Is Sortition Both Representative and Fair?

Sortition is a form of democracy built on random selection of representatives. Two of the key arguments in favor of sortition are that it provides representation (a random panel reflects the composition of the population) and fairness (everyone has a chance to participate). Uniformly random selection is perfectly fair, but is it representative? Towards answering this question, we introduce the notion of a representation metric on the space of individuals, and assume that the cost of an individual for a panel is determined by the $q$-th closest representative; the representation of a (random) panel is measured by the ratio between the (expected) sum of costs of the optimal panel for the individuals and that of the given panel. For $k/2 < q \le k-\Omega(k)$, where $k$ is the panel size, we show that uniform random selection is indeed representative by establishing a constant lower bound on this ratio. By contrast, for $q \leq k/2$, no random selection algorithm that is almost fair can give such a guarantee. We therefore consider relaxed fairness guarantees and develop a new random selection algorithm that sheds light on the tradeoff between representation and fairness.