This paper studies how society votes on the payroll taxes of a basic income and a social health insurance scheme. Individuals differ along the two most important dimensions when it comes to the design of the two welfare schemes, namely, income and risk. Even though the introduction of a basic income scheme opens up the possibility for additional redistribution, it also crowds out social health insurance. We show that when both welfare schemes are open for debate, the political equilibrium is such that only the basic income scheme prevails. At the constitutional stage we determine which welfare scheme society agrees to implement behind the veil of ignorance and with a Rawlsian objective. Since social health insurance not only redistributes income from rich to poor but also from low-risk to high-risk agents, the doubly disadvantaged in society – low-income and high-risk agents – may lose out in the political process when a basic income scheme is in place. Depending on the amount of health care expenditure and the inequalities in income and risk, it may well be that a society will find it optimal to set up an institutional framework for a social health insurance scheme only
