120 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
X THEN X: Manipulation of Same-System Runoff Elections
Do runoff elections, using the same voting rule as the initial election but
just on the winning candidates, increase or decrease the complexity of
manipulation? Does allowing revoting in the runoff increase or decrease the
complexity relative to just having a runoff without revoting? For both weighted
and unweighted voting, we show that even for election systems with simple
winner problems the complexity of manipulation, manipulation with runoffs, and
manipulation with revoting runoffs are independent, in the abstract. On the
other hand, for some important, well-known election systems we determine what
holds for each of these cases. For no such systems do we find runoffs lowering
complexity, and for some we find that runoffs raise complexity. Ours is the
first paper to show that for natural, unweighted election systems, runoffs can
increase the manipulation complexity
The Complexity of Kings
A king in a directed graph is a node from which each node in the graph can be
reached via paths of length at most two. There is a broad literature on
tournaments (completely oriented digraphs), and it has been known for more than
half a century that all tournaments have at least one king [Lan53]. Recently,
kings have proven useful in theoretical computer science, in particular in the
study of the complexity of the semifeasible sets [HNP98,HT05] and in the study
of the complexity of reachability problems [Tan01,NT02].
In this paper, we study the complexity of recognizing kings. For each
succinctly specified family of tournaments, the king problem is known to belong
to [HOZZ]. We prove that this bound is optimal: We construct a
succinctly specified tournament family whose king problem is
-complete. It follows easily from our proof approach that the problem
of testing kingship in succinctly specified graphs (which need not be
tournaments) is -complete. We also obtain -completeness
results for k-kings in succinctly specified j-partite tournaments, , and we generalize our main construction to show that -completeness
holds for testing k-kingship in succinctly specified families of tournaments
for all
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