Pre-print, Working paper: An unfunded Social Security system faces the major risk, sometimes referred to as "political risk", that future generations modify or even suppress the contributions. In order to account properly for this risk, the paper considers a political process in which the support to the system is asked from each new born generation. The analysis is conducted in an overlapping generations economy that is subject to macro-economic shocks. As a consequence, the political support varies with the evolution of the economy. The impact of various factors -intra-generational redistribution, risk aversion, financial markets, governmental debt- on the political sustainability of a pay-as-you-go system is discussed.