An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We examine political disintegration across eras, cultures and geographical scale to form a simple hypothesis that can be expressed verbally yet formulated mathematically. Factions within a state make choices described by game-theory about whether to accept the political status quo, or to attempt to better their circumstances through costly rebellion. In lieu of precise data we verify our model using sensitivity analysis. We find that a small amount of dissatisfaction is typically harmless to the state, but can trigger sudden collapse when there is a sufficient buildup of political inequality. Contrary to intuition, a state is predicted to be least stable when its leadership is at the height of its political power and thus most able to exert its influence through external warfare, lavish expense or autocratic decree.