A tournament is an oriented graph where there is exactly one edge between each pair of nodes, in one direction or the other, with the implicit interpretation that one node “beats” the other. If the binary relation induced by the tournament is transitive, then there is a natural notion of winner, which is the maximal element. But in the general case, it would be interesting to have a function that, to each tournament, associates a set of cowinners, and that has intuitively appealing properties. We will investigate such functions, called “tournament solutions”.
References:
Laslier, Jean-François. Tournament solutions and majority voting. Springer, 1997.
Brandt, Felix, Markus Brill and Paul Harrenstein. Tournament Solution. In: Brandt, Felix, Vincent Conitzer, Ulle Endriss, et al (ed.). Handbook of computational social choice. Cambridge University Press, 2016.