Games of Redistributive Politics Are Equivalent to All-Pay Auctions With Consolation Prizes

Myerson (1993) introduces a model of redistributive politics where candidates offer different transfers to different voters, in the attempt to win an election. He compares, under different electoral systems, the incentive for candidates to create inequalities among otherwise homogeneous voters.

Different electoral systems can fruitfully be reinterpreted as different all-pay auctions with consolation prizes. These are auctions where each bidder enters one bid and receives (at most) one prize, with the j-th highest bidder receiving the j-th most valuable prize. We show that, given any Rank-Scoring rule, the equilibrium in an election under that rule is equivalent to the equilibrium in an all-pay auction with appropriately chosen prizes.