New Approximations for Coalitional Manipulation in Scoring Rules

Keller, Orgad; Hassidim, Avinatan; Hazon, Noam

doi:10.1613/jair.1.11335

Cited by 10 publications

(8 citation statements)

References 17 publications

(45 reference statements)

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“…α 1 , m, and k? We note that a different approximation factor trade-off is provided in another work by the authors (Keller et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

“…As part of our (approximate) solutions to these problems, we will rely on our solution for min-margin-SR-WCM from Section 3 (whose approximation guarantees will better suit our needs than the one by Keller et al, 2019). Similar to our SR-WCM algorithm, the algorithm for SR-Bribery will also rely on an LP.…”

Section: Algorithm For Sr-weighted-$briberymentioning

confidence: 99%

“…Notice that the maximum competitor score is the only nontrivial value in this computation. Keller et al (2019) provide an additive approximation to the maximum competitor score for general values of |C|.…”

Section: Coalitional Manipulationmentioning

confidence: 99%

“…The first-as mentioned before-tries to approximate k, the number of manipulators (e.g., Zuckerman, Procaccia, & Rosenschein, 2009;Xia, Conitzer, & Procaccia, 2010). The second tries to approximate the minimal score margin-that is, the difference in points-between the highest non-preferred candidate and p, or some additive function thereof (e.g., Brelsford et al, 2008;Keller, Hassidim, & Hazon, 2019).…”

Section: Introductionmentioning

confidence: 99%

“…En route to providing our approximation for Weighted-$Bribery using the reduction to min-margin-WCM, we also present new approximations for WCM for both mentioned approximation objectives. The advantage of our new method (compared to e.g., the work by Keller et al, 2019) is that when it is used as a sub-procedure of our bribery algorithm, the additive term it introduces into the overall approximation factor is dominated (in the asymptotic sense) by the additive terms incurred by other stages of the bribery algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Approximating Weighted and Priced Bribery in Scoring Rules

Keller

Hassidim

Hazon

2019

jair

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The classic Bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win. Its important generalizations consider voters who are weighted and also have different prices. We provide an approximate solution for these problems for a broad family of scoring rules (which includes Borda and t-approval), in the following sense: for constant weights and prices, if there exists a strategy which costs k, we efficiently find a strategy which costs at most k+\widetilde{O}(sqrt(k)). An extension for non-constant weights and prices is also given. Our algorithm is based on a randomized reduction from these Bribery generalizations to weighted coalitional manipulation (WCM). To solve this WCM instance, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding a solution in the truncated search space yields a new algorithm for WCM, which is of independent interest.

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“…α 1 , m, and k? We note that a different approximation factor trade-off is provided in another work by the authors (Keller et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

Section: Algorithm For Sr-weighted-$briberymentioning

confidence: 99%

Section: Coalitional Manipulationmentioning

confidence: 99%