148 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
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
Combinatorial Voter Control in Elections
Voter control problems model situations such as an external agent trying to
affect the result of an election by adding voters, for example by convincing
some voters to vote who would otherwise not attend the election. Traditionally,
voters are added one at a time, with the goal of making a distinguished
alternative win by adding a minimum number of voters. In this paper, we
initiate the study of combinatorial variants of control by adding voters: In
our setting, when we choose to add a voter~, we also have to add a whole
bundle of voters associated with . We study the computational
complexity of this problem for two of the most basic voting rules, namely the
Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201
Possible Winners in Noisy Elections
We consider the problem of predicting winners in elections, for the case
where we are given complete knowledge about all possible candidates, all
possible voters (together with their preferences), but where it is uncertain
either which candidates exactly register for the election or which voters cast
their votes. Under reasonable assumptions, our problems reduce to counting
variants of election control problems. We either give polynomial-time
algorithms or prove #P-completeness results for counting variants of control by
adding/deleting candidates/voters for Plurality, k-Approval, Approval,
Condorcet, and Maximin voting rules. We consider both the general case, where
voters' preferences are unrestricted, and the case where voters' preferences
are single-peaked.Comment: 34 page
Solving Hard Control Problems in Voting Systems via Integer Programming
Voting problems are central in the area of social choice. In this article, we
investigate various voting systems and types of control of elections. We
present integer linear programming (ILP) formulations for a wide range of
NP-hard control problems. Our ILP formulations are flexible in the sense that
they can work with an arbitrary number of candidates and voters. Using the
off-the-shelf solver Cplex, we show that our approaches can manipulate
elections with a large number of voters and candidates efficiently
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