The Optimal Size of an Epistemic Congress

TL;DR

This paper investigates the optimal size of a representative congress from an epistemic perspective, showing it should scale linearly with population size, and compares theoretical predictions with real-world data.

Contribution

It derives a theoretical model for optimal congress size based on voter competence and compares it with actual congress sizes, highlighting discrepancies.

Findings

Optimal congress size is linear in population size.

Real-world congresses are smaller than the theoretical optimal.

Sub-optimal congresses can outperform direct democracy under certain conditions.

Abstract

We analyze the optimal size of a congress in a representative democracy. We take an epistemic view where voters decide on a binary issue with one ground truth outcome, and each voter votes correctly according to their competence levels in $[0, 1]$. Assuming that we can sample the best experts to form an epistemic congress, we find that the optimal congress size should be linear in the population size. This result is striking because it holds even when allowing the top representatives to be accurate with arbitrarily high probabilities. We then analyze real world data, finding that the actual sizes of congresses are much smaller than the optimal size our theoretical results suggest. We conclude by analyzing under what conditions congresses of sub-optimal sizes would still outperform direct democracy, in which all voters vote.