A strategic calculus of voting

Conclusion

There are several major insights which this game theoretic analysis has produced. First, we have shown that equilibria exist with substantial turnout even when both the majority is much larger than the minority and the costs of voting are exceptionally high. For example, in large electorates using the status quo rule, we show mixed-pure equilibria with turnout roughly equal to twice the size of the minority when the cost is nearly equal to 37% (e ⁻¹ × 100) of the reward (B). Second, with large electorates the many equilibria appear to reduce to just two types, the type just mentioned and a type with almost no turnout. Third, we have shown that turnout may rise as the costs of voting rise. This results when all members of a team “adjust” their turnout probabilities so that the probability of being pivotal increases to match the increased cost of voting. We have also shown that turnout is nearly invariant with costs in large electorates where turnout probabilities approach one or zero. Fourth, the actual split of the vote is likely to be a biased measure of the actual distribution of preferences in the electorate. Because majorities have greater incentives to free-ride, they will turn out less heavily than minorities. Elections can be relatively close, even when one alternative is supported by a substantial majority of the electorate. The probability that the majority will win does not seem to be closely related to the size of the electorate or its size relative to the minority. However, turnout is quite strongly correlated with the relative sizes of the minority and the majority.