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Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation

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Abstract

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions.

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References

  • Baral C., Kraus S., Minker J., Subrahmanian V.S. (1992). Combining knowledge bases consisting of first-order theories. Computational Intelligence, 8(1): 45–71

    Google Scholar 

  • Benferhat S., Dubois D., Prade H., Williams M.A. (1999). A practical approach to fusing prioritized knowledge bases. EPIA, 1999: 223–236

    Google Scholar 

  • Borgida A., Imielinski T. (1984). Decision making in committees: A framework for dealing with inconsistency and non-monotonocity. In Proceedings workshop on nonmonotonic reasoning (pp. 21–32).

  • Bovens L., Rabinowicz W. (2006). Democratic answers to complex questions An epistemic. Synthese, 150, 131–153

    Article  Google Scholar 

  • Brams S.J., Kilgour D.M., Sanver M.R. (2004). A minimax procedure for negotiating multilateral treaties. preprint Department of Politics, New York University

    Google Scholar 

  • Brennan G. (2001). Collective coherence?. International Review of Law and Economics, 21(2): 197–211

    Article  Google Scholar 

  • Chapman B. (1998). More easily done than said: Rules, reason and rational choice. Oxford Journal of Legal Studies, 18: 293–330

    Article  Google Scholar 

  • Chapman B. (2002). Rational aggregation. Politics, Philosophy and Economics, 1(3): 337–354

    Google Scholar 

  • Cholvy L. (1994). A logical approach to multi-sources reasoning. In: Masuch M., Polos L. (Eds), Knowledge representation and reasoning under uncertainty: Logic at work. Springer, LNAI 808, pp. 183–196

    Google Scholar 

  • Dietrich F. (2006). Judgment aggregation: (Im)possibility theorems. Journal of Economic Theory, 126(1): 286–298

    Article  Google Scholar 

  • Dietrich F., List C. (2004). A liberal paradox for judgment aggregation. Economics Working Paper Archive at WUSTL, http://ideas.repec.org/p/wpa/wuwppe/0405003.html

  • Dietrich F., List C. (2006). Arrow’s theorem in judgment aggregation. Social Choice and Welfare, forthcoming.

  • Dokow E., Holzman R. (2005). Aggregation of binary evaluations, Working paper, Technion, Israel. http://personal.lse.ac.uk/LIST/doctrinalparadox.htm

  • Eckert D., Pigozzi G. (2005). Belief merging, judgment aggregation, and some links with social choice theory. In J. Delgrande J. Lang H. Rott, J. M. Tallon, (Eds.), Belief change in rational agents: Perspectives from artificial intelligence, philosophy, and economics, Dagstuhl Seminar Proceedings 05321, Internationales Begegnungs- und Forschungszentrum (IBFI), http://drops. dagstuhl.de/opus/volltexte/2005/333/pdf/05321.PigozziGabriella1.Paper.333.pdf

  • Elster J. (Ed.). (1998). Deliberative democracy. Cambridge University Press.

  • Gärdenfors P. (1988). Knowledge in flux: Modeling the dynamics of epistemic states. The MIT Press.

  • Gärdenfors P. (2005). An Arrow-like theorem for voting with logical consequences. Economics and Philosophy, forthcoming.

  • Konieczny S. (1999). Sur la Logique du Changement: Révision et Fusion de Bases de Connaissance, Ph.D. dissertation, University of Lille I, France.

  • Konieczny S. (2000). On the difference between merging knowledge bases and combinig them. In Proceedings of KR’00 (pp. 135–144). Morgan Kaufmann, Breckenridge, Colorado, USA.

  • Konieczny S., Lang J., Marquis P. (2004). DA2 merging operators. Artificial Intelligence, 157: 49–79

    Article  Google Scholar 

  • Konieczny S., Pino-Pérez R. (1998). On the logic of merging. In Proceedings of KR’98 Morgan Kaufmann.

  • Konieczny S., Pino-Pérez R. (1999). Merging with integrity constraints. In Proceedings of (pp. 233–244). LNAI 1638.

