Democracy and Redistribution

In a probabilistic voting model with three jurisdictions with residents with different income levels, we demonstrate that it is always optimal to distribute tax revenues as public good to only the residents of richest and median income jurisdictions. In this context, we compare the overall welfare of all citizens in a one bracket Tax Structure where the poor contribute to tax and does not receive public goods, to that in a progressive Two bracket or a Three bracket Tax Structure where the poor face no taxes but neither do they receive any public goods. In a situation where the government extracts a part of the tax revenues as political rents and maximizes expected payoff rather than the probability of re-election, there is a possibility of complete extraction which implies taxing away all private income with no allocation of public good, if electoral uncertainty be high.