The transitive core: Inference of welfare from nontransitive preference relations

Abstract

This paper studies welfare criteria for decision makers endowed with nontransitive preference relations. If a person has nontransitive preferences, then the classical utilitarian welfare criterion does not identify her welfare order, and the problem of maximizing the welfare becomes unclear. In order to find a reliable method of welfare inference, I propose a series of welfare criteria that apply to nontransitive preference relations. Then, we show that these criteria characterize a unique rule of welfare inference from nontransi- tive preference relations. This rule, called the transitive core, is applied to a variety of nontransitive preference models, such as semiorders on the com- modity space, relative discounting time preferences, justifiable preferences over ambiguous acts, regret preferences on risky prospects, and collective preferences induced by majority voting. These examinations show that the proposed method provides nontrivial and sensible inference of welfare in re- spective contexts.