Boosting Sortition via Proportional Representation

Sortition is based on the idea of choosing randomly selected representatives for decision making. The main properties that make sortition particularly appealing are fairness -- all the citizens can be selected with the same probability -- and proportional representation -- a randomly selected panel probably reflects the composition of the whole population. When a population lies on a representation metric, we formally define proportional representation by using a notion called the core. A panel is in the core if no group of individuals is underrepresented proportional to its size. While uniform selection is fair, it does not always return panels that are in the core. Thus, we ask if we can design a selection algorithm that satisfies fairness and ex post core simultaneously. We answer this question affirmatively and present an efficient selection algorithm that is fair and provides a constant-factor approximation to the optimal ex post core. Moreover, we show that uniformly random selection satisfies a constant-factor approximation to the optimal ex ante core. We complement our theoretical results by conducting experiments with real data.