A balance for fairness: fair distribution utilising physics

Abstract

The problem of ‘uneven distribution of wealth’ accelerated during the COVID-19 pandemic. In the chaotic modern society, there is an increasing demand for the realisation of true ‘fairness’. In this study, we propose a fair distribution method ‘using physics’, which imitates the Greek mythology, Themis, having a ‘balance of judgement’ in her left hand, for the profit in games of characteristic function form. Specifically, we show that the linear programming problem for calculating ‘nucleolus (a solution for the fair distribution)’ can be efficiently solved by considering it as a physical system in which gravity works. In addition to significantly reducing the computational complexity, the proposed scheme provides a new perspective to open up a physics-based policymaker that is adaptable to real-time changes. We will be able to implement it not only in liquid systems but also in many other physical systems, including semiconductor chips. The fair distribution problem can be solved immediately using physical systems, which should reduce disputes and conflicts based on inaccurate information and misunderstandings, eliminating fraud and injustice.