Monotonic redistribution of performance-based allocations: a case for proportional taxation

Within a simple setup, we show that proportional taxation is implied by three properties: efficiency, symmetry, and monotonicity. Efficiency: redistribution has no cost. Symmetry: members of the society with the same performance obtain the same reward after redistribution. Monotonicity: whenever both the performance of a certain member of the society as well as the overall performance of the society do not decrease, then this member's reward after redistribution does not decrease.