How Hard Is it to Bribe the Judges? A Study of the Complexity of Bribery in Judgment Aggregation

Baumeister, Dorothea; Erdélyi, Gábor; Rothe, Jörg

doi:10.1007/978-3-642-24873-3_1

Cited by 21 publications

(35 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, m} and price p i := 1. Lobbying is also closely related to bribery in judgment aggregation (Baumeister, Erdélyi, & Rothe, 2011) where the judges submit binary opinions on different propositions and the goal is to bribe as few judges as possible in order to obtain a certain outcome. A Lobbying instance can be formulated as an equivalent instance of the bribery in judgment aggregation problem using a premise-based procedure.…”

Section: Related Workmentioning

confidence: 99%

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

Bredereck

Hartung

Kratsch

et al. 2014

jair

View full text Add to dashboard Cite

Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard Lobbying problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n×m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that showed parameterized intractability (W[2]-completeness) with respect to the number k of modified rows, we study how natural parameters such as n, m, k, or the "maximum number of 1s missing for any column to have a majority of 1s" (referred to as "gap value g") govern the computational complexity of Lobbying. Among other results, we prove that Lobbying is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves Lobbying even optimally if m ≤ 4. We also show empirically that this greedy algorithm performs well on general instances. As a further key result, we prove that Lobbying is LOGSNP-complete for constant values g ≥ 1, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism.

show abstract

Section: Related Workmentioning

confidence: 99%

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

Bredereck

Hartung

Kratsch

et al. 2014

jair

View full text Add to dashboard Cite

show abstract

“…This paper combines and extends previous work by Baumeister et al (2011Baumeister et al ( , 2013Baumeister et al ( , 2014b) that appeared in the proceedings of ADT'11, COMSOC'12, ADT'13, and COMSOC'14. The present version contains some additional results and it provides more discussion and a number of notational improvements.…”

Section: Our Contributionsmentioning

confidence: 64%

“…Decisionmaking processes are often susceptible to various types of interference, be it internal or external. In social choice theory and in ✩ This paper combines and extends the results from preliminary conference versions that appear in the proceedings of the 2nd and the 3rd International Conference on Algorithmic Decision Theory (ADT'11 and ADT'13) (Baumeister et al, 2011(Baumeister et al, , 2013 and of the 4th and the 5th International Workshop on Computational Social Choice (COMSOC'12 and COMSOC'14) (Baumeister et al, , 2014, and was presented at the ESSLLI Workshop on Logical Models of Group Decision Making (ESSLLI-LMGD'13). computational social choice, ways of influencing the outcome of elections -such as manipulation and bribery -have been studied intensely, with a particular focus on the complexity of the related problems.…”

Section: Introductionmentioning

confidence: 89%

Complexity of manipulation and bribery in judgment aggregation for uniform premise-based quota rules

Baumeister

Erdélyi

et al. 2015

Mathematical Social Sciences

Self Cite

View full text Add to dashboard Cite

“…Manipulation is not the only type of strategic behavior of interest in JA. Baumeister et al (2011) have initiated a study of the computational complexity of related problems in JA, namely bribery and control problem. For the former, we ask whether a given budget suffices to bribe sufficiently many judges to obtain a particular outcome.…”

Section: Bibliographic Notes and Further Readingmentioning

confidence: 99%