443 research outputs found
Voting and Bribing in Single-Exponential Time
We introduce a general problem about bribery in voting systems. In the R-Multi-Bribery problem, the goal is to bribe a set of voters at minimum cost such that a desired candidate wins the manipulated election under the voting rule R. Voters assign prices for withdrawing their vote, for swapping the positions of two consecutive candidates in their preference order, and for perturbing their approval count for a candidate.
As our main result, we show that R-Multi-Bribery is fixed-parameter tractable parameterized by the number of candidates for many natural voting rules R, including Kemeny rule, all scoring protocols, maximin rule, Bucklin rule, fallback rule, SP-AV, and any C1 rule. In particular, our result resolves the parameterized of R-Swap Bribery for all those voting rules, thereby solving a long-standing open problem and "Challenge #2" of the 9 Challenges in computational social choice by Bredereck et al.
Further, our algorithm runs in single-exponential time for arbitrary cost; it thus improves the earlier double-exponential time algorithm by Dorn and Schlotter that is restricted to the unit-cost case for all scoring protocols, the maximin rule, and Bucklin rule
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
Campaign Management under Approval-Driven Voting Rules
Approval-like voting rules, such as Sincere-Strategy Preference-Based
Approval voting (SP-AV), the Bucklin rule (an adaptive variant of -Approval
voting), and the Fallback rule (an adaptive variant of SP-AV) have many
desirable properties: for example, they are easy to understand and encourage
the candidates to choose electoral platforms that have a broad appeal. In this
paper, we investigate both classic and parameterized computational complexity
of electoral campaign management under such rules. We focus on two methods that
can be used to promote a given candidate: asking voters to move this candidate
upwards in their preference order or asking them to change the number of
candidates they approve of. We show that finding an optimal campaign management
strategy of the first type is easy for both Bucklin and Fallback. In contrast,
the second method is computationally hard even if the degree to which we need
to affect the votes is small. Nevertheless, we identify a large class of
scenarios that admit fixed-parameter tractable algorithms.Comment: 34 pages, 1 figur
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
Computational Complexity Characterization of Protecting Elections from Bribery
The bribery problem in election has received considerable attention in the
literature, upon which various algorithmic and complexity results have been
obtained. It is thus natural to ask whether we can protect an election from
potential bribery. We assume that the protector can protect a voter with some
cost (e.g., by isolating the voter from potential bribers). A protected voter
cannot be bribed. Under this setting, we consider the following bi-level
decision problem: Is it possible for the protector to protect a proper subset
of voters such that no briber with a fixed budget on bribery can alter the
election result? The goal of this paper is to give a full picture on the
complexity of protection problems. We give an extensive study on the protection
problem and provide algorithmic and complexity results. Comparing our results
with that on the bribery problems, we observe that the protection problem is in
general significantly harder. Indeed, it becomes -complete even for
very restricted special cases, while most bribery problems lie in NP. However,
it is not necessarily the case that the protection problem is always harder.
Some of the protection problems can still be solved in polynomial time, while
some of them remain as hard as the bribery problem under the same setting.Comment: 28 Pages. The Article has been accepted in the 26th International
Computing and Combinatorics Conference (COCOON 2020
Computational Complexity Characterization of Protecting Elections from Bribery
The bribery problem in election has received considerable attention in the literature, upon which various algorithmic and complexity results have been obtained. It is thus natural to ask whether we can protect an election from potential bribery. We assume that the protector can protect a voter with some cost (e.g., by isolating the voter from potential bribers). A protected voter cannot be bribed. Under this setting, we consider the following bi-level decision problem: Is it possible for the protector to protect a proper subset of voters such that no briber with a fixed budget on bribery can alter the election result? The goal of this paper is to give a full picture on the complexity of protection problems. We give an extensive study on the protection problem and provide algorithmic and complexity results. Comparing our results with that on the bribery problems, we observe that the protection problem is in general significantly harder. Indeed, it becomes Σp2 -complete even for very restricted special cases, while most bribery problems lie in NP. However, it is not necessarily the case that the protection problem is always harder. Some of the protection problems can still be solved in polynomial time, while some of them remain as hard as the bribery problem under the same setting
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