9 research outputs found
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 Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting
A central theme in computational social choice is to study the extent to
which voting systems computationally resist manipulative attacks seeking to
influence the outcome of elections, such as manipulation (i.e., strategic
voting), control, and bribery. Bucklin and fallback voting are among the voting
systems with the broadest resistance (i.e., NP-hardness) to control attacks.
However, only little is known about their behavior regarding manipulation and
bribery attacks. We comprehensively investigate the computational resistance of
Bucklin and fallback voting for many of the common manipulation and bribery
scenarios; we also complement our discussion by considering several campaign
management problems for Bucklin and fallback.Comment: 28 page
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
Multivariate Analyis of Swap Bribery
We consider the computational complexity of a problem modeling bribery in the
context of voting systems. In the scenario of Swap Bribery, each voter assigns
a certain price for swapping the positions of two consecutive candidates in his
preference ranking. The question is whether it is possible, without exceeding a
given budget, to bribe the voters in a way that the preferred candidate wins in
the election. We initiate a parameterized and multivariate complexity analysis
of Swap Bribery, focusing on the case of k-approval. We investigate how
different cost functions affect the computational complexity of the problem. We
identify a special case of k-approval for which the problem can be solved in
polynomial time, whereas we prove NP-hardness for a slightly more general
scenario. We obtain fixed-parameter tractability as well as W[1]-hardness
results for certain natural parameters.Comment: 20 pages. Conference version published at IPEC 201