  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.
