The James function, also known as the log5 method, assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J. Miller, exp
lores the analogous situation where a single team or player competes simultaneously against multiple opponents.
Confidence is an essential ingredient of success in a wide range of domains ranging from job performance and mental health, to sports, business, and combat. Some authors have suggested that not just confidence but overconfidence-believing you are bet
ter than you are in reality-is advantageous because it serves to increase ambition, morale, resolve, persistence, or the credibility of bluffing, generating a self-fulfilling prophecy in which exaggerated confidence actually increases the probability of success. However, overconfidence also leads to faulty assessments, unrealistic expectations, and hazardous decisions, so it remains a puzzle how such a false belief could evolve or remain stable in a population of competing strategies that include accurate, unbiased beliefs. Here, we present an evolutionary model showing that, counter-intuitively, overconfidence maximizes individual fitness and populations will tend to become overconfident, as long as benefits from contested resources are sufficiently large compared to the cost of competition. In contrast, rational unbiased strategies are only stable under limited conditions. The fact that overconfident populations are evolutionarily stable in a wide range of environments may help to explain why overconfidence remains prevalent today, even if it contributes to hubris, market bubbles, financial collapses, policy failures, disasters, and costly wars.
Hodge classes on the moduli space of admissible covers with monodromy group G are associated to irreducible representations of G. We evaluate all linear Hodge integrals over moduli spaces of admissible covers with abelian monodromy in terms of multip
lication in an associated wreath group algebra. In case G is cyclic and the representation is faithful, the evaluation is in terms of double Hurwitz numbers. In case G is trivial, the formula specializes to the well-known result of Ekedahl-Lando-Shapiro-Vainshtein for linear Hodge integrals over the moduli space of curves in terms of single Hurwitz numbers.
