Tactical Coordination in Plurality Electoral Systems

Simple plurality election systems (commonly known as `First-Past-The-Post`) are often associated with the dominance of two political parties. Such systems tend to reward leading parties with too many seats (known as the `mechanical` effect) and provoke tactical voting, where voters switch away from trailing parties (known as the `psychological` effect). We view tactical voting as a coordination problem. A group of voters wish to prevent a win by a disliked party (such as the Conservatives in recent UK elections) and must partially coordinate behind a single challenger (such as Labour or the Liberal Democrats) in order to do this. Crucially, voters have limited information on the situation within their constituency and hence there is no common knowledge of the game being played - tactical voting is a global game. We show that in this setting, voters will only partially coordinate. Furthermore, tactical voting exhibits negative feedback - tactical voting by others reduces the incentive for an individual to vote tactically, since they become concerned that they may switch in the wrong direction. We calibrate our model, and apply it to the UK General Election of 1997. Throughout England, we find that the `mechanical` and `psychological` effects tend to offset each other: Tactical voting serves to reverse the Conservative bias that results from the geographic distribution of votes.