Choosing from a tournament (Q1089228)

Given a finite set A of outcomes and a tournament T over A (a complete and asymmetric binary relation), a choice correspondence assigns a subset of A to T called the winners. (We can read aTb as a beats b.) The author gives an axiomatic characterization of Miller's uncovered set in which the winners are the outcomes that beat every other outcomes in at most two steps (a is a in this set if, for any b, either a beats b or beats some c which beats b). The Copeland set is made of outcomes that beat the greatest number of opponents. It is contained in the uncovered set but the author shows that it might be a dominated subset of the uncovered set. Finally, a third correspondence derived from the sophisticated algorithm [see \textit{J. S. Banks}, ibid. 1, 295-306 (1985; Zbl 0597.90011)] is studied. The author shows that it is a better correspondence than the Copeland set from the domination point of view.