# First-order transition in a model of prestige bias

### Submission summary

 As Contributors: Brian Skinner Arxiv Link: https://arxiv.org/abs/1910.05813v3 Date accepted: 2020-01-28 Date submitted: 2019-12-18 Submitted by: Skinner, Brian Submitted to: SciPost Physics Discipline: Physics Subject area: 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.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

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

Resubmission 1910.05813v3 on 18 December 2019
Submission 1910.05813v2 on 31 October 2019