Statistical Bounds on Equity

TL;DR

This paper derives probabilistic bounds on resource distribution in a society, showing that equity is naturally limited and depends on the structure of individual preferences and resource ownership.

Contribution

It introduces a probabilistic framework to determine the most probable resource distribution, highlighting how societal structure influences equity levels.

Findings

Probabilistic analysis restricts extreme equity distributions.

Equity increases with the growth rate of the indifference manifold.

Derived explicit formulas for a fixed population and resource model.

Abstract

We derive the most probable distribution of resources for a simple society. We find that a probabilistic analysis forbids both too much and too less equity, and selects instead a minimally ordered state. We give the detailed calculations for a special model where the population and resources are fixed, and resources are owned only by individuals. We show that in general the equity is greater whenever the volume of the indifference manifold grows faster as a function of individual rent.