## SciPost Submission Page

# First-order transition in a model of prestige bias

### by Brian Skinner

### 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:

Editorial decision:
For Journal SciPost Physics: Publish

(status: Editorial decision fixed and (if required) accepted by authors)

### Author comments upon resubmission

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.