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

  • Dorothea Baumeister
  • Gábor Erdélyi
  • Jörg Rothe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6992)


Endriss et al. [1,2] initiated the complexity-theoretic study of problems related to judgment aggregation. We extend their results for manipulating two specific judgment aggregation procedures to a whole class of such procedures, and we obtain stronger results by considering not only the classical complexity (NP-hardness) but the parameterized complexity (W[2]-hardness) of these problems with respect to natural parameters. Furthermore, we introduce and study the closely related issue of bribery in judgment aggregation, inspired by work on bribery in voting (see, e.g., [3,4,5]. In manipulation scenarios one of the judges seeks to influence the outcome of the judgment aggregation procedure used by reporting an insincere judgment set. In bribery scenarios, however, an external actor, the briber, seeks to influence the outcome of the judgment aggregation procedure used by bribing some of the judges without exceeding his or her budget. We study three variants of bribery and show W[2]-hardness of the corresponding problems for natural parameters and for one specific judgment aggregation procedure. We also show that in certain special cases one can determine in polynomial time whether there is a successful bribery action.


Hardness Result Natural Parameter Collective Outcome Judgment Aggregation Collective Judgment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dorothea Baumeister
    • 1
  • Gábor Erdélyi
    • 2
  • Jörg Rothe
    • 1
  1. 1.Institut für InformatikUniversität DüsseldorfDüsseldorfGermany
  2. 2.SPMSNanyang Technological UniversitySingapore

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