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Article Dans Une Revue Social Choice and Welfare Année : 2012

A counterexample to a conjecture of Schwartz

Résumé

In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice versa. But in fact there is such a tournament, as we show in this paper, and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method.
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hal-04639109 , version 1 (09-07-2024)

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Felix Brandt, Maria Chudnovsky, Ilhee Kim, Gaku Liu, Sergey Norin, et al.. A counterexample to a conjecture of Schwartz. Social Choice and Welfare, 2012, 40 (3), pp.739-743. ⟨10.1007/s00355-011-0638-y⟩. ⟨hal-04639109⟩
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