Politically Sustainable Probabilistic Minority Targeting

We show that a transfer targeting a minority of the population is sustained by majority voting, however small the minority targeted, when the probability to receive the transfer is decreasing and concave in income. We apply our framework to the French social housing program and obtain that empirically observed departures from these assumptions are small enough that a majority of French voters should support a positive size of this program. We also provide a sufficient condition on this probability function under which more targeting results in a lower equilibrium size of the transfer system.