We analyze the effect of the projected demographic transition on the political support for social security, and equilibrium outcomes. Embedding a probabilistic-voting setup of electoral competition in the Diamond (1965) OLG model, we find that intergenerational transfers arise in the absence of altruism, commitment, or trigger strategies. Closed-form solutions predict population ageing to lead to higher social security tax rates, a rising share of pensions in GDP, but eventually lower social security benefits per retiree. The response of equilibrium tax rates to demographic shocks reduces old-age consumption risk. Calibrated to match features of the U.S. economy, the model suggests that, in response to the projected demographic transition, social security tax rates will gradually increase to 16 percent; other policies that distort labor supply will become less important; and in contrast with frequently voiced fears, labor supply therefore will rise.