We model pay-as-you-go (PAYG) social sucurity systems as the outcome of majority voting within a standard OLG model with production and an exogenous population growth rateo At each point in time individuals work, save, consume and invest by taking the social security policy as given. The latter consists of a tax on current wages transferred to elderly people. When they vote, individuals have to make two choices: If they want to keep the committment made by the previous generation by paying the elderly the promised amount of benefits, and which amount they want paid to themselves next periodo We show that when the growth rate of population is high enough compared to the productivity of capital there exists an equilibrium where PAYG pensions are voted into existence and maintained. PAYG systems are kept even when everybody knows that they will surely be abondoned, and that some generation will pay and not be paid back. We characterize the steady state and dynamic properties of these equilibria and study their welfare properties. Equilibria achieved by voting are typically inefficient; however, they may be so due to overaccumulation, as well as, in other cases, due to under accumulation. On the other hand, the efficient steady states turn out to be dynamically unstable: so we are presenting an unpleasant alternative for policy making.