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

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

Social Choice and Welfare, 1999, vol. 16, issue 1, 137-143

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.

Date: 1998-11-16
Note: Received: 2 May 1997 / Accepted: 30 September 1997
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