Risk Taking and Gender in Hierarchies

If promotion in a hierarchy is based on a random signal of ability, rates of promotion are affected by risk-taking. Further, the statistical properties of the surviving populations of risk-takers and non-risk-takers will be different, and will be changing throughout the hierarchy. I define promotion hierarchies with and without memory, where memory means that promotion depends on the entire history of success. In both types of hierarchies, surviving risk-takers have lower average ability than surviving non risk-takers at any stage where they have a higher probability of survival. However, that will not apply in the limit. With a common set of promotion standards, risk-takers will survive with lower probability than non risk-takers, and will have higher average 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.