54 research outputs found
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
How Hard Is It to Control an Election by Breaking Ties?
We study the computational complexity of controlling the result of an
election by breaking ties strategically. This problem is equivalent to the
problem of deciding the winner of an election under parallel universes
tie-breaking. When the chair of the election is only asked to break ties to
choose between one of the co-winners, the problem is trivially easy. However,
in multi-round elections, we prove that it can be NP-hard for the chair to
compute how to break ties to ensure a given result. Additionally, we show that
the form of the tie-breaking function can increase the opportunities for
control. Indeed, we prove that it can be NP-hard to control an election by
breaking ties even with a two-stage voting rule.Comment: Revised and expanded version including longer proofs and additional
result
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
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
Resolving the Complexity of Some Fundamental Problems in Computational Social Choice
This thesis is in the area called computational social choice which is an
intersection area of algorithms and social choice theory.Comment: Ph.D. Thesi
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