An axiomatic approach to diversity

TL;DR

This paper proposes an axiomatic framework to define and measure diversity mathematically, addressing the lack of a precise formalization for this concept.

Contribution

It introduces an axiomatic approach to formalize and measure diversity, providing a foundation for consistent and rigorous analysis.

Findings

Proposed axioms for diversity measurement

Established a formal measure consistent with the axioms

Facilitated mathematical analysis of diversity concepts

Abstract

The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise mathematical definition exists. In this paper, we adopt an axiomatic approach to the problem, and attempt to produce a satisfactory measure.