Learning in Elections and Voter Turnout Equilibria

Economics

Further details

(with Stefano DeMichelis)

Game Theoretic Models of Voter Turnout (e.g. Palfrey and Rosenthal , 1983,1985) have the problem of multiple equilibria, some of which seem unreasonable. This happens in both complete and incomplete information models of voter participation. There are many equilibria typically and some with substantially high turnout. How can this be explained? Palfrey and Rosenthal (1985) suggest that it is due to the fact that the model is one of complete information and that even with mixed strategy equilibria, strategic uncertainty is too low to rule out the high turnout equilibria in the simplest case. We show that this is not the main problem with these equilibria-- incomplete information may exacerbate the problem of multiple equilibria sometimes introducing more of them, some with high turnout. We propose a very intuitive criterion based on voter learning to distinguish reasonable equilibria. Voters may learn about equilibrium through a process of continuous fictitious play -- if this converges to some point she will play the corresponding mixed strategy. We then investigate the likelihood of observing any particular equilibrium. Moreover, we look at the impact of changes in exogenous parameters-- e.g the cost of voting or the difference between the two parties, on the stability of the different types of equilibria. We can predict hysteresis or the phenomenon of high turnout for long periods of time in some situations depending on initial conditions. The model applies equally to incomplete information settings. We can make several qualitative predictions that can be tested.