The Swing Ratio and Game Theory

Abstract

We propose a simple game-theory model of single-member plurality electoral systems, two parties with unequal resources being the players. Strategies consist of allocations of resources among the n contests, and a party's payoff is the number of contests to which it has assigned more resources than the other party. Mixed strategies exist which are asymptotically optimal as n increases. Identifying a party's proportion of total resources with its total vote proportion, we predict that the swing ratio, or marginal seat proportion per vote proportion, is 2. This compares to empirical findings which range between 2 and 4, and to the hitherto unexplained cube law, which predicts 3. We suggest that the strategic problem modeled by this game accounts for the major part of the swing ratio effect. Factors which vary from system to system, such as proportion of hard-core support attached to parties, may amplify this effect.