A comparative study of scoring systems by simulations

Scoring rules aggregate individual rankings by assigning some points to each position in ranking such that the total sum of provides overall alternatives. They are widely used sports competitions consisting multiple contests. We study tradeoff between two risks this setting: (1) threat early clinch when title has been clinched before last contest(s) competition take place; (2) danger winning without finishing first any contest. In particular, four historical scoring systems Formula One World Championship compared with family geometric rules, recently proposed an axiomatic approach. The schemes practice found be competitive respect these goals, and current rule seems a reasonable compromise close Pareto frontier. Our results shed more light on evolution contribute issue choosing set point values.