How Should We Score Athletes and Candidates: Geometric Scoring Rules

Abstract

Scoring in Multi-Event Tournaments How much is a first place worth? Is the athlete who came first once and third twice better than the athlete who came second three times? Different sports value these positions differently: (60, 54, 48) in IBU biathlon, (25, 18, 15) in F1 racing, (8, 7, 6) in Diamond League athletics. Are these choices based on anything? Is there even a rational way to choose a scoring vector of arbitrary length to rank any number of athletes? In “How should we score athletes and candidates: Geometric scoring rules,” authors A.Y. Kondratev, E. Ianovski, and A.S. Nesterov investigate two approaches to how the problem of choosing a scoring vector for a tournament can be reduced to the choice of a single parameter: an axiomatic approach based on eliminating spoilers and an optimization approach based on maximizing the expected quality of the winner. Intriguingly, the vectors generated by the second approach are uncannily similar to those used in real sporting events.