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The complexity of bribery and control in group identification

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Abstract

The goal of this paper is to analyze the complexity of constructive/destructive bribery and destructive control in the framework of group identification. Group identification applies to situations where a group of individuals determine who among them are socially qualified. We consider consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule. Each consent rule is characterized by two positive integers s and t, and the socially qualified individuals are determined as follows. If an individual qualifies herself, then she is socially qualified if and only if there are in total at least s individuals qualifying her. Otherwise, she is NOT socially qualified if and only if there are in total at least t individuals disqualifying her. The liberal (resp. consensus)-start-respecting rule determines the socially qualified individuals recursively. In the first step, all individuals qualifying themselves (resp. qualified by all individuals) are socially qualified. Then, the procedure recursively adds individuals who are not socially qualified but are qualified by at least one socially qualified individual into the set of socially qualified individuals until no one can be added this way.

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Notes

  1. A preliminary version of this paper appeared in the 6th International Workshop on Computational Social Choice (COMSOC 2016).

  2. In fact, the Vertex Cover instance constructed in the proof of the NP-hardness of the problem fulfills these assumptions (see pages 54 and 55 in [35]).

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Acknowledgements

This paper was supported by the DFG (Grant No. ER 738/2-1, ER 738/2-2), the National Natural Science Foundation of China (Grant No. 61702557), and the Postdoctoral Science Foundation of China (Grant No. 2017M612584). The paper was written in part while the first and second authors were affiliated at University of Siegen.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Gábor Erdélyi

  2. School of Economic Disciplines, University of Siegen, Siegen, Germany

    Christian Reger

  3. Chair of Economic Theory, Saarland University, Saarbrücken, Germany

    Yongjie Yang

  4. School of Computer Science and Engineering, Central South University, Changsha, China

    Yongjie Yang

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  1. Gábor Erdélyi
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Correspondence to Yongjie Yang.

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A preliminary version of this paper appeared in Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2017) [28].

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Erdélyi, G., Reger, C. & Yang, Y. The complexity of bribery and control in group identification. Auton Agent Multi-Agent Syst 34, 8 (2020). https://doi.org/10.1007/s10458-019-09427-9

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