In this paper I analyse a probabilistic voting model where political candidates choose a direct taxation policy to maximise the probability of winning elections. Society is divided into groups which have different preferences for consumption of leisure or, in other words, are differently single-minded on the amount of leisure. The use of a probabilistic voting model characterized by the presence of single-minded groups breaks down the classic results obtained by using the median voter theorem, because it is no longer only the level of income which drives the equilibrium policies but also the ability of groups to focus on leisure. The robustness of these results is also demonstrated in the presence of heterogeneity in the labour income. Finally, using data from the Luxemburg Income Study, I demonstrate that the cohort-speci.c inequality is signifcantly affected by the structure of the taxation system and that policies chosen by politicians do not seem to be originated by the goal of equality.