40.0 (12) 60.0 (18)Control
60.0 (18)40.0 (12)56.7 (17) 43.3 (13)Outcome43.3 (13)56.7 (17)20.0 (6) 80.0 (24)

Table 4 Results of Log-Linear Analysis


Model

χ2

df

p



(1) F*E*R, F*E, E*R, F*R, F, E, R .0
(2) F*E, E*R, F*R, F, E, R
2.59
∆1-2: F*E*R
2.59(3) F*E, F*R, F, E, R
10.73
∆2-3: E*R
8.14(4) F*E, E*R, F, E, R
6.87
∆2-4: F*R
4.28

0
2
2
4
2
3
1

n.s.
p <.05p <.05

F, framing condition (positive/negative); E, emphasis (uncertainty/outcome/control); R, risk
attitude (reject risk/accept risk)

Experiment 2
The second experiment performed was a 3 (control-emphasis condition, outcome-emphasis
condition, and probability-emphasis condition) by 2 (positive frame condition and negative
frame condition) factorial experiment. In the experiment the Asian disease problem was used.
Under the outcome-emphasis condition and the probability-emphasis condition, a possible
outcome and a probability were emphasized in the same way as that described in the firstexperiment, respectively. The subjects for this experiment were 180 students and staff
members, different from those used in Experiment 1, from Kyoto University, Japan. Table 3
presents results from this experiment and Table 4 shows the results of a hierarchical log-linear
analysis.
Table 3 shows that the framing effect emerged under both the probability-emphasis condition
and the outcome-emphasis condition; namely, a majority of subjects avoided risk under the
positive frame condition, whereas a majority of subjects tended to be risk taking under thenegative frame condition. As can be seen in Table 4, risk attitudes were significantly
dependent on frame condition. These results were in line not only with Prospect theory but
also with the Contingent focus model. However, under the control-emphasis condition, theframing effect did not emerge. Nevertheless, more subjects tended to be risk taking under thenegative frame condition than under the positive frame condition. This result supports theContingent focus model rather than Prospect theory.
As can be seen in Table 3, more subjects were risk taking for the outcome-emphasis condition
than for the probability-emphasis condition. Table 4 indicates that risk attitudes weresignificantly dependent on the emphasis condition. These results cannot be predicted by
Prospect theory but are consistent with the basic idea of the Contingent focus model, which
9shows how focusing on possible outcomes and probabilities determines risk attitude.
under positive frame condition

under negative frame condition

frequency

01

focal parameter amore risk averse

more risk taking

Figure 4. Distributions of the focal parameter a under positive/negative frame
conditions
A Meta-Analysis of Asian Disease Problem
Heterogeneity in risk attitudes across decision makers can be always observed in any
experiments of decision making under risk. In the Asian disease problem, for example,
opposite responses to the prediction by Prospect theory, i.e. risk seeking under the positive
frame condition and risk aversion under the negative frame condition, have been always
observed, even if they were in the minority.
The Contingent focus model explains this heterogeneity by using a distribution of the focal
parameter a; that is, the heterogeneity in how subjects focus on possible outcomes andprobabilities is assumed to cause heterogeneity in risk attitudes. For example, in the Asian
disease problem, as shown in Figure 4, the expected range of distribution of the focal
parameters is expected to be larger under the negative frame condition than under the positive
frame condition.
If we accept parametric assumptions with respect to the distribution of the focal parameters,
the Contingent focus model can psychometrically analyze the decision framing under risk (seeAppendix). We applied the Contingent focus model to a meta-analysis of the Asian diseaseproblem, in order to disentangle contextual factors associated with decision frames.
Contextual Factors Influencing the Focal Parameter
There are several possible contextual factors which may influence the focal parameter, which
in turn is assumed to determine risk attitudes. Such factors include positive/negative frame
conditions and emphasis conditions, as has been shown in the two experiments of the present
study. The difference between the expected value of distribution of the focal parameters underpositive frame and negative frame conditions is conjectured to cause the
Asian-disease-problem-type's framing effect. Moreover, the effect of outcome emphasis on
the focal parameter is conjectured to bring about the result that more subjects are risk takers
under the outcome-emphasis condition than for the other conditions. On the other hand, theeffect of probability-emphasis is postulated to result in more subjects being risk averse under
the probability-emphasis condition than for the other conditions.
In addition, elaboration condition is another contextual factor influencing the focal parameter(Takemura, 1992, 1993, 1994b). For the elaboration condition, decision making is elaborated
upon by virtue of a long decision time or a need for decision justification. Under such a10

