Abstract
Abstract This paper generalizes the usual tournament structure to include both partial (some pairs of players do not compete) and multiple match (some pairs of players may compete more than once) cases. Beginning with the set of all partial tournaments, a set of axioms is introduced which any distance function on this set should satisfy. In the presence of these axioms, a unique distance function (the l p norm) is shown to exist. It is then shown that the minimum distance tournament, from the multiple match tournaments provided, is also the minimum violations ranking.
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