Due to the rapid progress in medical technology social insurance systems will soon no longer be able to grant health services without limits but must employ non-price rationing devices. This raises the question how these limits will be determined. Here we consider a direct democracy where the size of the social health insurance plan is determined in a popular referendum using simple majority rule. Moreover, two different kinds of rationing are distinguished according to whether additional private purchases of health care are allowed. For both systems we examine the size of the social insurance system in a political equilibrium, and we compare the results in particular with respect to their distributional effects.