11,133 research outputs found
Complexity of Manipulative Actions When Voting with Ties
Most of the computational study of election problems has assumed that each
voter's preferences are, or should be extended to, a total order. However in
practice voters may have preferences with ties. We study the complexity of
manipulative actions on elections where voters can have ties, extending the
definitions of the election systems (when necessary) to handle voters with
ties. We show that for natural election systems allowing ties can both increase
and decrease the complexity of manipulation and bribery, and we state a general
result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201
Bribery Can Get Harder in Structured Multiwinner Approval Election
We study the complexity of constructive bribery in the context of structured
multiwinner approval elections. Given such an election, we ask whether a
certain candidate can join the winning committee by adding, deleting, or
swapping approvals, where each such action comes at a cost and we are limited
by a budget. We assume our elections to either have the candidate interval or
the voter interval property, and we require the property to hold also after the
bribery. While structured elections usually make manipulative attacks
significantly easier, our work also shows examples of the opposite behavior. We
conclude by presenting preliminary insights regarding the destructive variant
of our problem.Comment: 23 pages, 1 figure, 1 table, published in the Proceedings of AAMAS-2
The Complexity of Manipulating -Approval Elections
An important problem in computational social choice theory is the complexity
of undesirable behavior among agents, such as control, manipulation, and
bribery in election systems. These kinds of voting strategies are often
tempting at the individual level but disastrous for the agents as a whole.
Creating election systems where the determination of such strategies is
difficult is thus an important goal.
An interesting set of elections is that of scoring protocols. Previous work
in this area has demonstrated the complexity of misuse in cases involving a
fixed number of candidates, and of specific election systems on unbounded
number of candidates such as Borda. In contrast, we take the first step in
generalizing the results of computational complexity of election misuse to
cases of infinitely many scoring protocols on an unbounded number of
candidates. Interesting families of systems include -approval and -veto
elections, in which voters distinguish candidates from the candidate set.
Our main result is to partition the problems of these families based on their
complexity. We do so by showing they are polynomial-time computable, NP-hard,
or polynomial-time equivalent to another problem of interest. We also
demonstrate a surprising connection between manipulation in election systems
and some graph theory problems
The Complexity of Manipulative Attacks in Nearly Single-Peaked Electorates
Many electoral bribery, control, and manipulation problems (which we will
refer to in general as "manipulative actions" problems) are NP-hard in the
general case. It has recently been noted that many of these problems fall into
polynomial time if the electorate is single-peaked (i.e., is polarized along
some axis/issue). However, real-world electorates are not truly single-peaked.
There are usually some mavericks, and so real-world electorates tend to merely
be nearly single-peaked. This paper studies the complexity of
manipulative-action algorithms for elections over nearly single-peaked
electorates, for various notions of nearness and various election systems. We
provide instances where even one maverick jumps the manipulative-action
complexity up to \np-hardness, but we also provide many instances where a
reasonable number of mavericks can be tolerated without increasing the
manipulative-action complexity.Comment: 35 pages, also appears as URCS-TR-2011-96
Reinstating Combinatorial Protections for Manipulation and Bribery in Single-Peaked and Nearly Single-Peaked Electorates
Understanding when and how computational complexity can be used to protect
elections against different manipulative actions has been a highly active
research area over the past two decades. A recent body of work, however, has
shown that many of the NP-hardness shields, previously obtained, vanish when
the electorate has single-peaked or nearly single-peaked preferences. In light
of these results, we investigate whether it is possible to reimpose NP-hardness
shields for such electorates by allowing the voters to specify partial
preferences instead of insisting they cast complete ballots. In particular, we
show that in single-peaked and nearly single-peaked electorates, if voters are
allowed to submit top-truncated ballots, then the complexity of manipulation
and bribery for many voting rules increases from being in P to being
NP-complete.Comment: 28 pages; A shorter version of this paper will appear at the 30th
AAAI Conference on Artificial Intelligence (AAAI-16
Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges
Computational Social Choice is an interdisciplinary research area involving
Economics, Political Science, and Social Science on the one side, and
Mathematics and Computer Science (including Artificial Intelligence and
Multiagent Systems) on the other side. Typical computational problems studied
in this field include the vulnerability of voting procedures against attacks,
or preference aggregation in multi-agent systems. Parameterized Algorithmics is
a subfield of Theoretical Computer Science seeking to exploit meaningful
problem-specific parameters in order to identify tractable special cases of in
general computationally hard problems. In this paper, we propose nine of our
favorite research challenges concerning the parameterized complexity of
problems appearing in this context
Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting
A central theme in computational social choice is to study the extent to
which voting systems computationally resist manipulative attacks seeking to
influence the outcome of elections, such as manipulation (i.e., strategic
voting), control, and bribery. Bucklin and fallback voting are among the voting
systems with the broadest resistance (i.e., NP-hardness) to control attacks.
However, only little is known about their behavior regarding manipulation and
bribery attacks. We comprehensively investigate the computational resistance of
Bucklin and fallback voting for many of the common manipulation and bribery
scenarios; we also complement our discussion by considering several campaign
management problems for Bucklin and fallback.Comment: 28 page
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