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April, 1966 Probabilistic Completion of a Knockout Tournament
J. A. Hartigan
Ann. Math. Statist. 37(2): 495-503 (April, 1966). DOI: 10.1214/aoms/1177699533


A knockout tournament is a procedure for selecting the best among $2^n$ players by, in the first round, splitting the $2^n$ players into $2^{n - 1}$ pairs who play each other; the $2^{n - 1}$ winners proceed to the next round and repeat the process; finally the one player left is declared the best. A method is given for estimating a complete ranking of the $2^n$ players given the results of the $(2^n - 1)$ matches in the tournament; the method is based on the assumption that all $(2^n)$! orderings of the players are equally probable before the tournament begins.


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J. A. Hartigan. "Probabilistic Completion of a Knockout Tournament." Ann. Math. Statist. 37 (2) 495 - 503, April, 1966.


Published: April, 1966
First available in Project Euclid: 27 April 2007

zbMATH: 0144.40803
MathSciNet: MR185727
Digital Object Identifier: 10.1214/aoms/1177699533

Rights: Copyright © 1966 Institute of Mathematical Statistics

Vol.37 • No. 2 • April, 1966
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