We study the trade-off between two risks for scoring rules used in sports competitions containing multiple contests: (1) the threat of early clinch when the title is clinched before the last contest(s) of the competition take place; and (2) the danger of winning the competition without finishing first in any contest. Four historical points scoring systems of the Formula One World Championship are compared with the family of geometric scoring rules. The current scheme seems to be a reasonable compromise close to the Pareto frontier. Our results contribute to the issue of choosing an optimal set of point values.
AppletonD. R. (1995). May the best man win?Journal of the Royal Statistical Society: Series D (The Statistician), 44(4), 529–538.
2.
ArrowK. J. (1950). A difficulty in the concept of social welfare. Journal of Political Economy, 58(4), 328–346.
3.
BekkerJ.LotzW. (2009). Planning Formula One race strategies using discrete-event simulation. Journal of the Operational Research Society, 60(7), 952–961.
4.
BramsS. J.FishburnP. C. (2002). Voting procedures. In K. J. Arrow, A. K. Sen, & K. Suzumura (Eds.), Handbook of Social Choice and Welfare, (Volume 1, Chapter 4, pp. 173–236). Amsterdam, The Netherlands: Elsevier.
5.
ChebotarevP. Y.ShamisE. (1998). Characterizations of scoring methods for preference aggregation. Annals of Operations Research, 80, 299–332.
6.
ChurilovL.FlitmanA. (2006). Towards fair ranking of Olympics achievements: The case of Sydney 2000. Computers & Operations Research, 33(7), 2057–2082.
7.
CoronaF.TenaJ. d. D.WiperM. P. (2017). On the importance of the probabilistic model in identifying the most decisive games in a tournament. Journal of Quantitative Analysis in Sports, 13(1), 11–23.
8.
CsatóL. (2021a). A simulation comparison of tournament designs for the World Men’s Handball Championships. International Transactions in Operational Research, 28(5), 2377–2401.
9.
CsatóL. (2021b). Tournament Design: How Operations Research Can Improve Sports Rules. Palgrave Pivots in Sports Economics. Cham, Switzerland: Palgrave Macmillan.
Garcia-del BarrioP.ReadeJ. J. (2021). Does certainty on the winner diminish the interest in sport competitions? The case of formula one. Empirical Economics, in press. https://doi.org/10.1007/s00181-021-02147-8.
12.
GeenensG. (2014). On the decisiveness of a game in a tournament. European Journal of Operational Research, 232(1), 156–168.
13.
GravesT.ReeseC. S.FitzgeraldM. (2003). Hierarchical models for permutations: Analysis of auto racing results. Journal of the American Statistical Association, 98(462), 282–291.
14.
HaighJ. (2009). Uses and limitations of mathematics in sport. IMA Journal of Management Mathematics, 20(2), 97–108.
15.
HeilmeierA.GrafM.LienkampM. (2018). A race simulation for strategy decisions in circuit motorsports. In 21st International Conference on Intelligent Transportation Systems (ITSC), pp. 2986–2993.
16.
HendersonD. A.KirraneL. J. (2018). A comparison of truncated and time-weighted Plackett–Luce mdels for probabilistic forecasting of Formula One results. Bayesian Analysis, 13(2), 335–358.
KaiserB. (2019). Strategy and paradoxes of Borda count in Formula 1 racing. Decyzje, 6(31), 115–132.
19.
KondratevA. Y.IanovskiE.NesterovA. S. (2022). How should we score athletes and candidates: geometric scoring rules. Manuscript. DOI: https://doi.org/10.48550/arXiv.1907.05082
20.
LlamazaresB.PeñaT, (2013). Aggregating preferences rankings with variable weights. European Journal of Operational Research, 230(2), 348–355.
21.
LlamazaresB.PeñaT. (2015). Scoring rules and social choice properties: Some characterizations. Theory and Decision, 78(3), 429–450.
22.
MerlinV. (2003). The axiomatic characterizations of majority voting and scoring rules. Mathématiques et Sciences Humaines, 41(161), 87–109.
23.
NitzanS.RubinsteinA. (1981). A further characterization of Borda ranking method. Public Choice, 36(1), 153–158.
24.
SitarzS. (2013). The medal points’ incenter for rankings in sport. Applied Mathematics Letters, 26(4), 408–412.
25.
SmithJ. H. (1973). Aggregation of preferences with variable electorate. Econometrica, 26(1), 1027–1041.
26.
SteinW. E.MizziP. J.PfaffenbergerR. C. (1994). A stochastic dominance analysis of ranked voting systems with scoring. European Journal of Operational Research, 74(1), 78–85.
27.
SyswerdaG. (1989). Uniform crossover in genetic algorithms. In J. D. Schaffer (Ed.), Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 2–9.
YoungH. P. (1975). Social choice scoring functions. SIAM Journal on Applied Mathematics, 28(4), 824–838.
30.
ZhaoY.WuF.ChenY. (2021). Sensitivity analyses and measurements for group decisions using weighted scoring rules. International Transactions in Operational Research, 28(2), 959–975.
