Rationality of Individual Opinions and Social Decisions

Abstract

This Chapter extends the ideas deal with description of individual opinions and social decisions that were briefly presented in Chapter 1. Section 2.2 investigates various types of binary relations and defines the notion of pair-dominant, or rationalizable by a binary relation, choice. In this Section main types of binary relations used in social choice theory are defined — linear orders, weak orders, strict partial orders, and acyclic relations. Section 2.3 gives another well-known concept of choice, based on the ‘extremization paradigm’ — that of a choice function rationalizable by some numerical (utility) function, studies the classical unicriterial and multicriterial choice models. We study three different types of multicriteral models — Paretian, weak Paretian, and joint-extremal ones. The equivalence of Paretian and weak Paretian models is shown. Section 2.4 lists Expansion-Contraction Axioms (rationality conditions) for choice functions, and studies their mutual relations. The axioms of Heredity, Concordance, Outcast, Arrow’s Choice Axiom in different versions, Choice Monotonicity, Choice Resolutness are studied. Section 2.5 establishes relations between the classes of rationalizable choice functions and the domains in the space of choice functions described in Section 2.4. The classical pair-dominant choice functions are shown to define a small, but important part of the models describing individual opinions and social decisions. Section 2.6 contains concluding remarks and gives a guide to the literature.