In a probabilistic voting model with three jurisdictions and residents with different incomes, we analyze inefficiencies in local public good allocation that emerge from trying to satisfy the median voter. The median voter and the rich may gain but the poor lose out. We analyze a uniform tax rate and progressive two and three bracket tax structures. If the government extracts part of tax revenues as political rents and maximizes expected payoff there is a possibility of taxing away all private income with no allocation of public good, if electoral uncertainty is high, especially when the government is risk neutral.