Only a Dictatorship is Efficient or Neutral

Abstract

In many, if not most, elections, several different seats must be filled, so that a group of candidates, or an assembly, is selected. Typically in these elections, voters cast their ballots on a seat-by-seat basis. We show that seat-by-seat procedures are efficient or neutral only under extreme conditions. We then provide a domain restriction, called full separability, that ensures the efficiency of seat-by-seat election procedures. How should a voting system be judged? A time-honoured approach judges a system on the basis of the properties it satisfies. The literature on voting has considered myriad properties, including anonymity, neutrality, efficiency, independence of irrelevant alternatives, monotonicity, and Condorcet consistency. Although Arrow’s impossibility theorem (1963) famously warned that a given property may be more subtle and difficult to satisfy than is initially apparent, some of these properties are generally taken to be obviously desirable and easily satisfied, both in theory and in practice. Three such properties are efficiency, anonymity, and neutrality. After all, efficiency merely requires that, when all voters prefer outcome A to outcome B ,o utcome B not be chosen, while anonymity and neutrality only ask, respectively, that all voters and all outcomes be treated equally. Nevertheless, we argue in this paper that, while anonymity is a pervasive feature of political voting