condition, subjects may more frequently discover, as distinct from the no-elaboration
condition, covert aspects of the decision problem which are not explicitly described. For
example, under the positive frame condition in the Asian disease problem, an outcome in an
option is expressed as "200 people will be saved". Nevertheless, subjects may frequently
discover under the elaboration condition, as distinct from the no-elaboration condition, thefact that this sentence implies "400 people will die". Due to the discovery of covert decision
aspects under the elaboration condition, the focal parameter would become smaller undernegative frame conditions, as shown in Figure 5 (a). This is because the distribution of the
focal parameters skews towards the value of 1 for negative frame conditions withoutelaboration of decision making. On the other hand, under positive frame conditions, due to theelaboration of decision making, the focal parameter would become larger (see Figure 5 (b)).
This is because the distribution skews toward the value of 0 for positive frame conditions
without elaboration of decision making. Accordingly, elaboration of decision making isassumed to have a positive effect on focal parameters under positive frame conditions, but tohave a negative effect under negative frame conditions. To summarize, positive/negative
frame conditions, emphasis conditions, and elaboration conditions are hypothesized to havethe following effects on the focal parameter:

effects of elaboration of decision making
frequency

01

focal parameter amore risk averse

more risk taking(a) under negative frame condition

effects of elaboration of decision making
frequency

01

focal parameter amore risk averse

more risk taking(b) under positive frame condition
Figure 5. The effects of elaboration on the focal parameter, a• under negative frame conditions the focal parameter is larger than that for positive frame
conditions (this is the reason for the Asian-disease-problem-type's framing effect),• outcome emphasis increases the value of the focal parameter,11• probability emphasis decreases the value of the focal parameter,• elaboration of decision making increases the value of the focal parameter under positive
frame conditions, and• elaboration of decision making decreases the value of the focal parameter under negative
frame conditions.

A Meta-Analysis
To test these hypotheses, we implemented a meta-analysis of subjects' responses in the Asian
Disease problem, which manipulated positive/negative frame condition, elaboration condition,and emphasis condition, and we applied the Contingent focus model to this meta-analysis.
The meta-analysis included the results of the original experiment by Kahneman & Tversky(1981), and the experiments which manipulated the elaboration of decision making of the
Asian disease problem (Takemura, 1994b). The results of Experiment 2 in this study, which
manipulated emphasis conditions, were also included. The total number of subjects used was
831, out of which 413 (49.7%) selected a risky option, and the remainder (418, 50.3%)
selected a riskless option.
In order to test the hypotheses associated with the focal parameters, let the function
representing contingency of decision framing on contextual factors Φ(θ) (see eq. (A3) inAppendix) be described as follows:Φ(θ) = β0 + β1PositiveFrame+ β2OutcomeEmphasis + β3ProbabilityEmphasis+ β4Elaboration(Negative) + β5 Elaboration(Positive)(10)

where, β0 - β5 denote parameters to be estimated; PositiveFrame is 1 if frame condition ispositive, otherwise 0; OutcomeEmphasis is 1 for outcome emphasis condition, otherwise 0;
ProabilityEmphasis is 1 for probability emphasis condition, otherwise 0;
Elaboration(Negative) is 1 for elaboration condition under negative frame condition,otherwise 0; and Elaboration(Positive) is 1 for elaboration condition under positive frame
condition, otherwise 0.
The parameters were estimated by maximizing likelihood formulated on the basis on eqs.
(A6) and (A7) in Appendix. Table 5 shows the results of the estimation. As can be seen in thetable, PositiveFrame has a significantly negative coefficient, which indicates that the focal
parameter a under positive frame conditions is significantly smaller than under negative frame
conditions. This result is in line with our hypothesis with respect to the
Asian-disease-problem-type's framing effect. The coefficient of Elaboration(Negative) was
significantly negative and that of Elaboration(Positive) was significantly positive. These
results indicate that the focal parameter becomes larger by elaboration of decision making
under positive frame conditions, but becomes smaller upon elaboration under negative frame
conditions. These results are also in line with our hypothesis with respect to elaboration
condition. The coefficient of OutcomeEmphasis is significantly positive, which indicates thatthe focal parameter becomes larger with outcome emphasis, a finding which is also in linewith our hypothesis. However, the coefficient of ProbabilityEmphasis was not significant,which is not in line with our hypothesis.
12

Table 5. Estimation results of meta-analysis of the Asian disease problem

parameterstd.
p
-1.72
0.172
.000
PositiveFrameβ1
OutcomeEmphasis
β2
0.919
0.314
.003
-0.23
0.299
.441
ProbabilityEmphasis
β3Elaboration(Negative)
β4-1.2270.254.000
Elaboration(Positive)
β5
0.777
0.251
.002
0.85
0.127
.000
constantβ0

