Implementation by vote-buying mechanisms∗

A vote-buying mechanism is such that each agent chooses a quantity of votes x to cast for an alternative at a cost c(x), and the outcome is determined by the total number of votes cast for each alternative. In the context of binary decisions, we prove that the welfare optima that can be implemented by vote-buying mechanisms in large societies are parameterized by a positive parameter ρ, which measures the importance of preference intensities on the social choice: The limit with ρ = 0 is in line with the majoritarian principle, ρ = 1 corresponds to utilitarianism, and ρ −→∞ agrees with the Rawlsian optimum. We show that any vote-buying mechanism with limit cost elasticity limx→0 c′(x)x c(x) = 1 + 1/ρ implements the welfare optimum defined by ρ. The utilitarian effi ciency of quadratic voting (Lalley and Weyl, 2016) follows as a special case.