Voting over selfishly optimal nonlinear income tax schedules

Majority voting over selfishly optimal nonlinear income tax schedules proposed by a continuum of individuals who have quasilinear-in-consumption preferences is considered. Röell (2012) has shown that individual preferences over these schedules are single-peaked. In this article, a complete characterization of selfishly optimal schedules is provided. Each selfishly optimal schedule has a bunching region in a neighborhood of the proposer's skill type, coincides with the maxi-max schedule below this region, and coincides with the maxi-min schedule above it. Using techniques introduced by Vincent and Mason (1967), the bunching region is identified by solving an unconstrained optimization problem. Information about the optimal schedules is used to provide a relatively simple proof of single-peakedness. The Condorcet-winning tax schedule features marginal tax rates that are negative (resp. positive) on the maxi-max (resp. maxi-min) part of the schedule except at the endpoints of the skill distribution where they are zero.