Representative Committees of Peers
This addresses the challenge of efficient representation in voting systems, offering a theoretical guarantee for committee-based decision-making, though it is incremental in the context of social choice theory.
The paper tackles the problem of approximating population preferences on binary issues using a small committee, showing that a random committee (k-sortition) achieves outcomes within a factor of 1+O(1/k) of optimal social cost for any number of voters and issues.
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.