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Committee ranking

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.