The computational difficulty of manipulating an election

Bartholdi, John J.; Tovey, Craig A.; Trick, Michael A.

doi:10.1007/bf00295861

Cited by 368 publications

(362 citation statements)

References 12 publications

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“…For example, for our election problems, the parameter will always be the number m of candidates in the election. A problem is fixed-parameter tractable (in FPT) if there exists an algorithm that, given an instance I with parameter k, can compute the answer to this problem in time f (k) · |I| O (1) , where f is a computable function and |I| is the length of the encoding of I. A parameterized problem is in XP if there exists an algorithm that, given an instance I with parameter k, can compute the answer to this problem in time |I| f (k) , where f is some computable function.…”

Section: Preliminariesmentioning

confidence: 99%

“…We test the running times of our algorithms empirically. Algorithmic problems that model the manipulation of elections include, among others, strategic voting problems [1,6] (where we are given an election with honest voters Supported by DFG project PAWS (NI 369/10). Supported by a DFG Mercator fellowship within project PAWS (NI 369/10) while staying at TU Berlin, and by AGH University grant 11.11.230.124 afterward.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Elections with Few Candidates: Prices, Weights, and Covering Problems

Bredereck

Faliszewski

Niedermeier

et al. 2015

Algorithmic Decision Theory

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Abstract. We show that a number of election-related problems with prices (such as, for example, bribery) are fixed-parameter tractable (in FPT) when parameterized by the number of candidates. For bribery, this resolves a nearly 10-year old family of open problems. Our results follow by a general technique that formulates voting problems as covering problems and extends the classic approach of using integer linear programming and the algorithm of Lenstra [19]. In this context, our central result is that WEIGHTED SET MULTICOVER parameterized by the universe size is fixed-parameter tractable. Our approach is also applicable to weighted electoral control for Approval voting. We improve previously known XP-memberships to FPT-memberships. Our preliminary experiments on real-world-based data show the practical usefulness of our approach for instances with few candidates.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Elections with Few Candidates: Prices, Weights, and Covering Problems

Bredereck

Faliszewski

Niedermeier

et al. 2015

Algorithmic Decision Theory

View full text Add to dashboard Cite

show abstract

“…6 A decision variable in the LP is the probability that a given outcome is chosen given that a certain type revelation vector (each agent reveals a type) occurs. For any constant number of agents, the number of decision variables is polynomial in the number of types and in the number of outcomes.…”

Section: Complexity Resultsmentioning

confidence: 99%

“…A novel way around this is to design mechanisms where finding a beneficial insincere type revelation is provably hard computationally. There has been work characterizing the complexity of manipulating known voting protocols [6,5,15,13], and recent work on designing small changes to voting protocols so that manipulation becomes hard [15,23]. Future research includes automatically designing mechanisms that are provably hard to manipulate.…”

Section: Multi-stage Mechanismsmentioning

confidence: 99%

Automated Mechanism Design: A New Application Area for Search Algorithms

Sandholm

2003

Principles and Practice of Constraint Programming – CP 2003

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Abstract. Mechanism design is the art of designing the rules of the game (aka. mechanism) so that a desirable outcome (according to a given objective) is reached despite the fact that each agent acts in his own selfinterest. Examples include the design of auctions, voting protocols, and divorce settlement procedures. Mechanisms have traditionally been designed manually for classes of problems. In 2002, Conitzer and Sandholm introduced the automated mechanism design approach, where the mechanism is computationally created for the specific problem instance at hand. This approach has several advantages: 1) it can yield better mechanisms than the ones known to date, 2) it applies beyond the problem classes studied manually to date, 3) it can circumvent seminal economic impossibility results, and 4) it shifts the burden of design from man to machine. In this write-up I overview the approach, focusing on problem representations, computational complexity, and initial applications. I also lay out an agenda for future research in this area.

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“…It is interesting that limited computational resources can be used as a positive tool within mechanism design, for example designing mechanisms in which the only computable equilibria are "good" from the perspective of systemwide design goals. As an example, the problem of strategic manipulation in voting protocols is known to be NP-hard [Bar89], and it is possible to use randomization within a mechanism to make manipulation hard without making the implementation problem for the mechanism hard [CS02a].…”

Section: Homogeneous/heterogeneous Goodsmentioning

confidence: 99%