Representative committees of peers

A population of voters elects 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 her preferences disagree with the decision. While an issue-by-issue majority vote by all voters would maximize the 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.