19 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
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
Complexity of Conformant Election Manipulation
It is important to study how strategic agents can affect the outcome of an
election. There has been a long line of research in the computational study of
elections on the complexity of manipulative actions such as manipulation and
bribery. These problems model scenarios such as voters casting strategic votes
and agents campaigning for voters to change their votes to make a desired
candidate win. A common assumption is that the preferences of the voters follow
the structure of a domain restriction such as single peakedness, and so
manipulators only consider votes that also satisfy this restriction. We
introduce the model where the preferences of the voters define their own
restriction and strategic actions must ``conform'' by using only these votes.
In this model, the election after manipulation will retain common domain
restrictions. We explore the computational complexity of conformant
manipulative actions and we discuss how conformant manipulative actions relate
to other manipulative actions.Comment: A version of this paper will appear in the Proceedings of FCT 202
Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability
We study the parameterized complexity of Winners Determination for three
prevalent -committee selection rules, namely the minimax approval voting
(MAV), the proportional approval voting (PAV), and the Chamberlin-Courant's
approval voting (CCAV). It is known that Winners Determination for these rules
is NP-hard. Moreover, these problems have been studied from the parameterized
complexity point of view with respect to some natural parameters recently.
However, many results turned out to be W[1]-hard or W[2]-hard. Aiming at
deriving more fixed-parameter algorithms, we revisit these problems by
considering more natural and important single parameters, combined parameters,
and structural parameters.Comment: 31 pages, 2 figures, AAMAS 201
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