Possible and necessary winners of partial tournaments

Aziz, H., Brill, M., Fischer, F., Harrenstein, P., Lang, J. and Seedig, H. G. (2015) Possible and necessary winners of partial tournaments. Journal of Artificial Intelligence Research, 54, pp. 493-534. (doi: 10.1613/jair.4856)

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.

• Item Type: Articles
• Additional Information: This material is based on work supported by the Deutsche Forschungsgemeinschaft under grants BR 2312/9-1, BR 2312/10-1, and FI 1664/1-1. Haris Aziz is supported by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program. Markus Brill has been supported by a Feodor Lynen research fellowship of the Alexander von Humboldt Foundation and by the ERC under Starting Grant 639945 (“ACCORD”). J´erˆome Lang has been supported by the ANR project CoCoRICoCoDec. Paul Harrenstein has been supported by the ERC under Advanced Grant 291528 (“RACE”).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fischer, Dr Felix
• Authors: Aziz, H., Brill, M., Fischer, F., Harrenstein, P., Lang, J., and Seedig, H. G.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Journal of Artificial Intelligence Research
• Publisher: AAAI Press
• ISSN: 1076-9757
• ISSN (Online): 1943-5037
• Copyright Holders: Copyright © 2015 AI Access Foundation
• First Published: First published in Journal of Artificial Intelligence Research 54: 493-534
• Publisher Policy: Reproduced in accordance with the publisher copyright policy