In many countries, collectively financed health insurance systems or health services delivery systems (such as the NHS) exist. Typically, these institutions are financed via general taxes or specific contributions levied on earnings. As benefits are not dependent upon income, this implies a redistribution from high to low earners. An exception can be found in Switzerland, where equal per-capita contributions are used. From a public-choice perspective it is natural to ask whether the combination of health insurance and income redistribution leads to an expansion or a contraction of the size of a public health care system, a question that is particularly relevant in view of the projected rapid increase of health care costs in the next decades due to population ageing and medical progress. Building upon the work of Gouveia (1997) and an earlier paper by the author (Breyer 1995) I use a simple model of direct democracy to analyze under what circumstances income redistribution tends to expand the size of a public health insurance system. The predictions of the model are confronted with existing evidence from Germany and Switzerland and are used to develop hypotheses on the future development of the systems.