Health insurance in a democracy: Why is it public and why are premiums income related?

Many democracies have public health insurance systems which combine redistribution from the rich to the poor and from the healthy to the sick. This paper shows that such systems can be in the interest of the poor and the rich from a constitutional perspective. Necessary conditions are that insurance markets are incomplete and that income inequality is neither too low nor too high. Then even the rich can prefer a public health insurance system financed by income-dependent contributions compared to a system financed by a flat fee or a private health insurance system.