Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting of multiple contests. We study the tradeoff between two risks in this setting: (1) the threat of early clinch when the title has been clinched before the last contest(s) of the competition take place; (2) the danger of winning the competition without finishing first in any contest. In particular, four historical points scoring systems of the Formula One World Championship are compared with the family of geometric scoring rules that have favourable axiomatic properties. The formers are found to be competitive or even better. The current scheme seems to be a reasonable compromise in optimising the above goals. Our results shed more light on the evolution of the Formula One points scoring systems and contribute to the issue of choosing the set of point values.
翻译:分法规则通过在每一排名中给每个职位分配一些分数,从而分数总和提供各种选择的总体等级,这些分数被广泛用于由多重比赛组成的体育竞赛。我们研究了在这种背景下两种风险之间的权衡:(1) 在竞争的最后一次比赛之前,头衔被剪切时过早摇摆的威胁;(2) 在任何比赛中不先结束竞争而赢得竞争的危险。特别是, " 公式一世界冠军 " 的四个历史分数评分制度与具有有利不言而喻特性的几何分评分规则体系进行了比较,前者被认为具有竞争力,甚至更好。现行办法似乎是优化上述目标的合理折中办法。我们的结果更清楚地说明了 " 公式一分评分制度 " 的演变,有助于选择一套点值的问题。