Representative Committees of Peers

TL;DR

This paper analyzes how small randomly selected committees can effectively approximate the collective preferences of a population in binary decision-making, showing near-optimal social welfare outcomes.

Contribution

It proves that k-sortition committees achieve near-optimal social cost within a factor of 1+O(1/k) for any number of voters and issues, and explores delegation for small issue sets.

Findings

k-sortition achieves social cost within 1+O(1/k) of optimal

Delegation improves accuracy for small number of issues

k-sortition is worst-case optimal among certain committee rules

Abstract

A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the committee) leads to an outcome within the factor 1+O(1/k) of the optimal social cost for any number of voters n, any number of issues $m$, and any preference profile. For a small number of issues m, the social cost can be made even closer to optimal by delegation procedures that weigh committee members according to their number of followers. However, for large m, we demonstrate that the k-sortition is the worst-case optimal rule within a broad family of committee-based rules that take into account metric information about the preference profile of the whole population.