Majority rule and selfishly optimal nonlinear income tax schedules with discrete skill levels

Röell (Voting over nonlinear income tax schedules, unpublished manuscript, School of International and Public Affairs, Columbia University, New York, 2012) shows that Black’s median voter theorem for majority voting with single-peaked preferences applies to voting over nonlinear income tax schedules that satisfy the constraints of a finite type version of the Mirrlees optimal income tax problem when voting takes place over the tax schedules that are selfishly optimal for some individual and preferences are quasilinear. An alternative way of establishing Röell’s median voter result is provided that offers a different perspective on her findings, drawing on insights obtained by Brett and Weymark (Games Econ Behav 101:172–188, 2017) in their analysis of a version of this problem with a continuum of types. In order to characterize a selfishly optimal schedule, it is determined how to optimally bunch different types of individuals.