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How well do governments represent the societies they serve? A key aspect of this question concerns the extent to which leaders reflect the demographic features of the population they represent. To address this important issue in a systematic manner, we propose a unified approach for measuring descriptive representation. We apply this approach to newly collected data describing the ethnic, linguistic, religious, and gender identities of over fifty thousand leaders serving in 1,552 political bodies across 156 countries. Strikingly, no country represents social groups in rough proportion to their share of the population. To explain this shortfall, we focus on compositional factors—the size of political bodies as well as the number and relative size of social groups. We investigate these factors using a simple model based on random sampling and the original data described above. Our analyses demonstrate that roughly half of the variability in descriptive representation is attributable to compositional factors.

AbstractSome scholars build models to classify documents into chosen categories. Others, especially social scientists who tend to focus on population characteristics, instead usually estimate the proportion of documents in each category—using either parametric "classify-and-count" methods or "direct" nonparametric estimation of proportions without individual classification. Unfortunately, classify-and-count methods can be highly model-dependent or generate more bias in the proportions even as the percent of documents correctly classified increases. Direct estimation avoids these problems, but can suffer when the meaning of language changes between training and test sets or is too similar across categories. We develop an improved direct estimation approach without these issues by including and optimizing continuous text features, along with a form of matching adapted from the causal inference literature. Our approach substantially improves performance in a diverse collection of 73 datasets. We also offer easy-to-use software that implements all ideas discussed herein.