Voting when Rankings Matter : Truthful Equilibria, Efficiency, and Abstention

Ranked voting is an election format in which each voter ranks candidates on a ballot, and individual rankings are aggregated using a general rule to produce a social ranking. This paper proposes a non-cooperative model of this electoral system. The setting allows for unequal voting rights, abstention, and social incomparability of candidates, and each voter's utility is measured by how close his or her true preferences are to the social ranking. The analysis uncovers three main findings. First, it proves the existence of a pure strategy Nash equilibrium. Second, it shows that truthtelling is always a Nash equilibrium regardless of the voting rule and the structure of individual preferences. Third, under mild conditions, truthtelling is Pareto-efficient when voters have strict preferences. Extending the analysis to majoritarian elections with costly voluntary participation shows that truthtelling is an equilibrium if and only if the costs of participation are not too high and the election is tight. The findings have implications for the design of ranked voting systems that are compatible with truthtelling and efficiency while allowing unrestricted freedom in the choice of the voting rule. A reinterpretation of the model in the context of intrapersonal bargaining, where the decision-maker has multiple rational selves, has implications for the occurrence of cyclic individual choices that reflect stable and efficient behavioral patterns.