Preference, Utility, and Choice: Classic Models

Abstract

In this Chapter we present the basic models used in individual and social choice theory, microeconomics, decision theory, etc., to describe individual preferences and choices over alternatives, and the links between those models. Section 2.2 bears on the main types of binary relations used to represent preferences, namely, linear orders, weak orders, partial orders and acyclic relations. We also define here the notion of a partition of the set of alternatives and study the relation between the class of ordered partitions and the class of weak orders. Section 2.3 defines the notion of choice rationalizable by a binary relation, also called ‘pair-dominant choice’. Each class of preference relations has a class of pair-dominant choice functions rationalizable by the relations from this class associated with it. Another classic model of choice described in Section 2.4 deals with the selection of the alternatives that are ‘optimal’ according to one or several criteria. The case of one criterion leads to the utility maximization model whereas one of its generalizations is the Paretian multicriterion model. It is shown that the choice functions defined by these utility models are the classes of pair-dominant choice functions rationalizable by linear orders, weak orders and partial orders, respectively. Section 2.5 presents several rationality conditions for choice functions and studies their relations.