The central purpose of this paper is to introduce a new political economy approach which explains the characteristics of Social Security Systems. This approach is based on the Single Mindedness Theory, which assumes that the more single minded groups are able to exert a greater power of influence on Governments and eventually obtain what they ask. Governments are seen as voting-maximizer policy-makers, whose unique goal is winning elections. Using an OLG model and a probabilistic voting approach, I analyze a society divided into two groups, the old and the young, which only differ as for their preferences for leisure. I show that, to win elections, the Government sets the marginal tax rates taking into account the numerosity and the density of groups; eventually, the old receive a positive transfer, whose burden is entirely carried by the young. Furthermore, the more single minded group (the old) is taxed with higher tax rates; this result can be explained by the necessity that the group of the old have to find a way out to solve a free-riding problem among its members. Indeed, higher tax rates induce the old to retire earlier, so that retirees may have more time to participate in political activities and support the old group’s goals.