Dividing Profits Three Ways: Impartiality vs. Consensuality

A rule for three-way division of profits based on peer evaluation reports is impartial if the calculation of each partner’s share ignores her report, and is consensual if it respects evaluations when the three partners’ reports are in agreement. We give an approximate solution to the problem of finding a three-way impartial division rule of minimal average deviation from consensuality. We also use a calculus of variations technique to give an exact solution to a simple version of the problem.