# Diversity and its decomposition into variety, balance and disparity

## TL;DR

This paper introduces a new unified framework for measuring diversity and its components—variety, balance, and disparity—using feature-based similarities, enabling more accurate analysis of diversity in various contexts.

## Contribution

It proposes a novel diversity measure based on feature similarities, along with the ABC decomposition to separately analyze variety, balance, and disparity.

## Key findings

- The new measure captures total disparity more effectively than pairwise similarity methods.
- Application to industrial diversity from 1850 to present demonstrates the framework's utility.
- Extension to high-dimensional data offers a versatile tool for complex diversity analysis.

## Abstract

Diversity is a central concept in many fields. Despite its importance, there is no unified methodological framework to measure diversity and its three components of variety, balance and disparity. Current approaches take into account disparity of the types by considering their pairwise similarities. Pairwise similarities between types do not adequately capture total disparity, since they fail to take into account in which way pairs are similar. Hence, pairwise similarities do not discriminate between similarity of types in terms of the same feature and similarity of types in terms of different features. This paper presents an alternative approach which is based similarities of features between types over the whole set. The proposed measure of diversity properly takes into account the aspects of variety, balance and disparity, and without having to set an arbitrary weight for each aspect of diversity. Based on this measure, the 'ABC decomposition' is introduced, which provides separate measures for the variety, balance and disparity, allowing them to enter analysis separately. The method is illustrated by analyzing the industrial diversity from 1850 to present while taking into account the overlap in occupations they employ. Finally, the framework is extended to take into account disparity considering multiple features, providing a helpful tool in analysis of high-dimensional data.