Duality, dissimilarity, and diversity: The use of ecological approaches to cross-nested affiliation data

Abstract

While many recent examinations of the idea of duality build upon it to quantify the similarity of entities in a data matrix, there is a potential avenue for quantifying the diversity of some ensemble, but this has not yet been given attention. We here draw on a robust line of work in mathematical ecology that has developed a family of entropy-related diversity measures, and we explore generalizing them to cases of dual nesting. Combining duality-based thinking with ecological diversity measures helps resolves some inherent ambiguities in the way that social scientists often think about diversity: the same relations that appear to increase diversity in some respects may, from a different perspective, decrease diversity. Such ambiguities can interfere with examining some of the most interesting theories of the effects of development on social life. We illustrate with network data from a sample of residents of 75 Indian villages, also cross-nested in 38 castes (jati).