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Some Impossibilities of Ranking in Generalized Tournaments

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  • László Csató

    (Research Group of Operations Research and Decision Systems, Laboratory on Engineering and Management Intelligence, Institute for Computer Science and Control, Hungarian, Academy of Sciences, 1111 Budapest, Kende Street 13-17., Hungary2Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, 1093 Budapest, Fővám Square 13-15., Hungary)

Abstract

In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with lower and upper bounds. An axiomatic approach is applied to the problem of ranking the competitors. Self-consistency (SC) requires assigning the same rank for players with equivalent results, while a player showing an obviously better performance than another should be ranked strictly higher. According to order preservation (OP), if two players have the same pairwise ranking in two tournaments where the same players have played the same number of matches, then their pairwise ranking is not allowed to change in the aggregated tournament. We reveal that these two properties cannot be satisfied simultaneously on this universal domain.

Suggested Citation

  • László Csató, 2019. "Some Impossibilities of Ranking in Generalized Tournaments," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-15, March.
    • Handle: RePEc:wsi:igtrxx:v:21:y:2019:i:01:n:s0219198919400024
    DOI: 10.1142/S0219198919400024
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    Cited by:

    1. Csató, László, 2019. "Journal ranking should depend on the level of aggregation," Journal of Informetrics, Elsevier, vol. 13(4).
    2. Arlegi, Ritxar & Dimitrov, Dinko, 2020. "Fair elimination-type competitions," European Journal of Operational Research, Elsevier, vol. 287(2), pages 528-535.

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