Arrow’s Impossibility Theorem: The Logic of Dictatorship and the Meaning of Social Choice

The paper pays critical tribute to Arrow’s (1951) analysis of social choice by focusing on a number of the foundational, conceptual and interpretational issues to which it gives rise. It begins with a discussion of justifications of other formal requirements, namely unrestricted domain, Pareto optimality and independence of irrelevant alternatives, before proceeding to a detailed analysis of the way in which Arrow’s famous Theorem formalises the concept of dictatorship. The term and the formalisation still play a central role in contemporary social choice theory though we shall argue that, for a variety of reasons, the formalisation provides neither necessary nor sufficient conditions for the existence of an agent with powers of inappropriate influence. Subsequently, the paper examines the claim that Arrow believed had been accepted by critics of his theory, namely that social choice is fundamentally about preference aggregation and suggests that preference aggregation should only be regarded as a special case of social choice. (In this regard, I closely follow critics of utilitarianism and of its economic implementation in conventional welfare economics, and offer some empirical evidence which helps to illustrate the criticisms theorists have made and make sense of people’s objections to social choice procedures such as QALY maximisation.) Finally, I conclude that, whilst not decisive in conceptual terms, the Theorem is an important contribution to C20th thought, offers a platform for mathematical, philosophical and even empirical work pertaining to a broadening conception of social choice.