This paper introduces a three-income class, overlapping-generations model with borrowing constraints. The labor income tax for financing pay-as-you-go social security is determined in a majoritarian voting game played by successive generations. When the interest-rate elasticity of consumption is low, the political equilibrium might be characterized by an equilibrium where the old and the middle-income young individuals form a coalition in favor of a higher tax rate and greater social security, while the low- and the high-income young individuals favor a lower tax rate and less social security. In this equilibrium, the size of social security is decreased by the mean-preserving reduction of a decisive voter's wage if he/she is borrowing-constrained.