Can a Few Decide for Many? The Metric Distortion of Sortition

Abstract: Recent works have studied the design of algorithms for selecting representative sortition panels. However, the most central question remains unaddressed: Do these panels reflect the entire population's opinion? We present a positive answer by adopting the concept of metric distortion from computational social choice, which aims to quantify how much a panel's decision aligns with the ideal decision of the population when preferences and agents lie on a metric space. We show that uniform selection needs only logarithmically many agents in terms of the number of alternatives to achieve almost optimal distortion. We also show that Fair Greedy Capture, a selection algorithm introduced recently by Ebadian & Micha (2024), matches uniform selection's guarantees of almost optimal distortion and also achieves constant ex-post distortion, ensuring a "best of both worlds" performance.