Discovering manipulated social choices: The coincidence of cycles and manipulated outcomes

Abstract

In his recent book William Riker (1982) argues that the results of socialchoice theory require that we lower our traditional aspirations for the role of elections in democratic theory. In particular, he concludes that socialchoice theory sounds the death knell for the 'populist' interpretation of voting, the view that election outcomes embody the 'collective will' of the electorate. Other, more modest claims about elections also fall to the theorems of social-choice, until we remain with the extremely modest claim embodied in Riker's 'liberal' interpretation of voting. On this view elections provide the possibility of rejecting unpopular leaders, and the major value of elections is as a weapon against government tyranny. Riker's argument proceeds in several stages. First, he reviews the analysis of social-choice in n-dimensional issue spaces. This literature conclusively demonstrates that the necessary and sufficient conditions for a majority voting equilibrium are so strict that one cannot expect them to ever be met.' Thus Riker consigns the notion of a 'majority will' to the same 'dust bin' to which earlier liberals (from Madison to Bentley) had consigned Rousseau's general will. Having discovered at the most abstract level that the search for a collective will of the electorate is pointless, for no such will exists, Riker proceeds to review the conclusions of social-choice theory about elections with a finite number of candidates. Here Arrow's theorem (1963) and its progeny take over. Not only do majority cycles still occur, but different systems with strong axiomatic credentials may select different candidates. Thus, even at this level the prospect is slight that we can endow election outcomes with great normative significance. But the prospects disappear almost entirely, in Riker's judgment, when we consider the manipulability theorems of