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A smallest tournament for which the Banks set and the Copeland set are disjoint

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  • Olivier Hudry

    (êcole Nationale SupÊrieure des TÊlÊcommunications, 46, rue Barrault, F-75634 Paris Cedex 13, France)

Abstract

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Copeland winner of T is a vertex with a maximum out-degree. In this paper, we show that 13 is the minimum number of vertices that a tournament must have so that none of its Copeland winners is a Banks winner: for any tournament with less than 13 vertices, there is always at least one vertex which is a Copeland winner and a Banks winner simultaneously.

Suggested Citation

  • Olivier Hudry, 1999. "A smallest tournament for which the Banks set and the Copeland set are disjoint," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(1), pages 137-143.
    • Handle: RePEc:spr:sochwe:v:16:y:1999:i:1:p:137-143
    Note: Received: 2 May 1997 / Accepted: 30 September 1997
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