The transitive core of preference relations

Much evidence suggests that a preference relation of a decision maker is often not transitive in reality. Armstrong [1, 2, 3] and Luce [11] argued that, in contrast to the standard utility theory, a preference relation of a decision maker is suffered from nontransitive indifferences due to the imperfect powers of discrimination. Kahneman and Tversky [8] presented the extensive experimental results that show that subjects violate the expected utility hypothesis in a consistent manner leading to cyclic preferences over prospects. To accommodate such choice anomalies, Loomes and Sugden [10] developed a nontransitive evaluation of prospects that accounts for the experience of regret. Roelofsma and Read [15], followed by Read [14] and Ok and Masatlioglu [13] studied intertemporal choice problems in which a decision maker exhibits cyclic choice patterns. In the context of the social choice theory, the classical paradox by Condorcet shows that a collective preference relation can be cyclic under the majority voting rule even when individual preferences behave nicely. While nontransitive preference relations are recognized as a convincing descriptive phenomenon as such, many economists on the other hand appear not to view them as the normative concept. In addition, due to the issues of preference cycles, especially the inability of choices and the instability to the framing effects, the nontransitive preference relations are seldom, if not ever, employed in applied studies. Consequently, there seems to be a serious gap between the efforts made from the descriptive perspective and the applied works adopting the normative assumption within their foundation. Facing this situation, the following questions is