Measuring Descriptive Representation

In the last two weeks I had several conversations on how to best measure descriptive representation (i.e. the numerical representation of groups). I treated this in my recent monograph, but also in a conference paper in 2011. In my view, there are three important points: (1) What’s best depends on your research question. (2) It is important to include the population and the representatives. (3) I recommend two measures as follows: R_i / P_i for measuring the representation of a single group (e.g. a specific minority group, or all minorities combined as opposed to the majority population); for the situation at the national level, I prefer the Rose index (1 – 0.5 * |R_i – P_i|) over the Gallagher index (but following recent simulations I have undertaken, less strongly than previously). R_i stands for the proportion of a group among the representatives, P_i for the proportion among the population.