Optimal sophisticated voting strategies in single ballot elections involving three candidates

Abstract

A model of a rational, sophisticated voter is developed based on the assumption that a voter in a three-candidate election acts to maximize the weighted value of the available voting strategies. The model is used to analyze strategic voting behavior in various traditional and more modern single-ballot systems that employ plurality as a decision rule. In each case, the analysis proceeds by first determining the subset of admissable strategies which are undominated by other valid strategies under the assumption that a voter is not risk-averse. The analysis next involves determining isopreference contours that describe the conditions under which a voter is indifferent between a pair of admissable strategies. These contours are interpreted as decision thresholds which mark the boundaries where a voter shifts from one strategy to another and, hence, govern voting behavior in a particular system. Based on these analyses, an insincerity index, which calibrates the extent to which sophistication produces voting that is inconsistent with actual preferences, is computed. In addition, it is determined for each system whether there are conditions where a group of like-minded, independent voters will vote as a block even though no explicit coalition is formed. Finally, assuming that voting is sophisticated and not risk-averse, we analyze the properties of formal equivalence and symmetry between pairs of systems and, in addition, determine whether a system is formally a mixture of other systems.