Plurality and Probability of Victory: Some Equivalence Results

This paper examines decision-making by political candidates under three different objective functions. In particular, we are interested in when the optimal strategies for expected vote share, expected plurality, and probability of victory maximizing candidates coincide in simple plurality elections. It is shown here that if voters' behavior, conditional on the policies proposed by the candidates, is identical from the candidates' perspective, and candidates are restricted to choosing pure strategies, then all three objectives lead to the same best response function when there are two candidates and abstention is not allowed. We then provide a counter-example to Hinich's claim of general asymptotic equivalence in two candidate elections without abstention in which voter types are independently, but not identically distributed. In addition, we provide a counterexample to general best response equivalence between these objective functions in two candidate elections in which abstention is allowed, but our other assumptions are satisfied. Finally, an example of why our result can not be immediately extended to arbitrary numbers of candidates is provided.