Why are Bismarckian social security systems associated with larger public pension expenditures, a smaller fraction of private pension and lower income in-equality than Beveridgean systems? These facts are puzzling for political economy theories of social security which predict that Beveridgean systems, involving intra-generational redistribution, should enjoy larger support among low-income people and thus be larger. This paper explains these features in a bidimensional political economy model. In an economy with three income groups, low-income support a large, redistributive system; middle-income favor an earning-related system, while high-income oppose any public system, since they have access to a superior saving technology, a private system. We show that, if income inequality is large, the voting majority of high-income and low-income supports a (small) Beveridgean system, and a large private pillar arises; the opposite occurs with low inequality. Additionally, when the capital market provides higher returns, a Beveridgean system is more likely to emerge.