Possible and necessary winners of partial tournaments

Authors:
Haris Aziz;Paul Harrenstein;Markus Brill;Jérôme Lang;Felix Fischer;Hans Georg Seedig
Affiliations:
Institut für Informatik, TU München, Germany;Institut für Informatik, TU München, Germany;Institut für Informatik, TU München, Germany;LAMSADE, Université, Paris-Dauphine, France;University of Cambridge, UK;Institut für Informatik, TU München, Germany
Venue:
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Year:
2012

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Abstract

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.