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First-order transition in a model of prestige bias

by Brian Skinner

This Submission thread is now published as SciPost Phys. 8, 030 (2020)

Submission summary

As Contributors: Brian Skinner
Arxiv Link: (pdf)
Date accepted: 2020-01-28
Date submitted: 2019-12-18 01:00
Submitted by: Skinner, Brian
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Statistical and Soft Matter Physics
Approach: Theoretical


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.

Ontology / Topics

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Bayesian statistical inference

Published as SciPost Phys. 8, 030 (2020)

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.

Submission & Refereeing History

Published as SciPost Phys. 8, 030 (2020)

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Resubmission 1910.05813v3 on 18 December 2019

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