First-order transition in a model of prestige bias
arXiv:1910.05813 · doi:10.21468/SciPostPhys.8.2.030
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.
7+1 pages, 7 figures. Inspired by my experience as a postdoc at MIT; references and discussion added; notation corrected; Submission to SciPost