The Boltzmann fair division for distributive justice

TL;DR

This paper introduces a novel fair division method based on the Boltzmann distribution, offering a unbiased, flexible, and utility-maximizing approach suitable for complex real-world social and economic justice issues.

Contribution

It develops a new mathematical model for fair division using the Boltzmann distribution, applicable to diverse and complex problems involving multiple factors.

Findings

Maximizes players' total utility in division

Successfully integrates contributions, needs, and preferences

Applicable to real-world issues like wealth redistribution

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.