On the possibility of political change: Outcomes in between local and global equilibria

We study voting over education subsidies where poor individuals may be excluded and the rich may chose private alternatives. With plausible changes of the standard game we show that this problem typically has multiple equilibria; one with low taxes, many excluded, and many in private schooling; another with high taxes, everyone in schooling, and few choosing the private alternative. Shifts between these equilibria can only happen through jumps in policy, not through gradual change. The method we develop identifies the global, as well as all local majority rule equilibria, and it characterizes stability regions around each local equilibrium. Introducing costs into the political system can make the local equilibria the globally stable outcome which, for example, implies that identical countries with different starting points could end up with completely different redistributive systems. Outcomes change in intuitive ways with the parameters and several insights with respect to the possibilities of political change seem general for problems of redistribution with excludability.