Possible and Necessary Winners of Partial Tournaments

Haris Aziz (1) , Markus Brill (2) , Felix Fischer , Paul Harrenstein (3) , Jérôme Lang (4) , Hans-Georg Seedig (5)

1 University of South Wales
2 Duke University
3 Oxford University
4 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
5 Department of Informatics of the Technische Universität München

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them, possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

Mots clés: computational social choice

Domaines: Informatique [cs]

Haris Aziz, Markus Brill, Felix Fischer, Paul Harrenstein, Jérôme Lang, et al.. Possible and Necessary Winners of Partial Tournaments. Journal of Artificial Intelligence Research, 2015, 54, ⟨10.1613/jair.4856⟩. ⟨hal-01434599⟩