First-order transition in a model of prestige bias

TL;DR

This paper models how prestige bias in repeated evaluations can cause a runaway effect, leading to a sharp first-order transition in the influence of prior prestige as evaluation precision varies.

Contribution

It introduces a Bayesian framework to analyze prestige bias, revealing a first-order transition in its strength during iterative evaluations.

Findings

Prestige bias can cause a runaway effect in evaluations.

A first-order transition occurs in bias strength as evaluation precision changes.

The model highlights the impact of prior prestige on future assessments.

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.