Open Access
May, 1975 On Most Effective Tournament Plans With Fewer Games than Competitors
Willi Maurer
Ann. Statist. 3(3): 717-727 (May, 1975). DOI: 10.1214/aos/1176343135


Let $\Omega_n$ denote a set of $n$ players, $p_{ij}$ the probability that player $i$ defeats player $j$ and $\Gamma$ the class of preference matrices $(p_{ij})$ with $p_{1j} \geqq \frac{1}{2}, j > 2$. Under the assumption that the outcomes of games are independent and distributed according to $(p_{ij}) \in \Gamma$, the effectiveness (relative to $(p_{ij})$) of a tournament plan, together with a rule to select a winner, is measured by the probability that player 1 (the "best" player) wins the tournament. A k.o. plan is a tournament plan in which a player is eliminated from the tournament if he loses one game. It is shown that there are no plans on $\Omega_n$ with $n - 1$ games that are more effective than k.o. plans relative to all matrices contained in certain reasonable subclasses of $\Gamma$. Among the k.o. plans for $2^m + k, 0 \leqq k < 2^m$, players, those which consist of a preliminary round of $k$ games followed by a "symmetric" k.o. tournament on the remaining $2^m$ players are more effective than all other plans relative to the preference matrices contained in two large subclasses of $\Gamma$. In order to prove these assertions, the tournament plans are interpreted as mappings with directed digraphs as domain and range.


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Willi Maurer. "On Most Effective Tournament Plans With Fewer Games than Competitors." Ann. Statist. 3 (3) 717 - 727, May, 1975.


Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0349.90138
MathSciNet: MR371712
Digital Object Identifier: 10.1214/aos/1176343135

Primary: 62K05
Secondary: 05B30 , 05C20‎

Keywords: complete digraph , dominance structure , knockout plan , preference matrix , Tournament plan , winner rule

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 3 • May, 1975
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