General Discussion
Focusing Hypothesis and Contingent Focus Hypothesis
The Contingent focus model hypothesizes that attention to possible outcomes andprobabilities determines decision making under risk. Based on this basic idea, we propose thefocusing hypothesis and the contingent focus hypothesis. The focusing hypothesis states that arisk attitude for decision making under risk depends on the extent to which a subject focuseson possible outcomes and probabilities. The contingent focus hypothesis states that focusing
on possible outcomes and probabilities, or attention to possible outcomes and probabilities,
are contingent on decisional contexts. In order to test these hypotheses, we attempted in theexperiments presented here to manipulate attention towards possible outcomes andprobabilities by manipulating the relative sizes of letters describing possible outcomes orprobabilities compared to the remaining letters in written alternatives.
The results of Experiment 1 (a decision problem highlighting the reflection effect) andExperiment 2 (Asian disease problem) indicated that subjects took risks more frequently
under an outcome-emphasis condition than under a probability-emphasis condition, regardlessof positive/negative frame conditions. This result seems to indicate that risk attitudes dependon how a subject focuses on possible outcomes and probabilities, or attention to outcome andprobability, and is compatible with the focusing hypothesis and contingent focus hypothesis.
This finding is well-known to advertising marketers, who often manipulate the salience of
certain letters, e.g. letters dealing with price or special features of products, by manipulating
their relative size or color. The current study may explain the theoretical influence of suchmanipulations on decision making, and why such practices are frequently adopted in theadvertising industry.
Prospect theory predicts that subjects accept risk under negative frame conditions and rejectrisk under positive frame conditions, since the hypothetical value function, whose shape does
not change depending on decisional contexts, is assumed to be convex for losses and concave
for gains. However, for the probability-emphasis and control-emphasis conditions inExperiment 1, subjects under negative frame conditions did not show any significant
difference in relation to preference for risky options compared to riskless options. Withsimilar results found in Experiment 2, these findings were not compatible with Prospect
theory. Nevertheless, subjects selected risky options more frequently under negative frame
conditions than under positive frame conditions, regardless of the emphasis conditions. This
result is compatible with the Contingent focus model, which hypothesizes that subjects pay
more attention to negative outcomes than to positive outcomes.
13

A meta-analysis of the Asian disease problem using the Contingent focus model, whichassumes a parametric distribution of the focal parameters, yielded results that were consistent
with our hypothetical predictions. The analysis indicated that the focal parameter undernegative frame conditions was larger than that found under positive frame conditions. This
supports the basic hypotheses of the Contingent focus model. It was also indicated thatemphasizing the possible outcome resulted in an increase in the focal parameter, which is also
in line with the basic hypotheses of the Contingent focus model.
With respect to an effect of elaboration of decision making by asking subjects’ justificationsof their responses or by providing longer periods of time for decision making, wehypothesized that subjects would more frequently discover covert frames within the decision
problems when decision makings were elaborated. As a result, the distribution of the focal
parameters then becomes less skewed as shown in Figure 5, regardless of thepositive/negative frame conditions. Accordingly, we predicted that the elaboration has apositive effect on the focal parameter under positive frame conditions, but a negative effectunder negative frame conditions. The results of the meta-analysis were consistent with thisprediction. These results provide a theoretical explanation of the empirical findings by Fagley& Miller (1987), Takemura (1992, 1993, 1994b) and Kühberger (1995) that elaboration ofdecision making eliminates the framing effect.
Although the effect of outcome emphasis on decision making was in line with our hypothesis,
we did not find an effect of probability emphasis. This result may indicate that it is not theemphasis on probabilities, but the emphasis on the outcomes that has an impact on decision
making. Furthermore, based on this result, one may propose an hypothesis that bothdecisional attentions towards a possible outcome and probability do not determine a risk
attitude together, but decisional attention only on a possible outcome in fact determines a risk
attitude. However, the data presented in this study is not sufficient to test this, and further
experiments are required in order to elucidate this result.
Relations to the Other Theories
In terms of the mathematical formulations, the difference between Prospect theory and theContingent focus model is the flexibility (or stability) of value functions of outcome. In
Prospect theory, a value function of outcome and a weighting function of probability are
assumed to be fixed across different conditions. From this viewpoint, Prospect theory has thesame premise as have various utility theories. What is assumed to be changeable in Prospect
theory is the reference point. In this regard, Prospect theory is different from utility theories.
On the other hand, the Contingent focus model is similar to utility theories in terms of thedefinition of outcome because the definition of outcomes does not depend on reference point.
However, the Contingent focus model is different from both utility theories and Prospect
theory in terms of flexibility of value functions. Because the Contingent focus model has suchflexibility in these functions, it can explain various types of framing effects, including thoseyielded by elaboration or emphasis on outcomes, which can not be explained by utility
theories or Prospect theory.
Such flexibility of evaluation of functions describing decision making under risk is also
hypothesized in Venture theory (Hogarth & Einhorn, 1990). In Venture theory, the weighting
function of probability is assumed to be contingent on other factors, e.g., the size of outcome
or ambiguity, whereas the value function of outcome is assumed to be fixed. Venture theory issimilar to the Contingent focus model in terms of mathematical formulation, because thefunctions of outcome are contingent on decisional conditions in the two theories. However, adifference between these two theories lies in hypotheses used to explain such contingency offunctions of outcome. In the Contingent focus model, the contingency of value functions is14

