Cumulative Dominance and Heuristic Performance in Binary Multiattribute Choice

We study the effectiveness of simple heuristics in multiattribute decision making. We consider the case of an additive separable utility function with nonnegative, nonincreasing attribute weights. In this case, cumulative dominance ensures that the so–called cumulative dominance compliant heuristics will choose a best alternative. For the case of binary attribute values and under two probabilistic models of the decision environment generalizing a simple Bernoulli model, we obtain the probabilities of simple and cumulative dominance. In contrast with the probability of simple dominance, the probability of cumulative dominance is shown to be large in many cases, explaining the effectiveness of cumulative dominance compliant heuristics in those cases. Additionally, for the subclass of the so–called fully cumulative dominance compliant heuristics, we obtain an upper bound for the expected loss that only depends on the weights being nonnegative and nonincreasing. The low values of the upper bound for cases in which the probability of cumulative dominance is not large provide an additional explanation for the effectiveness of fully cumulative dominance compliant heuristics. Examples of cumulative dominance compliant heuristics and fully cumulative dominance compliant heuristics are discussed, including the deterministic elimination by aspects (DEBA) heuristic that motivated our work.