Institute for Mathematical Behavioral Sciences

Transitivity of preference is defined as follows: if a person, group or society prefers choice option A to B and they prefer B to C then, in order to be transitive, they must prefer A to C. This colloquium will discuss methodological concerns about past research on preference (in)transitivity in individual decision makers. The starting point is the insight that the usual operationalization of transitive preference via “weak stochastic transitivity” suffers from conceptual shortfalls, most notably the “Condorcet paradox” of social choice theory. The Condorcet paradox shows that transitive individuals may violate weak stochastic transitivity at the level of aggregated data. The talk explores the alternative route of generalized mixture models, in which the sample space of permissible latent preference states is a family of transitive binary relations (e.g., partial orders, weak orders, linear orders). Choice data are modeled as being governed by a probability distribution over such a sample space. This leads to the study of certain convex polytopes, such as, e.g., the linear ordering polytope for binary choice data. The most famous empirical work on intransitivity of individual decision makers' preference is a seminal paper by Tversky (1969, Psychological Review) in which some respondents apparently violated weak stochastic transitivity. The talk will revisit Tversky's data within the framework of the generalized mixture model approach and discuss a new study designed to address some of the methodological problems. This research is sponsored by the Decision and Cognition Program of the Air Force Office of Scientific Research.