2015/08/17 by Tobias Colding, Tobias Holck Colding, Colding, Tobias Holck +3
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #Computer science #Distributed Control Multi-Agent Systems #FOS: Mathematics #Game Theory and Voting Systems #Information retrieval #Opinion Dynamics and Social Influence #Political science #Probability (math.PR) #Ranking (information retrieval) #math.AP #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.1508.04013
arxiv created 2015/08/17 · openalex publication_date 2015/08/17 · arxiv updated 2015/08/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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.