The Boltzmann fair division for distributive justice

Abstract

Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to realworld problems because of their complexity and unrealistic assumptions about human behaviors. Here we propose a fair division method from a completely different perspective, using the Boltzmann distribution. The Boltzmann distribution adopted from the physical sciences gives the most probable and unbiased distribution derived from a goods-centric, rather than a player-centric, division process. The mathematical model of the Boltzmann fair division was developed for both homogeneous and heterogeneous division problems, and the players' key factors (contributions, needs, and preferences) could be successfully integrated. We show that the Boltzmann fair division is a well-balanced division method maximizing the players' total utility, and it could be easily finetuned and applicable to complex real-world problems such as income/wealth redistribution or international negotiations on fighting climate change.