Abstract

In the final part, Arrow's own formal treatment of the social choice problem is examined and its relation to the preference aggregation model is analyzed. Particular attention is paid to Arrow's discussion of independence of irrelevant alternatives, and, with the aid of some additional formal work, much of what has been found problematic in this is resolved. Finally, this analysis is used as the basis of a critique of the "received view" in the literature about independence of irrelevant alternatives. ;In the second part, several formal results from the literature are adapted to the present formal framework and interpreted in preference aggregation terms. These include both characterization theorems for specific classes of decision rules, and impossibility results, such as the Arrow theorem itself. Most of these results utilize the requirement of context-independence, and its role in the proofs is analyzed. Some discussion as well is offered about the characterization of rules that do not satisfy the requirement of context--independence. ;The treatment of these matters is divided into three parts. In the first part, the basic formal representation of preference aggregation rules is laid out. A variety of the formal conditions from the literature are stated and discussed in preference aggregation terms. Several of the conditions usually called "rational choice" or "revealed preference" conditions are included. One of these, here called the "Weak Axiom of Revealed Preference", is singled out as the formal embodiment of the requirement of context-independence. Various examples of preference aggregation rules are stated and assessed vis-a-vis the formal conditions presented. ;A subsidiary theme, which is dealt with throughout much of the discussion, is the nature, import, and desirability of independence-or-irrelevant-alternatives conditions. A general informal requirement on preference aggregation rules, which is called "the requirement of context-independence", is characterized. This requirement, it is argued, is a basis for the proper understanding of the several formal conditions that have been called "independence of irrelevant alternatives" in the literature. A variety of formal results, including a new version of Arrow's "General Possibility Result" for social choice rules, are offered in support of this contention. ;The purpose of this work is to provide an analysis of the interrelationships among formal models for choice under conditions of uncertainty, social choice, and multicriterial decision-making. A simplified version of the usual formalism for the first named of these problems is adopted. It is argued that this can be used, with appropriate interpretations, for all three problems. Decision rules for these problems are construed in the abstract form of preference aggregation rules: rules for the selection of alternatives which are "best", in some sense, in the face of conflicting evaluations. The multicriterial interpretation is taken as a touchstone for the understanding of the proposed model