The theory of social choice since 1951

Abstract

Starting point for our analysis is Arrow's famous impossibility result from 1951. Arrow had proved that within an ordinal framework no non-dictatorial social welfare function exists that satisfies the condition of unrestricted domain, the weak Pareto principle and the requirement of independence of irrelevant alternatives. In the first few sections, we discuss what kinds of positive results can be obtained once we relax one or the other of his axioms. The simple majority rule, for example, is an Arrow social welfare function under a domain restriction that is more general than single-peakedness. The Borda rule violates Arrow's independence axiom but satisfies a weak independence requirement together with some other rather attractive properties. We next look at preference domains that admit the existence of Arrovian social welfare functions, i.e. aggregation rules fulfilling both the Pareto and the independence condition and being non-dictatorial. We also characterize domains for non-manipulable voting procedures. The subsequent section analyzes social aggregation functions that allow for an interpersonal comparison of both utility levels and utility gains. Utilitarian rules and the Rawlsian lexicographic maximin principle are discussed in particular. We finally examine the exercise of individual rights within the social choice context, which means that non-utility information is considered as well.