Abstract
Transitivity is a compelling requirement of rational choice, and a transitivity axiom is included in all classical theories of both individual and group choice. Nonetheless, choice contexts exist in which choice might well be systematically intransitive. Moreover, this can occur even when the context is transparent, and the decision maker is reflective. The present paper catalogues such choice contexts, dividing them roughly into the following classes:
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Contexts where the intransitivity results from the employment of a choice rule which is justified on ethical or moral grounds (typically, choice by or on behalf of a group).
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Contexts where the intransitivity results from the employment of a choice rule that is justified on economic or pragmatic grounds (typically, multi-attribute choice).
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Contexts where the choice is intrinsically comparative, namely, where the utility from any chosen alternative depends intrinsically on the rejected alternative(s) as well (typically, certain competitive contexts).
In the latter, independence from irrelevant alternatives may be violated, as well as transitivity. However, the classical money-pump argument against intransitive choice cycles is inapplicable to these contexts. We conclude that the requirement for transitivity, though powerful, is not always overriding.
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We wish to thank the colleagues and students, too many to list, with whom we have discussed the ideas in this paper, and in particular to acknowledge our heavy intellectual debt to Amos Tversky, who helped and inspired us in all stages of this study.
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Bar-Hillel, M., Margalit, A. How vicious are cycles of intransitive choice?. Theor Decis 24, 119–145 (1988). https://doi.org/10.1007/BF00132458
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DOI: https://doi.org/10.1007/BF00132458