Who Reviews The Reviewers? A Multi-Level Jury Problem

TL;DR

This paper investigates a multi-level jury problem where chairs assign weights to reviewers with uncertain competence, analyzing conditions for optimal weighting and comparing the effectiveness of more chairs versus more reviewers through simulations.

Contribution

It introduces a multi-level jury model with uncertain reviewer competence and provides conditions for optimal weighting, analyzing the trade-offs between more chairs and more reviewers.

Findings

More chairs can be beneficial in some cases.

Increasing the number of reviewers often improves accuracy.

Optimal weighting depends on competence distribution.

Abstract

We consider the problem of determining a binary ground truth using advice from a group of independent reviewers (experts) who express their guess about a ground truth correctly with some independent probability (competence). In this setting, when all reviewers are competent (competence greater than one-half), the Condorcet Jury Theorem tells us that adding more reviewers increases the overall accuracy, and if all competences are known, then there exists an optimal weighting of the reviewers. However, in practical settings, reviewers may be noisy or incompetent, i.e., competence below half, and the number of experts may be small, so the asymptotic Condorcet Jury Theorem is not practically relevant. In such cases we explore appointing one or more chairs (judges) who determine the weight of each reviewer for aggregation, creating multiple levels. However, these chairs may be unable to correctly identify the competence of the reviewers they oversee, and therefore unable to compute the optimal weighting. We give conditions when a set of chairs is able to weight the reviewers optimally, and depending on the competence distribution of the agents, give results about when it is better to have more chairs or more reviewers. Through numerical simulations we show that in some cases it is better to have more chairs, but in many cases it is better to have more reviewers.