  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.
