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First-order transition in a model of prestige bias

by Brian Skinner

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Submission summary

Authors (as registered SciPost users): Brian Skinner
Submission information
Preprint Link: https://arxiv.org/abs/1910.05813v3  (pdf)
Date accepted: 2020-01-28
Date submitted: 2019-12-18 01:00
Submitted by: Skinner, Brian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Statistical and Soft Matter Physics
Approach: Theoretical

Abstract

One of the major benefits of belonging to a prestigious group is that it affects the way you are viewed by others. Here I use a simple mathematical model to explore the implications of this "prestige bias" when candidates undergo repeated rounds of evaluation. In the model, candidates who are evaluated most highly are admitted to a "prestige class", and their membership biases future rounds of evaluation in their favor. I use the language of Bayesian inference to describe this bias, and show that it can lead to a runaway effect in which the weight given to the prior expectation associated with a candidate's class becomes stronger with each round. Most dramatically, the strength of the prestige bias after many rounds undergoes a first-order transition as a function of the precision of the examination on which the evaluation is based.

Author comments upon resubmission

In the previous round of review, the referee expressed concern about referring to the variable $p$ as the "precision". "Precision" has a specific meaning in statistics, and refers to the inverse square of the variance, while in this model larger p means that the exam is _less_ precise. So referring to p as "precision" is likely to confuse readers.

I have corrected this bad terminology by replacing $p$ with $w$ and referring to this parameter as the "standard error of the exam." This term should be unambiguous. (The term "power", suggested by the referee, also has a specific meaning in statistics that is not exactly the same as the standard error of the exam, so I have avoided using it.)

Regarding the result $p_c = 1/\sqrt{3}$, unfortunately I don't have a more "intuitive" derivation than the one given in Section III of the text.

List of changes

- I replaced $w$ with $p$ and the term "precision" with "standard error".
- I corrected a couple small typos.

Published as SciPost Phys. 8, 030 (2020)

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