  • Konieczny S., Pino-Pérez R. (2002a). Merging information under constraints: A logical framework. Journal of Logic and Computation, 12(5): 773–808

    Article  Google Scholar 

  • Konieczny S., Pino-Pérez R. (2002b). On the frontier between arbitration and majority. In Proceedings of the eight international conference on principles of knowledge representation and reasoning (KR ’02) (pp. 109–118).

  • Konieczny S., Pino-Pérez R. (2005). Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory. European Journal of Operational Research, 160(3): 785–802

    Article  Google Scholar 

  • Kornhauser L.A. (1992). Modeling collegial courts II. Legal doctrine. Journal of Law, Economics and Organization, 8, 441–470

    Google Scholar 

  • Kornhauser L.A., Sager L.G. (1986). Unpacking the court. Yale Law Journal, 96, 82–117

    Article  Google Scholar 

  • Kornhauser L.A., Sager L.G. (1993). The one and the many: Adjudication in collegial courts. California Law Review, 81, 1–51

    Google Scholar 

  • Kowalski R. (1978). Logic for data description. In: Minker H.G.J., (Ed), Logic and data bases. New York, Plenum, pp. 77–102

    Google Scholar 

  • Liberatore P., Schaerf M. (2000). Brels: A system for the integration of knowledge bases. In Proceedings of KR 2000 (pp. 145–152).

  • Lin J. (1996). Integration of weighted knowledge bases. Artificial Intelligence, 83, 363–378

    Article  Google Scholar 

  • Lin J., Mendelzon A. (1996). Merging databases under constraints. International Journal of Cooperative Information Systems, 7, 55–76

    Article  Google Scholar 

  • Lin J., Mendelzon A. (1999). Knowledge base merging by majority. In: Pareschi R., Fronhoefer B. (Eds), Dynamic worlds: From the frame problem to knowledge management. Kluwer.

  • List C. (2005). The probability of inconsistencies in complex collective decisions. Social Choice and Welfare, 24(1): 3–32

    Article  Google Scholar 

  • List C. (2006a). Judgment aggregation—A bibliography on the discursive dilemma, the doctrinal paradox and decisions on multiple propositions. http://personal.lse.ac.uk/LIST/doctrinalparadox.htm

  • List C. (2006b). The discursive dilemma and public reason. Ethics, 116(2): 362–402

    Article  Google Scholar 

  • List C., Pettit P. (2002). Aggregating sets of judgments. An impossibility result. Economics and Philosophy, 18, 89–110

    Google Scholar 

  • List C., Pettit P. (2004). Aggregating sets of judgments. Two impossibility results compared. 140, 207–235

    Google Scholar 

  • Maynard-Reid P., Shoham Y. (1998). From belief revision to belief fusion. In Proceedings of the third conference on logic and the foundations of game and decision theory (LOFT3), ICER, Torino, Italy.

  • Nehring K., Puppe C. (2005). Consistent judgment aggregation: A characterization. Working paper. University of Karlsruhe.

  • Pauly M., van Hees M. (2006). Logical constraints on judgment aggregation. Journal of Philosophical Logic, 35

  • Pettit P. (2001). Deliberative democracy and the discursive dilemma. Philosophical Issues, 11, 268–299

    Article  Google Scholar 

  • Pigozzi G. (2005). Two aggregation paradoxes in social decision making: The Ostrogorski paradox and the discursive dilemma. Episteme: A Journal of Social Epistemology, 2(2): 33–42

    Article  Google Scholar 

  • Reiter R. (1988). On integrity constraints. In: Vardi M.Y. (Eds), Proceedings of the second conference on the theoretical aspects of reasoning about knowledge. San Francisco Calif, Morgan Kaufmann, pp. 97–111

    Google Scholar 

  • Revesz P. (1997). On the semantics of arbitration. International Journal of Algebra and Computation, 7(2): 133–160

    Article  Google Scholar 

Download references

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  1. Department of Computer Science, King’s College London, Strand, WC2R 2LS, London, UK

    Gabriella Pigozzi

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  1. Gabriella Pigozzi
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Pigozzi, G. Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152, 285–298 (2006). https://doi.org/10.1007/s11229-006-9063-7

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