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Revenue allocation in Formula One: a pairwise comparison approach

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  • D'ora Gr'eta Petr'oczy
  • L'aszl'o Csat'o

Abstract

A model is proposed to allocate Formula One World Championship prize money among the constructors. The methodology is based on pairwise comparison matrices, allows for the use of any weighting method, and makes possible to tune the level of inequality. We introduce an axiom called scale invariance, which requires the ranking of the teams to be independent of the parameter controlling inequality. The eigenvector method is revealed to violate this condition in our dataset, while the row geometric mean method always satisfies it. The revenue allocation is not influenced by the arbitrary valuation given to the race prizes in the official points scoring system of Formula One and takes the intensity of pairwise preferences into account, contrary to the standard Condorcet method. Our approach can be used to share revenues among groups when group members are ranked several times.

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  • D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2019. "Revenue allocation in Formula One: a pairwise comparison approach," Papers 1909.12931, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:1909.12931
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    1. Scott E. Atkinson & Linda R. Stanley & John Tschirhart, 1988. "Revenue Sharing as an Incentive in an Agency Problem: An example from the National Football League," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 27-43, Spring.
    2. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    3. Fichtner, John, 1986. "On deriving priority vectors from matrices of pairwise comparisons," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 341-345.
    4. Lundy, Michele & Siraj, Sajid & Greco, Salvatore, 2017. "The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis," European Journal of Operational Research, Elsevier, vol. 257(1), pages 197-208.
    5. Camilla Mastromarco & Marco Runkel, 2009. "Rule changes and competitive balance in Formula One motor racing," Applied Economics, Taylor & Francis Journals, vol. 41(23), pages 3003-3014.
    6. Bozóki, Sándor & Fülöp, János, 2018. "Efficient weight vectors from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 264(2), pages 419-427.
    7. Oliver Budzinski & Anika Müller‐Kock, 2018. "Is The Revenue Allocation Scheme Of Formula One Motor Racing A Case For European Competition Policy?," Contemporary Economic Policy, Western Economic Association International, vol. 36(1), pages 215-233, January.
    8. Chao, Xiangrui & Kou, Gang & Li, Tie & Peng, Yi, 2018. "Jie Ke versus AlphaGo: A ranking approach using decision making method for large-scale data with incomplete information," European Journal of Operational Research, Elsevier, vol. 265(1), pages 239-247.
    9. Stefan Szymanski & Stefan Késenne, 2010. "Competitive Balance and Gate Revenue Sharing in Team Sports," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 7, pages 229-243, Palgrave Macmillan.
    10. László Csató, 2013. "Ranking by pairwise comparisons for Swiss-system tournaments," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 783-803, December.
    11. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    12. Stefan Kesenne, 2000. "Revenue Sharing and Competitive Balance in Professional Team Sports," Journal of Sports Economics, , vol. 1(1), pages 56-65, February.
    13. A. Anderson, 2014. "Maximum likelihood ranking in racing sports," Applied Economics, Taylor & Francis Journals, vol. 46(15), pages 1778-1787, May.
    14. George Rabinowitz, 1976. "Some Comments on Measuring World Influence," Conflict Management and Peace Science, Peace Science Society (International), vol. 2(1), pages 49-55, February.
    15. Ossadnik, Wolfgang, 1996. "AHP-based synergy allocation to the partners in a merger," European Journal of Operational Research, Elsevier, vol. 88(1), pages 42-49, January.
    16. Dominik Schreyer & Benno Torgler, 2018. "On the Role of Race Outcome Uncertainty in the TV Demand for Formula 1 Grands Prix," Journal of Sports Economics, , vol. 19(2), pages 211-229, February.
    17. Alejandro Corvalan, 2018. "How to rank rankings? Group performance in multiple-prize contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 361-380, August.
    18. Ramanathan, R. & Ganesh, L. S., 1995. "Using AHP for resource allocation problems," European Journal of Operational Research, Elsevier, vol. 80(2), pages 410-417, January.
    19. Chris Judde & Ross Booth & Robert Brooks, 2013. "Second Place Is First of the Losers," Journal of Sports Economics, , vol. 14(4), pages 411-439, August.
    20. Bozóki, Sándor & Csató, László & Temesi, József, 2016. "An application of incomplete pairwise comparison matrices for ranking top tennis players," European Journal of Operational Research, Elsevier, vol. 248(1), pages 211-218.
    21. R. Blanquero & E. Carrizosa & E. Conde, 2006. "Inferring Efficient Weights from Pairwise Comparison Matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 271-284, October.
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