Determining possible and necessary winners under common voting rules given partial orders


Journal Article

Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a voting rule, a profile of partial orders, and an alternative (candidate) c, two important questions arise: first, is it still possible for c to win, and second, is c guaranteed to win? These are the possible winner and necessary winner problems, respectively. Each of these two problems is further divided into two sub-problems: determining whether c is a unique winner (that is, c is the only winner), or determining whether c is a co-winner (that is, c is in the set of winners). We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We completely characterize the complexity of possible/necessary winner problems for the following common voting rules: a class of positional scoring rules (including Borda), Copeland, maximin, Bucklin, ranked pairs, voting trees, and plurality with runoff. © 2011 AI Access Foundation. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Xia, L; Conitzer, V

Published Date

  • May 1, 2011

Published In

Volume / Issue

  • 41 /

Start / End Page

  • 25 - 67

Electronic International Standard Serial Number (EISSN)

  • 1076-9757

Digital Object Identifier (DOI)

  • 10.1613/jair.3186

Citation Source

  • Scopus