Social Choice for General Utilities

Without monetary payments, the Gibbard-Satterthwaite theorem proves that under mild requirements all truthful social choice mechanisms must be dictatorships. When payments are allowed, the Vickrey-Clarke-Groves mechanism truthfully implements the value-maximizing choices, assuming agents’ utilities are quasi-linear in money. We study social choice with payments where utilities are non-quasi-linear. The main result of this paper is a tight characterization of the maximal non-quasi-linear utility domain, which we call the largest parallel domain, for which where there exist nondictatorial mechanisms that are strategy-proof, onto, deterministic, individually rational and that do not not make positive transfers to the agents. In particular, mechanisms satisfying the above conditions must be dictatorial when the type domain is quasi-linear together with any single non-parallel type. We then show that for richer utility domains which still differ very slightly from quasi-linearity, every strategy-proof, onto and deterministic mechanism must be a dictatorship.