2007/03/20 by Gábor Erdélyi, Gabor Erdelyi, Erdelyi, Gabor +6
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computational Complexity (cs.CC) #Computer Science and Game Theory (cs.GT) #F.1.3 #F.2.2 #FOS: Computer and information sciences #Game Theory and Applications #Game Theory and Voting Systems #I.2.11 #Multiagent Systems (cs.MA) #cs.CC #cs.GT #cs.MA
paper · pdf · doi:10.48550/arxiv.cs/0703097
arxiv created 2007/03/20 · openalex publication_date 2007/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate issues related to two hard problems related to voting, the optimal weighted lobbying problem and the winner problem for Dodgson elections. Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is intractable in the sense of parameterized complexity. We provide an efficient greedy algorithm that achieves a logarithmic approximation ratio for this problem and even for a more general variant--optimal weighted lobbying. We prove that essentially no better approximation ratio than ours can be proven for this greedy algorithm. The problem of determining Dodgson winners is known to be complete for parallel access to NP [HHR97]. Homan and Hemaspaandra [HH06] proposed an efficient greedy heuristic for finding Dodgson winners with a guaranteed frequency of success, and their heuristic is a ``frequently self-knowingly correct algorithm.'' We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently self-knowingly correct polynomial-time algorithm. Furthermore, we study some features of probability weight of correctness with respect to Procaccia and Rosenschein's junta distributions [PR07].