Abstract

The origins of single-peaked preferences in multiattribute choice behavior are analyzed. The starting point is Coombs and Avrunin's ( Psychological Review, 1977, 84, 216–230; Journal of Mathematical Psychology, 1977 , 16, 261–266) theory which explains single-peakedness as the joint effect of task and behavior characteristics. Whereas the task conditions—so-called efficient sets—are retained, and their importance is even more stressed, it is argued that Coombs and Avrunin's behavioral assumptions—classical marginally decreasing preference functions—may not be representative of actually displayed choice behavior. Rather, the information processing approach to decision research has shown that multiattribute choices are often based on simplifying heuristic rules which, due to their possible intransitivity, are inconsistent with Coombs and Avrunin's behavioral requirements. Tversky's ( Psychological Review, 1969 , 76, 31–48) additive difference model is used as an algebraic framework for analyzing such so-called attribute-based choice rules. Sufficient (and in the continuous case also necessary) conditions are presented which guarantee that the additive difference model will also be single-peaked on efficient sets. These conditions show that the behavioral principles yielding single-peaked preferences are far more general than Coombs and Avrunin assumed and include most of the empirically substantiated forms of attribute-based choice rules. Further, a necessary and sufficient condition is derived which insures that elimination rules, like the conjunctive rule, for instance, and generalizations thereof are single-peaked. Finally, making use of a result by Edgeworth, ( Mathematical Psychics, London, Paul, 1881 ), it is shown that efficient sets per se may originate in quite different ways. It is concluded that the phenomenon of single-peakedness is mainly a function of the task rather than of some specific behavior.

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