On Approximating Optimal Weighted Lobbying, and Frequency of Correctness versus Average-Case Polynomial Time

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dc.creatorErdelyi, Gabor
dc.creatorHemaspaandra, Lane A.
dc.creatorRothe, Joerg
dc.creatorSpakowski, Holger
dc.date2007-03-20
dc.date.accessioned2026-07-07T07:53:01Z
dc.date.available2026-07-07T07:53:01Z
dc.descriptionWe 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].
dc.identifierhttps://arxiv.org/abs/cs/0703097
dc.identifierhttp://arxiv.org/abs/cs/0703097
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126094
dc.subjectComputer Science and Game Theory
dc.subjectComputational Complexity
dc.subjectMultiagent Systems
dc.subjectI.2.11; F.2.2; F.1.3
dc.titleOn Approximating Optimal Weighted Lobbying, and Frequency of Correctness versus Average-Case Polynomial Time
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