Intransitive choices based on transitive preferences: The case of menu-dependent information

Abstract

The paper considers decision contexts in which the set of alternatives from which choices have to be made (the ‘menu’) may convey information about the desirability of these alternatives. Our analysis is motivated by the fact that in specifying an appropriate description of a choice situation an outside observer always has to neglect some ‘dimensions’ of the decision problem. The central claim is that properties of observed behaviour may depend crucially on the neglected dimensions even when their influence is arbitrarily small. Specifically, we prove the following result. Suppose that in a discrete choice model an agent's beliefs about the ‘quality’ of the available alternatives depend on the specific menu to choose from. Then, even when the difference in beliefs given different menus is arbitrarily small (but positive), any practicable description of the decision situation necessarily implies that cyclic choices will be observed. The result suggests that transitivity - as a condition on observable behaviour - is rather questionable in any context where one cannot completely exclude the possibility that menu-dependent information may play some role.