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First-order transition in a model of prestige bias
by Brian Skinner
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Brian Skinner |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1910.05813v3 (pdf) |
| Date accepted: | 2020-01-28 |
| Date submitted: | 2019-12-18 01:00 |
| Submitted by: | Skinner, Brian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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.
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.
Published as SciPost Phys. 8, 030 (2020)