The institution of electoral politics is considered. The authors use the classical Downsian model of electoral competition in which two parties compete for the vote of the electorate in a symmetric zero-sum, perfect information game. This paper raises the question of the level of inequality generated by Downsian competition for redistribution. The apparatus of a general spatial model of elections is applied. In the division problem the basic results are threefold: 1. The authors derive how far one can go by sticking to pure strategies and narrowing the set of possible outcomes on the basis of dominance-like arguments; 2. optimal strategies are exhibited; 3. the authors offer a sample of quantitative estimates of how unequal the distributions proposed at equilibrium are.