## 3 Results
### Ratio Assignment Techniques
#### 3.1.2 Simple Multi Attribute Rating Technique (SMART)  
The Simple Multi Attribute Rating Technique (SMART) [71; 72] is an approach for determining weighting factors indirectly through systematic comparison of attributes against the one deemed to be the least important. SMART consists of two general activities: (1) rank order attributes according to the relative importance overall, and (2) select either the least or most important attribute as a reference point and assess how much more or less important the other attributes are with respect to the reference point. This step involves calculating attribute weights from ratios of individual attribute scores to the total score across all attributes. Methodological improvements to SMART, known as SMARTS and SMARTER, were proposed by [PERSON] and [PERSON] (73). SMARTS (SMART using Swings) uses linear approximations to single-dimension utility functions, an additive utility model, and swing weights to improve weighting [73]. SMARTER (SMART Exploiting Ranks) builds on SMARTS but substitutes the second of the SMARTS swing weighting steps, instead using calculations based on ranks. The SMART technique is comprised of the following four steps: (1) rank order attributes, (2) establish the reference attribute, (3) estimate the importance of other attributes with respect to the reference attribute, and (4) calculate weights. SMART Step 1: Rank Order Attributes  
Consider a finite set of attributes or criteria deemed relevant by an individual or group of experts to a particular decision problem. This first step asks experts to agree on a rank ordering of these attributes according to their relative contribution to the expert's overall preference within an additive utility (or value) function framework. Ranking can be either \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Abbreviation** & **Criteria** & **Formula** & **Weight** \\ \hline (P) & Purchase Price & 400/1000 & =0.40 \\ (R) & Reliability & 300/1000 & =0.30 \\ (S) & Safety & 150/1000 & =0.15 \\ (A) & Attractiveness & 100/1000 & =0.10 \\ (G) & Gas Mileage & 50/1000 & =0.05 \\  & Sum & 1000 points & =1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DAT weight evaluation. from most to least important or from least to most important. A number of approaches exist to assist in holistic ranking, the most popular and well known being pairwise ranking [74]. For example, consider our automobile purchase problem. The output from Elicitation Step 1 would be a rank ordering of the five relevant criteria from least to most important as shown in Table 3.  
SMART Step 2: Establish the Reference Attribute  
In this second step, experts select a common reference attribute, assign it a fixed score, and estimate the extent to which the remaining attributes are more or less important than the reference attribute. Any attribute can assume the role of reference attribute. For SMART, however, it is common to assign this role to the least important attribute and assign a reference score of 10 points. SMART Step 3: Score Attributes Relative to the Reference Attribute  
Given a fixed reference attribute (i.e., the least important attribute), experts are asked how much more important the remaining attributes are with respect to the reference attribute. For example, if the least important attribute is used as the reference point with a reference score of 50 points, experts would be asked to judge how many points should be allocated to each remaining attribute with respect to this reference attribute in a relative sense (e.g., 50 more points) or absolute sense (e.g., 100 points). It is common to systematically evaluate the remaining attributes in order of increasing importance to ensure individual or group consistency between the results from this step and the ordinal rankings from step 1; however, it may be worthwhile to randomize the order in which attributes are assessed as a means for uncovering any inconsistencies in preference. Consider the car buying example discussed in Step 1.