Introduction to welfare economics

We show that a transfer received by a minority of the population may be sustained by majority voting, however small the minority targeted may be, when the attribution of the transfer is seen as stochastic by voters. We build a simple model wherein voters differ in income and vote over a proportional tax whose proceeds are distributed lump-sum, and each voter has a probability of receiving the transfer that depends on his income. In progressive steps, we present intuitively appealing sufficient conditions on this probability function for the social program to be supported by majority voting. We also develop intuitive conditions for the emergence of the “paradox of redistribution”, whereby more focused targeting reduces the size of the transfer program chosen by the majority. We finally apply our framework to the French social housing program and obtain that our model is consistent with a majority of French voters supporting a positive size for that program.