3,589 research outputs found
A Second Step Towards Complexity-Theoretic Analogs of Rice's Theorem
Rice's Theorem states that every nontrivial language property of the
recursively enumerable sets is undecidable. Borchert and Stephan initiated the
search for complexity-theoretic analogs of Rice's Theorem. In particular, they
proved that every nontrivial counting property of circuits is UP-hard, and that
a number of closely related problems are SPP-hard.
The present paper studies whether their UP-hardness result itself can be
improved to SPP-hardness. We show that their UP-hardness result cannot be
strengthened to SPP-hardness unless unlikely complexity class containments
hold. Nonetheless, we prove that every P-constructibly bi-infinite counting
property of circuits is SPP-hard. We also raise their general lower bound from
unambiguous nondeterminism to constant-ambiguity nondeterminism.Comment: 14 pages. To appear in Theoretical Computer Scienc
The Complexity of Online Manipulation of Sequential Elections
Most work on manipulation assumes that all preferences are known to the
manipulators. However, in many settings elections are open and sequential, and
manipulators may know the already cast votes but may not know the future votes.
We introduce a framework, in which manipulators can see the past votes but not
the future ones, to model online coalitional manipulation of sequential
elections, and we show that in this setting manipulation can be extremely
complex even for election systems with simple winner problems. Yet we also show
that for some of the most important election systems such manipulation is
simple in certain settings. This suggests that when using sequential voting,
one should pay great attention to the details of the setting in choosing one's
voting rule. Among the highlights of our classifications are: We show that,
depending on the size of the manipulative coalition, the online manipulation
problem can be complete for each level of the polynomial hierarchy or even for
PSPACE. We obtain the most dramatic contrast to date between the
nonunique-winner and unique-winner models: Online weighted manipulation for
plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive
case) and NP-hard (destructive case) in the unique-winner model. And we obtain
what to the best of our knowledge are the first P^NP[1]-completeness and
P^NP-completeness results in the field of computational social choice, in
particular proving such completeness for, respectively, the complexity of
3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition
manipulation of veto elections.Comment: 24 page
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
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