Cumulative dominance in multi-attribute choice: benefits and limits

Guided decision processes improve decisions by employing personalized rules that are simple and perform well. In multi-attribute choice, simple rules such as deterministic elimination by aspects can achieve maximum utility because they choose a cumulative-dominant alternative when one exists and because of the combination of two results: (i) a cumulative-dominant alternative has maximum utility when the utility function is linear and (ii) a cumulative-dominant alternative exists frequently in the majority of choice problems when the attributes are binary. We test the limits of (i) and (ii) by relaxing their assumptions about the utility function and the attributes: First, for a linear utility function that also includes multiplicative attribute interactions, we analytically show that a cumulative-dominant alternative has maximum utility when attributes are binary. Whereas this is not necessarily true for continuous attributes, we empirically find that it is essentially always true for a range of probability distributions of the attributes and parameterizations of the utility function. Second, we empirically find that when attributes are continuous, a cumulative-dominant alternative exists frequently only in the minority of choice problems. In sum, cumulative dominance legitimates guiding decision processes by simple rules when it exists but its existence should not be taken for granted.