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

TL;DR

This paper investigates how well randomly selected panels represent the entire population's preferences using metric distortion, showing that simple uniform selection can achieve near-optimal representation with few agents and that a new algorithm improves this further.

Contribution

The paper introduces the application of metric distortion to assess the representativeness of sortition panels and demonstrates that uniform selection and a new algorithm achieve near-optimal and constant ex-post distortion.

Findings

Uniform selection requires logarithmically many agents for near-optimal distortion.

Fair Greedy Capture algorithm matches uniform selection's guarantees.

The algorithms ensure the panel's decisions closely reflect the population's preferences.

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.