356 research outputs found
Universal Voting Protocol Tweaks to Make Manipulation Hard
Voting is a general method for preference aggregation in multiagent settings,
but seminal results have shown that all (nondictatorial) voting protocols are
manipulable. One could try to avoid manipulation by using voting protocols
where determining a beneficial manipulation is hard computationally. A number
of recent papers study the complexity of manipulating existing protocols. This
paper is the first work to take the next step of designing new protocols that
are especially hard to manipulate. Rather than designing these new protocols
from scratch, we instead show how to tweak existing protocols to make
manipulation hard, while leaving much of the original nature of the protocol
intact. The tweak studied consists of adding one elimination preround to the
election. Surprisingly, this extremely simple and universal tweak makes typical
protocols hard to manipulate! The protocols become NP-hard, #P-hard, or
PSPACE-hard to manipulate, depending on whether the schedule of the preround is
determined before the votes are collected, after the votes are collected, or
the scheduling and the vote collecting are interleaved, respectively. We prove
general sufficient conditions on the protocols for this tweak to introduce the
hardness, and show that the most common voting protocols satisfy those
conditions. These are the first results in voting settings where manipulation
is in a higher complexity class than NP (presuming PSPACE NP)
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
Dominating Manipulations in Voting with Partial Information
We consider manipulation problems when the manipulator only has partial
information about the votes of the nonmanipulators. Such partial information is
described by an information set, which is the set of profiles of the
nonmanipulators that are indistinguishable to the manipulator. Given such an
information set, a dominating manipulation is a non-truthful vote that the
manipulator can cast which makes the winner at least as preferable (and
sometimes more preferable) as the winner when the manipulator votes truthfully.
When the manipulator has full information, computing whether or not there
exists a dominating manipulation is in P for many common voting rules (by known
results). We show that when the manipulator has no information, there is no
dominating manipulation for many common voting rules. When the manipulator's
information is represented by partial orders and only a small portion of the
preferences are unknown, computing a dominating manipulation is NP-hard for
many common voting rules. Our results thus throw light on whether we can
prevent strategic behavior by limiting information about the votes of other
voters.Comment: 7 pages by arxiv pdflatex, 1 figure. The 6-page version has the same
content and will be published in Proceedings of the Twenty-Fifth AAAI
Conference on Artificial Intelligence (AAAI-11
Combining Voting Rules Together
We propose a simple method for combining together voting rules that performs
a run-off between the different winners of each voting rule. We prove that this
combinator has several good properties. For instance, even if just one of the
base voting rules has a desirable property like Condorcet consistency, the
combination inherits this property. In addition, we prove that combining voting
rules together in this way can make finding a manipulation more computationally
difficult. Finally, we study the impact of this combinator on approximation
methods that find close to optimal manipulations
How Hard Is It to Control an Election by Breaking Ties?
We study the computational complexity of controlling the result of an
election by breaking ties strategically. This problem is equivalent to the
problem of deciding the winner of an election under parallel universes
tie-breaking. When the chair of the election is only asked to break ties to
choose between one of the co-winners, the problem is trivially easy. However,
in multi-round elections, we prove that it can be NP-hard for the chair to
compute how to break ties to ensure a given result. Additionally, we show that
the form of the tie-breaking function can increase the opportunities for
control. Indeed, we prove that it can be NP-hard to control an election by
breaking ties even with a two-stage voting rule.Comment: Revised and expanded version including longer proofs and additional
result
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
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