5,895 research outputs found
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
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
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
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 Shield that Never Was: Societies with Single-Peaked Preferences are More Open to Manipulation and Control
Much work has been devoted, during the past twenty years, to using complexity
to protect elections from manipulation and control. Many results have been
obtained showing NP-hardness shields, and recently there has been much focus on
whether such worst-case hardness protections can be bypassed by frequently
correct heuristics or by approximations. This paper takes a very different
approach: We argue that when electorates follow the canonical political science
model of societal preferences the complexity shield never existed in the first
place. In particular, we show that for electorates having single-peaked
preferences, many existing NP-hardness results on manipulation and control
evaporate.Comment: 38 pages, 2 figure
On the Hardness of Bribery Variants in Voting with CP-Nets
We continue previous work by Mattei et al. (Mattei, N., Pini, M., Rossi, F.,
Venable, K.: Bribery in voting with CP-nets. Ann. of Math. and Artif. Intell.
pp. 1--26 (2013)) in which they study the computational complexity of bribery
schemes when voters have conditional preferences that are modeled by CP-nets.
For most of the cases they considered, they could show that the bribery problem
is solvable in polynomial time. Some cases remained open---we solve two of them
and extend the previous results to the case that voters are weighted. Moreover,
we consider negative (weighted) bribery in CP-nets, when the briber is not
allowed to pay voters to vote for his preferred candidate.Comment: improved readability; identified Cheapest Subsets to be the
enumeration variant of K.th Largest Subset, so we renamed it to K-Smallest
Subsets and point to the literatur; some more typos fixe
- …