2011/08/22 by Dorothea Baumeister, Baumeister, Dorothea, Rothe, Joerg +1 · 1 citation
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Game Theory and Voting Systems #Internet Traffic Analysis and Secure E-voting #Legal and Constitutional Studies #cs.CC
paper · pdf · doi:10.48550/arxiv.1108.4436
9 pages, to appear in Information Processing Letters
openalex publication_date 2011/08/22 · arxiv created 2011/11/28 · arxiv updated 2011/11/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The Possible Winner problem asks, given an election where the voters' preferences over the candidates are specified only partially, whether a designated candidate can become a winner by suitably extending all the votes. Betzler and Dorn [1] proved a result that is only one step away from a full dichotomy of this problem for the important class of pure scoring rules in the case of unweighted voters and an unbounded number of candidates: Possible Winner is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule with vector (2,1,...,1,0), but is solvable in polynomial time for plurality and veto. We take the final step to a full dichotomy by showing that Possible Winner is NP-complete also for the scoring rule with vector (2,1,...,1,0).