Implementation By Vote-Buying Mechanisms

Vote-buying mechanisms allow agents to express any level of support for their preferred alternative at an increasing cost. Focusing on large societies with wealth inequality, we prove that the family of binary social choice rules implemented by well-behaved vote-buying mechanisms is indexed by a single parameter, which determines the importance assigned to the agents' willingness to pay to affect outcomes and to the number of supporters for each alternative. This parameter depends solely on the elasticity of the cost function near its origin: as this elasticity decreases, the intensities of support matter relatively more for outcomes than the supporters' count.