Abstract
Automated reasoning techniques for multi-agent scenarios need to address the possibility that procedures for collective decision making may fall prey to manipulation by self-interested agents. In this paper we study manipulation in the context of belief merging, a framework for aggregating agents’ positions, or beliefs, with respect to a set of issues represented by propositional atoms. Within this framework agents submit their positions as propositional formulas that are to be aggregated into a single formula. To reach a final decision, we employ well-established acceptance notions and extract the skeptical and credulous consequences (i.e., atoms true in all and, respectively, at least one model) of the resulting formula. We find that, even in restricted cases, most aggregation procedures are vulnerable to manipulation by an agent acting strategically, i.e., one that is able to submit a formula not representing its true position. Our results apply when the goal of such an agent is either that of (i) affecting an atom’s skeptical or credulous acceptance status, or (ii) improving its satisfaction with the result. With respect to latter task, we extend existing work on manipulation with new satisfaction indices, based on skeptical and credulous reasoning. We also study the extent to which an agent can influence the outcome of the aggregation, and show that manipulation can often be achieved by submitting a complete formula (i.e., a formula having exactly one model), yet, the complexity of finding such a formula resides, in the general case, on the second level of the polynomial hierarchy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We note that the notions of skeptical (cautious) and credulous (brave) consequences are not uniformly used throughout the literature. For instance, skeptical consequences may be defined as those consequences that follow (e.g., by classical logic) from all formulas in a set of formulas, and skeptical acceptance may refer to membership of an object in all sets of a given set of sets. We make use of the latter interpretation.
- 2.
As such, our indices can be interpreted as dissatisfaction indices; nevertheless we stick to the term satisfaction index.
References
Amanatidis, G., Barrot, N., Lang, J., Markakis, E., Ries, B.: Multiple referenda and multiwinner elections using Hamming distances: complexity and manipulability. In: Weiss, G., Yolum, P., Bordini, R.H., Elkind, E. (eds.) Proceedings of the AAMAS 2015, pp. 715–723. ACM (2015)
Barrot, N., Lang, J., Yokoo, M.: Manipulation of Hamming-based approval voting for multiple referenda and committee elections. In: Larson, K., Winikoff, M., Das, S., Durfee, E.H. (eds.) Proceedings of the AAMAS 2017, pp. 597–605. ACM (2017)
Baumeister, D., Erdélyi, G., Erdélyi, O.J., Rothe, J.: Complexity of manipulation and bribery in judgment aggregation for uniform premise-based quota rules. Math. Soc. Sci. 76, 19–30 (2015)
Baumeister, D., Rothe, J., Selker, A.K.: Strategic behavior in judgment aggregation. In: Endriss, U. (ed.) Trends in Computational Social Choice, pp. 145–168. AI Access (2017)
Brams, S.J., Kilgour, D.M., Sanver, M.R.: A minimax procedure for electing committees. Public Choice 132(3), 401–420 (2007)
Conitzer, V., Walsh, T.: Barriers to manipulation in voting. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice, pp. 127–145. Cambridge University Press, Cambridge (2016)
Delobelle, J., Haret, A., Konieczny, S., Mailly, J., Rossit, J., Woltran, S.: Merging of abstract argumentation frameworks. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) Proceedings of the KR 2016, pp. 33–42. AAAI Press (2016)
DĂaz, A.M., PĂ©rez, R.P.: Impossibility in belief merging. Artif. Intell. 251, 1–34 (2017)
Diaz, A.M., Perez, R.P.: Epistemic states, fusion and strategy-proofness. In: Ferme, E., Villata, S. (eds.) Proceedings of the NMR, pp. 176–185 (2018)
Endriss, U.: Judgment aggregation. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice, pp. 399–426. Cambridge University Press, Cambridge (2016)
Everaere, P., Konieczny, S., Marquis, P.: The strategy-proofness landscape of merging. J. Artif. Intell. Res. 28, 49–105 (2007)
Everaere, P., Konieczny, S., Marquis, P.: Belief merging versus judgment aggregation. In: Weiss, G., Yolum, P., Bordini, R.H., Elkind, E. (eds.) Proceedings of the AAMAS 2015, pp. 999–1007. ACM (2015)
Faliszewski, P., Procaccia, A.D.: AI’s war on manipulation: are we winning? AI Mag. 31(4), 53–64 (2010)
Faliszewski, P., Skowron, P., Slinko, A., Talmon, N.: Multiwinner voting: a new challenge for social choice theory. In: Endriss, U. (ed.) Trends in Computational Social Choice, pp. 27–47. AI Access (2017)
Gabbay, D.M., Rodrigues, O., Pigozzi, G.: Connections between belief revision, belief merging and social choice. J. Log. Comput. 19(3), 445–446 (2009)
Haret, A., Pfandler, A., Woltran, S.: Beyond IC postulates: classification criteria for merging operators. In: Kaminka, G.A., et al. (eds.) Proceedings of the ECAI 2016, pp. 372–380 (2016)
Haret, A., Wallner, J.P.: Manipulation of semantic aggregation procedures for propositional knowledge bases and argumentation frameworks. In: Ferme, E., Villata, S. (eds.) Proceedings of the NMR, pp. 146–155 (2018)
Haret, A., Wallner, J.P.: Manipulating skeptical and credulous consequences when merging beliefs. Technical report DBAI-TR-2019-114, TU Wien (2019). https://www.dbai.tuwien.ac.at/research/report/dbai-tr-2019-114.pdf
Konieczny, S., Lang, J., Marquis, P.: Distance based merging: a general framework and some complexity results. In: Fensel, D., Giunchiglia, F., McGuinness, D.L., Williams, M. (eds.) Proceedings of the KR 2002, pp. 97–108. Morgan Kaufmann (2002)
Konieczny, S., Lang, J., Marquis, P.: DA\(^{{2}}\) merging operators. Artif. Intell. 157(1–2), 49–79 (2004)
Konieczny, S., Pérez, R.P.: Logic based merging. J. Philosop. Log. 40(2), 239–270 (2011)
Lang, J., Xia, L.: Voting in combinatorial domains. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice, pp. 197–222. Cambridge University Press, Cambridge (2016)
Meir, R., Procaccia, A.D., Rosenschein, J.S., Zohar, A.: Complexity of strategic behavior in multi-winner elections. J. Artif. Intell. Res. 33, 149–178 (2008)
Strasser, C., Antonelli, G.A.: Non-monotonic logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, summer 2018 edn. (2018)
Zwicker, W.S.: Introduction to the theory of voting. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice, pp. 23–56. Cambridge University Press, Cambridge (2016)
Acknowledgements
We thank the anonymous reviewers for their helpful comments on an earlier version of the paper. This work was supported by the Austrian Science Fund (FWF): P30168-N31 and W1255-N23.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Haret, A., Wallner, J.P. (2019). Manipulating Skeptical and Credulous Consequences When Merging Beliefs. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-19570-0_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-19569-4
Online ISBN: 978-3-030-19570-0
eBook Packages: Computer ScienceComputer Science (R0)