The transitive core: Inference of welfare from nontransitive preference relations

In this paper, we study methods of inferring a decision maker's true preference relation when observed choice data reveal a nontransitive preference relation due to choice mistakes. We propose some sensible properties of such methods and show that these properties characterize a unique rule of inference, called the transitive core. This rule is applied to a variety of nontransitive preference models, such as semiorders on the commodity space, relative discounting time preferences, justifiable preferences over ambiguous acts, regret preferences over risky prospects, and collective preferences induced by majority voting. We show that the transitive core offers a nontrivial and reasonable inference of the decision maker's true preference relation in these contexts.