## 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/1910.05813v2 |

Date submitted: | 2019-10-31 |

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.