Monotonic Redistribution: Reconciling Performance-Based Allocation and Weighted Division

We show that a proportional taxation redistribution rule regarding heterogeneity among members of a society is implied by four axioms: efficiency, total wealth monotonicity, contribution monotonicity and additivity. Moreover, we offer another axiomatization with dropping additivity. Our rule is an extension of [Casajus, A. [2015] Monotonic distribution of performance-based allocations: A case for proportional taxation, Theor. Econ. 10, 887–892]’s redistribution rule in which each member of a society is identified only with his/her income.