Abstract
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.
This work was supported in part by DFG grant RO 1202/12-1 and the European Science Foundation’s EUROCORES program LogICCC. The second author was supported by National Research Foundation (Singapore) under grant NRF-RF 2009-08.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Endriss, U., Grandi, U., Porello, D.: Complexity of judgment aggregation: Safety of the agenda. In: Proceedings of the 9th International Joint Conference on Autonomous Agents and Multiagent Systems, IFAAMAS, pp. 359–366 (May 2010)
Endriss, U., Grandi, U., Porello, D.: Complexity of winner determination and strategic manipulation in judgment aggregation. In: Conitzer, V., Rothe, J. (eds.) Proceedings of the 3rd International Workshop on Computational Social Choice, Universität Düsseldorf, pp. 139–150 (September 2010)
Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: How hard is bribery in elections? Journal of Artificial Intelligence Research 35, 485–532 (2009)
Elkind, E., Faliszewski, P., Slinko, A.: Swap bribery. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 299–310. Springer, Heidelberg (2009)
Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Llull and Copeland voting computationally resist bribery and constructive control. Journal of Artificial Intelligence Research 35, 275–341 (2009)
List, C., Pettit, P.: Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18(1), 89–110 (2002)
List, C., Pettit, P.: Aggregating sets of judgments: Two impossibility results compared. Synthese 140(1-2), 207–235 (2004)
Kornhauser, L.A., Sager, L.G.: Unpacking the court. Yale Law Journal 96(1), 82–117 (1986)
Pettit, P.: Deliberative democracy and the discursive dilemma. Philosophical Issues 11, 268–299 (2001)
Bovens, L., Rabinowicz, W.: Democratic answers to complex questions – an epistemic perspective. Synthese 150(1), 131–153 (2006)
List, C.: The discursive dilemma and public reason. Ethics 116(2), 362–402 (2006)
Conitzer, V.: Making decisions based on the preferences of multiple agents. Communications of the ACM 53(3), 84–94 (2010)
Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.: Using complexity to protect elections. Communications of the ACM 53(11), 74–82 (2010)
Faliszewski, P., Procaccia, A.: AI’s war on manipulation: Are we winning? AI Magazine 31(4), 53–64 (2010)
Dietrich, F., List, C.: Strategy-proof judgment aggregation. Economics and Philosophy 23(3), 269–300 (2007)
Christian, R., Fellows, M., Rosamond, F., Slinko, A.: On complexity of lobbying in multiple referenda. Review of Economic Design 11(3), 217–224 (2007)
Erdélyi, G., Fernau, H., Goldsmith, J., Mattei, N., Raible, D., Rothe, J.: The complexity of probabilistic lobbying. In: Rossi, F., Tsoukias, A. (eds.) ADT 2009. LNCS, vol. 5783, pp. 86–97. Springer, Heidelberg (2009)
Dietrich, F., List, C.: Arrow’s theorem in judgment aggregation. Social Choice and Welfare 29(1), 19–33 (2007)
Dietrich, F., List, C.: Judgment aggregation by quota rules: Majority voting generalized. Journal of Theoretical Politics 19(4), 391–424 (2007)
Papadimitriou, C.: Computational Complexity, 2nd edn. Addison-Wesley, Reading (1995) Reprinted with corrections
Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baumeister, D., Erdélyi, G., Rothe, J. (2011). How Hard Is it to Bribe the Judges? A Study of the Complexity of Bribery in Judgment Aggregation. In: Brafman, R.I., Roberts, F.S., Tsoukiàs, A. (eds) Algorithmic Decision Theory. ADT 2011. Lecture Notes in Computer Science(), vol 6992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24873-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-24873-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24872-6
Online ISBN: 978-3-642-24873-3
eBook Packages: Computer ScienceComputer Science (R0)