9,922 research outputs found
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
An Empirical Study of the Manipulability of Single Transferable Voting
Voting is a simple mechanism to combine together the preferences of multiple
agents. Agents may try to manipulate the result of voting by mis-reporting
their preferences. One barrier that might exist to such manipulation is
computational complexity. In particular, it has been shown that it is NP-hard
to compute how to manipulate a number of different voting rules. However,
NP-hardness only bounds the worst-case complexity. Recent theoretical results
suggest that manipulation may often be easy in practice. In this paper, we
study empirically the manipulability of single transferable voting (STV) to
determine if computational complexity is really a barrier to manipulation. STV
was one of the first voting rules shown to be NP-hard. It also appears one of
the harder voting rules to manipulate. We sample a number of distributions of
votes including uniform and real world elections. In almost every election in
our experiments, it was easy to compute how a single agent could manipulate the
election or to prove that manipulation by a single agent was impossible.Comment: To appear in Proceedings of the 19th European Conference on
Artificial Intelligence (ECAI 2010
How many candidates are needed to make elections hard to manipulate?
In multiagent settings where the agents have different preferences,
preference aggregation is a central issue. Voting is a general method for
preference aggregation, but seminal results have shown that all general voting
protocols are manipulable. One could try to avoid manipulation by using voting
protocols where determining a beneficial manipulation is hard computationally.
The complexity of manipulating realistic elections where the number of
candidates is a small constant was recently studied (Conitzer 2002), but the
emphasis was on the question of whether or not a protocol becomes hard to
manipulate for some constant number of candidates. That work, in many cases,
left open the question: How many candidates are needed to make elections hard
to manipulate? This is a crucial question when comparing the relative
manipulability of different voting protocols. In this paper we answer that
question for the voting protocols of the earlier study: plurality, Borda, STV,
Copeland, maximin, regular cup, and randomized cup. We also answer that
question for two voting protocols for which no results on the complexity of
manipulation have been derived before: veto and plurality with runoff. It turns
out that the voting protocols under study become hard to manipulate at 3
candidates, 4 candidates, 7 candidates, or never
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)
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
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