Affirmative Action in Hierarchies
If promotion in a hierarchy is based on a random signal of ability, rates of promotion will be affected by risk-taking. Further, the numbers and abilities of risk-takers and non-risk-takers will be different at each stage of the hierarchy, and the ratio will be changing. I show that, under mild conditions, more risk-takers than non-risk-takers will survive at early stages, but they will have lower ability. At later stages, this will be reversed: Fewer risk-takers than non-risk-takers survive, but they will have higher ability. I give several interpretations for how these theorems relate to affirmative action, in light of considerable evidence that males are more risk-taking than females.