11. Distributive politics

In a model of electoral competition in which a position is a distribution of wealth, the citizens have preferences over the candidates about which the candidates are uncertain, each citizen's payoff function over wealth is strictly concave, and a Nash equilibrium exists, the candidates propose the same distribution. In simple examples, swing voters and citizens whose votes are more likely to be pivotal are assigned more wealth.

If individuals differ in their earning power, can choose their hours of work, and care about both their consumption and their hours of work, under some conditions the collective choice problem in which the alternatives are the individuals' favorite tax-subsidy schemes has a Condorcet winner, which is the favorite scheme of the individual with median earning power. In a variant of the model in which which the alternatives are finitely many linear tax-subsidy schemes and the individuals are ordered by pre-tax income independently of the tax-subsidy scheme, the favorite alternative of median individual is a strict Condorcet winner.

In a model in which the tax-subsidy scheme is the outcome of society-wide bargaining in which any majority can expropriate the complementary minority and any minority can withhold its resources, a tax-subsidy scheme in which the tax rate is 50% and tax revenue is shared equally is the outcome of both the Shapley value and the dissatisfaction-minimizing distribution.