Strategic Electoral Choice in Multi-Member Districts: Approval Voting in Practice?

Abstract

The chief aim of this paper is to elucidate the theory of electoral choice in an important but previously neglected electoral context: multi-member districts. Taking the simplest case of a threecandidate election in a double-member district, the paper develops a model of electoral choice as a standard decision under risk. It is found that this simplest case is essentially equivalent to approval voting with three candidates; thus, voting in double elections with three candidates is in the same sense that approval voting is, and a unique sincere strategy exists when preferences are dichotomous. Nonetheless, it is shown that electoral choice in double (and approval) elections is inherently strategic in the sense that voters' beliefs about how others will vote affect their decisions (when preferences are not dichotomous). This point is important because it has been claimed that sincerity of choice is an important property, guaranteeing that choices reflect preferences directly. This paper shows that there are fairly severe restrictions on the sense in which this is true, due to the strategic nature of choice. In the later sections of the paper, an examination of actual voting behavior in double-member districts is made to see if theoretically predicted strategic behavior is evident in practice. The evidence is positive.