hypothesized to be the result of the contingency of decisional attention to outcomes andprobabilities.
Concluding Remarks
Herbert A. Simon states the following in his famous paper;"Human rational behavior is shaped by a scissors whose two blades are the structure of task environments
and the computational capabilities of the actor (Simon, 1990, p. 7.)"This argument indicates that human behavior should be understood not only as an outcome ofcovert cognitive decision making but also an overt response to environments. In a similar vein,
the Contingent focus model describes the covert psychological contingency of decision
making on contextual factors in the environment, as well as overt behavioral decision making
under actual environmental conditions, by virtue of parametric assumptions of attention to
outcome.
Of course, in order to demonstrate the hypotheses of the Contingent Focus model, including
the focusing hypothesis and various hypotheses with respect to contingency of decisional
attentions to outcome on contextual factors (e.g. positive/negative frame conditions orelaboration conditions), further empirical research is called for. Possible further experiments
include utilizing an eye gaze recorder in order to observe more directly a relation between
decision making and attention to outcomes and probabilities. Information board technique isanother possibility. Although such further empirical research is necessary, we believe that theContingent focus model could possibly serve as the "scissors" as stated by Simon (1990) in
order to understand human behavioral decision making.
Acknowledgement
Draft versions of this paper were presented at the 17th biennial conference on SPUDM, the28th Annual meeting of the Behaviormetric Society of Japan, and at the International
Congress of Psychology 2000 in Stockholm, Sweden. We received many valuablecomments from the participants at these meetings for which we are most grateful. In
particular, the authors also wish to thank Dr. Kazuo Shigemasu of the Universty of Tokyo, Dr.
Tommy Gärling of Göteborg University, and Dr. Yutaka Nakamura of the University ofTsukuba, Japan, for their thorough examination of the draft of this paper, including kindreviews on the formulation of the model, the indication of mistakes in the draft, and much
valuable advice for future study.
Appendix: Mathematical Formulation for Psychometric Analysis
If function F( ) and G( ) in eq. (1) are assumed to be linear, the Contingent focus model, then,predicts that a decision maker chooses an alternative whose U(X, P) formulated below ismaximum:U(X, P) = XaP(1-a)(A1)

If only a non-zero possible outcome is attached to each alternative, as is the case of the Asian
disease problem, orders of alternatives yielded by this U(X, P) are identical with orders
described by U'(X, P) as follows:
U'(X, P) = Xa/(1-a)P(A2)This is because 1- a is positive. Equation (A2) indicates that a decision maker whose a/(1-a)
is larger than 1 is a risk taker, and one whose a/(1-a) is less than 1 avoids risk (see Figure A).
15

Xa/(1-a)Xa/(1-a)convex(risk taking)concave(risk aversive)XX（a/(1-a) > 1）（a/(1-a) > 1）a(1-a)
Figure A. Curvature of X
depending on a/(1-a)
Since the focal parameter a is contingent on contextual factors as formulated in eq.(2), a/(1-a)
is also contingent on them. In addition, since the focal parameter is assumed to be distributed
across all decision makers, a/(1-a) is assumed also to be distributed. Now, let a/(1-a) be
formulated as follows:a/(1-a) = exp{Φ(θ)+ ε}(A3)where ε is an error term giving rise to a range of distribution of a/(1-a), and Φ(θ) is a function
representing contingency of decision framing on contextual factors θ.
Accordingly, the probability that a decision maker is a risk taker, i.e. P(take), and theprobability that one avoids risk, i.e. P(averse), are;P(take)= P (a/(1-a) > 1)
= P (exp{Φ(θ)+ ε}> 1)= P (Φ(θ)+ ε > 0)P(averse)(A4)= P (a/(1-a) < 1)
= P (exp{Φ(θ)+ ε}< 1)= P (Φ(θ)+ ε < 0)

(A5)

When an error term ε is assumed to have a logistic distribution, these probabilities can be
described as follows (e.g. McFadden, 1973):
P(take)P(averse)= exp[Φ(θ)] / (exp[Φ(θ)] + 1)

(A6)
= 1 / (exp[Φ(θ)] + 1)

By maximizing the likelihood function derived from these probability functions, the effects ofcontextual factors on the distribution of the focal parameter or risk attitude can be estimated.

16

(A7)

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