In this paper, we present a simple model of health insurance with asymmetric information, where we compare two alternative ways of organizing the insurance market. Either as a competitive insurance market, where some risks remain uninsured, or as a compulsory scheme, where however, the level of reimbursement of loss is to be determined by majority decision. In a simple welfare comparison, the compulsory scheme may in certain environments yield a solution which is inferior to that obtained in the market. We further consider the situation where the compulsory scheme may be supplemented by voluntary competitive insurance; this situation turns out to be at least as good as either of the alternatives