Procedural fairness and redistributive proportional tax

We study the implications of procedural fairness on the share of income that should be redistributed. We formulate procedural fairness as a particular non-cooperative bargaining game and examine the stationary subgame perfect equilibria of the game. The equilibrium outcome is called tax equilibrium and is shown to be unique. The procedurally fair tax rate is defined as the tax rate that results in the limit of tax equilibria when the probability that negotiations break down converges to zero. The procedurally fair tax rate is shown to be unique. We also provide a characterization of the procedurally fair tax rate that involves the probability mass of below average income citizens and a particular measure of the citizens' boldness. This characterization is then used to show that in a number of interesting cases, the procedurally fair tax rate equals the probability mass of below average income citizens.