Diversity and its decomposition into variety, balance and disparity.

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 may not adequately capture total disparity, since they do not take into account in which way pairs are similar. Hence, pairwise similarities do not discriminate between similarities of types in terms of the same feature and similarities in which all pairs share different features. This paper presents an alternative approach which is based on the overlap of features over the whole set of types. This results in a measure of diversity that takes into account the aspects of variety, balance and disparity. Based on this measure, the ' decomposition' is introduced, which provides separate measures for the variety, balance and disparity, allowing them to enter analysis separately. The method is illustrated by analysing 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.