The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis

The fact that voters can manipulate election outcomes by misrepresenting their true preferences over competing political parties or candidates is commonly viewed as a major law of democratic voting systems. It is argued that insincere voting typically leads to suboptimal voting outcomes. However, it is also understood that insincere voting is rational behavior as it may result in the election of a candidate preferred by the voter to the candidate who would otherwise be selected. The relative magnitude of the welfare gains and losses of those who benefit from and those adversely affected by insincere voting behavior is consequently an important empirical issue. We address this question by providing exact asymptotic bounds on the welfare effects, in equilibrium, of insincere voting for an infinite class of democratic rules. We find, for instance, that preference manipulation benefits one-half to two-thirds of the population in three-candidate elections held under first-past-the-post, and one-third to one-hundred percent of the population in antiplurality elections. These bounds differ from those obtained under out-of-equilibrium manipulation. Our partial identification analysis provides a novel approach to evaluating mechanisms as a function of attitude towards risk, and it has practical implications for the choice of election rules by a mechanism designer facing a worst-case or a best-case objective. It also provides a new answer to the longstanding question of why certain rules, such as first-past-the-post, are more common in practice.