In this paper, I relate the degree of progressivity of the income tax scheme to the prevailing income inequality in the society. I find that, consistent with the data, more unequal societies implement more progressive income tax systems. I build a model of political coalition formation, where different income groups have to agree on a tax scheme to finance the public good. I show that, the greater income inequality is, i.e. the further away the rich are from the rest of the population, the less able they are to credibly commit to participating in a coalition. Therefore, as income inequality rises, the rich are increasingly excluded from the design of the income tax scheme. Consequently, the rich bear a larger fraction of the public good, and the tax system becomes more progressive.