Committee ranking

TL;DR

This paper models committee ranking interactions using a discrete quasilinear heat equation, showing exponential consensus emergence and clustering effects, with implications for opinion dynamics and influence decay.

Contribution

It introduces a novel deterministic model linking committee ranking dynamics to a quasilinear heat equation on graphs, analyzing convergence and clustering behavior.

Findings

Consensus emerges exponentially fast over time.

Clusters of similar opinions converge faster than the entire committee.

Variance of rankings decreases by a fixed amount, independent of initial variance.

Abstract

This paper deals with interactions between committee members as they rank a large list of applicants for a given position and eventually reach consensus. We will see that for a natural deterministic model the ranking can be described by solutions of a discrete quasilinear heat equation with time dependent coefficients on a graph. We show first that over time consensus emerges exponentially fast. Second, if there are clusters of members whose views are closer than those of the rest of the committee, then over time the clusters' views become closer at a faster exponential rate than the views of the entire committee. We will also show that the variance of the rankings decays a definite amount, independent of the initial variance, when the influence of the members does not decay too quickly as opinions differ. When the influence between members is exactly a negative power, then the variance is convex and satisfies a three circles theorem.