An indifference trap of voting

Abstract

In this paper strategic situations of voting and abstentions are analysed in a three-candidate voting model where voters are indifferent to various alternatives and candidates are interested in winning the election and seeing their most preferred alternative being realized. A specific decision problem is analysed, described by an Indifference Trap Game, with respect to, e.g., the corresponding Nash equilibria, perfect equilibria, and maximin solution. A second-best outcome is contained in the choice set of all three solutions while the Nash equilibrium concept is compatible with the Pareto efficient outcomes of the game.

An alternative scenario where candidates suffer from incumbency but voters still are indifferent to some alternatives also supports the second-best outcome. Again, various solutions concepts are applied. We conclude that indifferent voters imply an eminent coordination problem for the candidates in the given voting game which, in general, ends up in inefficient outcomes. The inherent complexity of the decision situation cannot be sufficiently reduced to single out one and only one outcome.