Judgment aggregation and minimal change: a model of consensus formation by belief revision
- 26 Downloads
When a group of agents attempts to reach an agreement on certain issues, it is usually desirable that the resulting consensus be as close as possible to the original judgments of the individuals. However, when these judgments are logically connected to further beliefs, the notion of closeness should also take into account to what extent the individuals would have to revise their entire belief set to reach an agreement. In this work, we present a model for generation of agreement with respect to a given agenda which allows individual epistemic entrenchment to influence the value of the consensus. While the postulates for the transformation function and their construction resemble those of AGM belief revision, the notion of an agenda is adapted from the theory of judgment aggregation. This allows our model to connect both frameworks.
KeywordsJudgment aggregation Belief revision Consensus formation Distance-based aggregation
I would like to thank Franz Dietrich and two anonymous referees very much for their detailed and constructive comments on an earlier version of this paper. I am very grateful to Olivier Roy for his extensive feedback and support. Part of this research has been supported by the DFG-GARC research project SEGA (RO 4548/6-1).
- Alchourrón, C. E., & Makinson, D. (1982). On the logic of theory change: Contraction functions and their associated revision functions. Theoria, 48(1), 14–37. https://doi.org/10.1111/j.1755-2567.1982.tb00480.x.CrossRefGoogle Scholar
- Chacón, J. L., & Pérez, R. P. (2012). Duality between merging operators and social contraction operators. In: Logic for programming, artificial intelligence, and reasoning. Springer, Berlin (pp. 183–196). https://doi.org/10.1007/978-3-642-28717-6 _16
- Dietrich, F., & List, C. (2016). Probabilistic opinion pooling. In A. Hájek & C. Hitchcock (Eds.), The Oxford handbook of probability and philosophy. Oxford: Oxford University Press.Google Scholar
- Everaere, P., Konieczny, S., & Marquis, P. (2015). Belief merging versus judgment aggregation. In Proceedings of the 2015 international conference on autonomous agents and multiagent systems (pp. 999–1007). Richland: International Foundation for Autonomous Agents and Multiagent Systems.Google Scholar
- Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of epistemic states. Massachusetts: MIT Press.Google Scholar
- Jeffrey, R. C. (1983). The logic of decision. Chicago: University of Chicago Press.Google Scholar
- Konieczny, S., & Pino Pérez, R. (2002). Merging information under constraints: A logical framework. Journal of Logic and Computation, 12(5), 773–808. https://doi.org/10.1093/logcom/12.5.773.
- Lang, J., Pigozzi, G., Slavkovik, M., & van der Torre, L. (2011). Judgment aggregation rules based on minimization . In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge. (pp. 238–246). New York: ACM Press. https://doi.org/10.1145/2000378.2000407.