Name
Abstract | ||
|---|---|---|
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 article, and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s00355-011-0638-y | Social Choice and Welfare |
Keywords | Field | DocType |
Econ Theory, Tournament Solution, Sophisticated Vote, Random Tournament, Transitive Subset | Discrete mathematics,Mathematical economics,Tournament,Combinatorics,Vertex (geometry),Probabilistic method,Counterexample,Partition (number theory),Conjecture,Mathematics,Transitive relation | Journal |
Volume | Issue | ISSN |
40 | 3 | 1432-217X |
Citations | PageRank | References |
5 | 0.72 | 3 |
Authors | ||
8 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Felix Brandt | 1 | 666 | 64.71 |
| Maria Chudnovsky | 2 | 390 | 46.13 |
| Ilhee Kim | 3 | 9 | 1.87 |
| Gaku Liu | 4 | 7 | 1.23 |
| Sergey Norin | 5 | 47 | 10.86 |
| Alex Scott | 6 | 251 | 40.93 |
| Paul D. Seymour | 7 | 2786 | 314.49 |
| Stéphan Thomassé | 8 | 651 | 66.03 |