Spatial models of party competition constitute a recent and incrementally developing literature which seeks to explore the relationships between citizens' decisions and candidates' strategies. Despite the mathematical and deductive rigor of this approach, it is only now that political scientists can begin to see the incorporation of those considerations which less formal analyses identify as salient, and perhaps crucial, features of election contests.One such consideration concerns the candidates' objectives. Specifically, spatial analysis often confuses the distinction between candidates who maximize votes and candidates who maximize plurality. Downs and Garvey, for example, assume explicitly that candidates maximize votes, though plurality maximization is clearly the assumption which Garvey actually employs, while Downs frequently assumes that vote maximization, plurality maximization, and the goal of winning are equivalent. Downs, nevertheless, attempts to disentangle these objectives, observing that plurality maximization is the appropriate objective for candidates in a single-member district, while vote maximization is appropriate in proportional representation systems with many parties. All subsequent spatial analysis research, however, assumes either implicitly or explicitly that candidates maximize plurality. If Downs is correct, therefore, this research may not be relevant for a general understanding of electoral competition in diverse constitutional or historical circumstances. The question then is whether those strategies that maximize votes differ from those strategies that maximize plurality.
Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems