We create a rotating bandit model of executive turnover in politics with autocratic presidents, large and centralized governments, and limited reelection. The model is an extension of McGuire and Olson's 1996 work. We apply our model by studying the relationship between electoral cycles and economic growth and inflation uncertainty in Mexico, a country with a highly centralized and powerful government, no reelection, and until recently, little political competition. We find a significant postelection economic collapse but no preelection boom, which is contrary to the predictions of the traditional political business cycle model. We also find evidence that elections create, rather than resolve, inflation uncertainty, which contradicts the predictions of the rational partisan model. While our rotating bandit model is largely consistent with the results we find, more work is needed on the real effects of politics in the developing world.