When More Selection Is Worse

We demonstrate a paradox of selection: the average level of skill among the survivors of selection may initially increase but eventually decrease. This result occurs in a simple model in which performance is not frequency dependent, there are no delayed effects, and skill is unrelated to risk-taking. The performance of an agent in any given period equals a skill component plus a noise term. We show that the average skill of survivors eventually decreases when the noise terms in consecutive periods are dependent and drawn from a distribution with a “long” tail—a sub-class of heavy-tailed distributions. This result occurs because only agents with extremely high level of performance survive many periods, and extreme performance is not diagnostic of high skill when the noise term is drawn from a long-tailed distribution.