Descriptive Representation in Politics : A Measurement Proposal and Application for Brazil

This paper introduces a new measure of descriptive representation in politics. It improves upon simple measures such as the share or the number of elected minorities by also taking into account the minority size among the represented. Moreover, contrary to disproportionality measures that are sometimes employed in the context of descriptive representation, our measure attains the upper bound in more usual situations. Based on the statistical properties of our index, we derive hypothesis tests that can be used to assess the likelihood of a representative body's observed composition being the result of an unbiased process.To illustrate its use, we apply the proposed index to evaluate the racial imbalances in the 2014 and 2018 Brazilian National and State legislative elections. This exercise shows that the inclusion of Non-whites in institutional politics has been partial and restricted only to candidacies. The imbalance among elected representatives is considerably larger than among candidates and we can reject the hypothesis that it was generated by chance in the majority of Brazilian states. We also investigate differences between left-wing and right-wing parties, observing lower imbalances among candidates in the left, but no difference when we restrict the analysis to elected representatives