This paper explores the relationship between democracy and redistribution in a probabilistic voting model with three jurisdictions, each inhabited by residents with different income levels. The authors demonstrate that it is optimal for the central government to distribute tax revenues as public goods only to the residents of the richest and median-income jurisdictions. They compare the welfare of citizens under a one-bracket tax structure where the poor contribute to taxes but do not receive public goods, and under progressive two-bracket or three-bracket tax structures where the poor face no taxes but also do not receive any public goods. The paper also examines scenarios where part of the tax revenues are extracted as political rents, maximizing expected payoff rather than the probability of re-election. In such cases, complete extraction of private income with no allocation of public goods is possible if electoral uncertainty is high. The findings suggest that income rather than numerical numbers of rich, poor, or middle-class individuals plays a more central role in resource allocation. The paper concludes by discussing the implications for policy and the potential for complete extraction of resources under certain conditions.This paper explores the relationship between democracy and redistribution in a probabilistic voting model with three jurisdictions, each inhabited by residents with different income levels. The authors demonstrate that it is optimal for the central government to distribute tax revenues as public goods only to the residents of the richest and median-income jurisdictions. They compare the welfare of citizens under a one-bracket tax structure where the poor contribute to taxes but do not receive public goods, and under progressive two-bracket or three-bracket tax structures where the poor face no taxes but also do not receive any public goods. The paper also examines scenarios where part of the tax revenues are extracted as political rents, maximizing expected payoff rather than the probability of re-election. In such cases, complete extraction of private income with no allocation of public goods is possible if electoral uncertainty is high. The findings suggest that income rather than numerical numbers of rich, poor, or middle-class individuals plays a more central role in resource allocation. The paper concludes by discussing the implications for policy and the potential for complete extraction of resources under certain conditions.