Preference Modeling and Choice Theory: A Set-Theoretic Approach to Rationality

In this thesis we explore some classical assumptions in preference modeling and rational choice theory, and then extend them by means of set-theoretic methods. The first half of this work mainly focuses on the modelization of the preference structure of a decision maker by means of binary relations. Our starting point is the presentation of some very recent approaches to preference modeling. These approaches employ two or more binary relations in the process of modeling preferences, thus ensuring a more accurate and realistic description of the agent’s attitude. The resulting preference structures that we obtain still satisfy the two basic tenets of economic rationality, namely the two properties of transitivity and completeness, distributing them along the whole structure rather than requiring that they hold for a single binary relation. Next, we deal with the properties of transitivity and completeness on their own: first, we provide an explicit characterizations of various known properties of possibly intransitive (but complete) structures; then, we study the representation of possibly incomplete (but transitive) binary relations. Finally, we extend classical revealed preference theory by introducing a novel paradigm of rationality. In the second half of this work, we focus on choice theory. First, we explicitly represent many known models of bounded rationality as special cases of choice under ‘limited attention’. Next, we introduce a novel notion of choice independence for multidimensional choices, which captures the possible invariance of some of the dimensions involved in the decision process. The next chapter deals with the classical dichotomy between rational and irrational choice behavior, and provides a much more accurate partition of the family of irrational choices according to their degree of rationality. The last chapter of this work extends to a stochastic setting the recent notion of choice resolution, which is an operation that captures types of selection displaying hierarchical features.