318 research outputs found
Anyone but Him: The Complexity of Precluding an Alternative
Preference aggregation in a multiagent setting is a central issue in both
human and computer contexts. In this paper, we study in terms of complexity the
vulnerability of preference aggregation to destructive control. That is, we
study the ability of an election's chair to, through such mechanisms as
voter/candidate addition/suppression/partition, ensure that a particular
candidate (equivalently, alternative) does not win. And we study the extent to
which election systems can make it impossible, or computationally costly
(NP-complete), for the chair to execute such control. Among the systems we
study--plurality, Condorcet, and approval voting--we find cases where systems
immune or computationally resistant to a chair choosing the winner nonetheless
are vulnerable to the chair blocking a victory. Beyond that, we see that among
our studied systems no one system offers the best protection against
destructive control. Rather, the choice of a preference aggregation system will
depend closely on which types of control one wishes to be protected against. We
also find concrete cases where the complexity of or susceptibility to control
varies dramatically based on the choice among natural tie-handling rules.Comment: Preliminary version appeared in AAAI '05. Also appears as
URCS-TR-2005-87
Downward Collapse from a Weaker Hypothesis
Hemaspaandra et al. proved that, for and : if
\Sigma_i^p \BoldfaceDelta DIFF_m(\Sigma_k^p) is closed under complementation,
then . This sharply asymmetric
result fails to apply to the case in which the hypothesis is weakened by
allowing the to be replaced by any class in its difference
hierarchy. We so extend the result by proving that, for and : if DIFF_s(\Sigma_i^p) \BoldfaceDelta DIFF_m(\Sigma_k^p) is closed
under complementation, then
What's Up with Downward Collapse: Using the Easy-Hard Technique to Link Boolean and Polynomial Hierarchy Collapses
During the past decade, nine papers have obtained increasingly strong
consequences from the assumption that boolean or bounded-query hierarchies
collapse. The final four papers of this nine-paper progression actually achieve
downward collapse---that is, they show that high-level collapses induce
collapses at (what beforehand were thought to be) lower complexity levels. For
example, for each it is now known that if \psigkone=\psigktwo then
\ph=\sigmak. This article surveys the history, the results, and the
technique---the so-called easy-hard method---of these nine papers.Comment: 37 pages. an extended abstract appeared in SIGACT News, 29, 10-22,
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