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Smarts and Smarter
SMARTS (Simple Multi-Attribute Rating Technique Using Swings) and SMARTER (Simple Multi-Attribute Rating Technique Exploiting Ranks) are two prescriptive techniques for making choices under certainty between options evaluated on multiple attributes proposed by Edwards and Barron in 1994 to replace the original SMART proposed by Edwards in 1977. Each assumes a weighted, additive, multi-attribute utility model, and each seeks to simplify the operations necessary to estimate the multi-attribute utility of each option under consideration. The techniques differ primarily in the procedure for weighting the importance of attributes.
Consider a headache sufferer making a choice between three pain relievers, each of which has a different level of provided relief, duration of relief, and potential for side effects. For example, Pain reliever A provides excellent relief for 2 hours with rare side effects, Pain reliever B provides good relief for 4 hours with rare side effects, and Pain reliever C provides limited relief for 12 hours with no side effects. How should the patient choose between these options?
| Table 1 An option-by-attribute matrix for pain relievers | ||||||
|---|---|---|---|---|---|---|
| Option | Attribute | |||||
| Level of Relief | Level of Relief (Value) | Duration of Duration of Relief (hr) Relief (Value) | Side Effects | Side Effects (Value) | ||
| A | Excellent | 100 | 2 | 0 | Rare | 0 |
| B | Good | 50 | 4 | 30 | Rare | 0 |
| C | Limited | 0 | 12 | 100 | None | 100 |
SMART
In the SMART technique, the decision maker directly assesses the values of the choice options on each attribute rather than performing a (large) series of choices between hypothetical alternatives from which attribute values are inferred, which was characteristic of earlier approaches. Edwards and Barron refer to this simplification as “the strategy of heroic approximation.” It results in a substantially shorter assessment procedure. After identifying the decision purpose, decision makers, value structure for the decision, and choice options, the analyst constructs an option-by-attribute matrix and directly assigns single-attribute utility values to options in this matrix. An example of such a matrix appears in Table 1. Subjective values are assigned to each attribute by the decision maker on a scale from 0 (worst) to 100 (best).
Dominated options, which outperform another option on all attributes, are then removed. Mathematical tests of the value structure may be performed to confirm that it meets assumptions required of additive models (e.g., tests for conditional monotonicity). If an additive model is to be assumed, attributes are then weighted to reflect their relative importance. In SMART, these weights are derived by asking the decision maker to judge the ratio of the importance of each attribute to all others. Finally, the multi-attribute utility is computed by summing the product of attribute weight and attribute value for each attribute for each option and selecting the option that maximizes the sum. For example, if the attributes of level of relief, duration of relief, and side effects had relative weights of .5, .3, and .2, respectively, the multi-attribute utility of pain reliever A would be .5 × 100 + .3 × 0 + .2 × 0 = 50. Similarly, the multi-attribute utilities of B and C would be 34 and 50, respectively. The decision maker should be indifferent between A and C and prefer either to B.
SMARTS
The SMARTS technique corrects an error in the process of assigning attribute weights that was present in SMART. This is easily illustrated in our example by considering the side effects attribute. While side effects might seem to warrant a large relative weight in the abstract, in this particular decision, the range of side effect values is from “none” to “rare.” That is, the meaning of a 100 point change in the side effect attribute is not very large in this context.
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