Voter preferences, simple electoral games, and equilibria in two-candidate contests

Abstract

The fundamental assumption of spatial models of party competition is that voters possess cardinal utility functions defined on all combinations of issue positions which candidates may adopt. Furthermore, spatial theorists usually assume that utility functions have a shape common to all voters and that voters' most preferred positions are distributed in some regular manner. Employing these and attendant assumptions, the spatial theorist seeks to ascertain what deductions can be made about candidate strategies, i.e., the positions which vote or plurality-maximizing candidates should adopt in an election. It has been found that, in many situations, convergence to an opponent's positions and/or adoption of the median/mean of the most preferred positions of all voters is an important candidate strategy. In this context, two main problems have arisen: (1) difficulties of empirical or statistical analysis; (2) the abovementioned candidate strategy is generally not applicable to elections in so-called ‘plural’ societies. One path out of this latter problem has been formulated by Rabushka and Shepsle (1972). This article explores another potential solution by addressing the following question: If voters arenot characterized by cardinal utility functions, but some other type, what are the consequences for candidate strategies? The alternate assumption employed is that voters are characterized bylexicographic utility functions. The consequences for candidate strategies of this assumption are then determined for two plurality-maximizing candidates in some one- and two-dimensional, three-, five-, and seven-voter electoral games.