Abstract
Intelligent agents have to be able to merge inputs received from different sources in a coherent and rational way. Recently, several proposals have been made for the merging of structures in which it is possible to encode the preferences of sources [5,4,12,13,14,1]. Information merging has much in common with the goals of social choice theory: to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection it seems reasonable to require that any framework for the merging of information has to provide satisfactory ways of dealing with the problems raised in social choice theory. In this paper we investigate the link between the merging of epistemic states and two important results in social choice theory. We show that Arrow’s well-known impossibility theorem [2] can be circumvented when the preferences of sources are represented in terms of epistemic states. This is achieved by providing a consistent set of properties for merging from which Arrow-like properties can be derived. We extend this to a consistent framework which includes properties corresponding to the notion of being strategy-proof. The existence of such an extended framework can be seen as a circumvention of the impossibility result of Gibbard and Satterthwaite [8,17,18] and related results [6,3].
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
Preview
Unable to display preview. Download preview PDF.
References
H. Andreka, M. D. Ryan, and P.-Y. Schobbens. Operators and laws for combining preference relations. Journal of Logic and Computation (in print), 2001.
K. J. Arrow. Social choice and individual values (2nd edition). Wiley, New York, 1963.
S. Barberá, B. Dutta, and A. Sen. Strategyproof Social Choice Correspondences. Journal of Economic Theory (forthcoming), 2000.
S. Benferhat, D. Dubois, S. Kaci, and H. Prade. Encoding information in possibilistic logic: A general framework for rational syntactic merging. In Werner Horn, editor, ECAI2000. 14th European Conference on Artificial Intelligence, Amsterdam, 2000. IOS Press.
S. Benferhat, D. Dubois, H. Prade, and M-A. Williams. A Practical Approach to Fusing Prioritized Knowledge Bases. In Progress in Artificial Intelligence, volume 1695 of Lecture Notes In Artificial Intelligence, pages 222–236, Berlin, 1999. Springer-Verlag.
Jean-Pierre Benoit. Strategyproofness for Lotteries and When Ties are Permitted. Unpublished manuscript, Department of Economics, New York University, January 2000.
Didier Dubois, Jerome Lang, and Henri Prade. Possibilistic logic. In Handbook of Logic in Artificial Intelligence and Logic Programming, volume 3, pages 439–513. 1994.
Allan Gibbard. Manipulation of Voting Schemes: A General Result. Econometrica, 41(4):587–601, 1973.
J. S. Kelly. Arrow impossibility theorems. Series in economic theory and mathematical economics. Academic Press, New York, 1978.
Sébastien Konieczny and Ramón Pino-Pérez. On the logic of merging. In A. G. Cohn, L. Schubert, and S. C. Shapiro, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Sixth International Conference (KR’ 98), pages 488–498, San Francisco, California, 1998. Morgan Kaufmann.
Sébastien Konieczny and Ramón Pino-Pérez. Merging with Integrity Constraints. Unpublished manuscript, 1999.
C. Lafage and J. Lang. Logical representation of preferences for group decision making. In Proceedings of the 7th International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), San Mateo, CA, 2000. Morgan Kaufmann.
Thomas Meyer. Merging Epistemic States. In Riichiro Mizoguchi and John Slaney, editors, PRICAI2000: Topics in Artificial Intelligence, volume 1886 of Lecture Notes In Artificial Intelligence, pages 286–296, Berlin, 2000. Springer-Verlag.
Thomas Meyer. On the semantics of combination operations. Journal of Applied Non-Classical Logics (to appear), 2001.
Thomas Meyer, Aditya Ghose, and Samir Chopra. Context-based merging. In Common Sense 2001: Fifth symposium on logical formalizations of commonsense reasoning, 2001.
Thomas Meyer, Aditya Ghose, and Samir Chopra. Syntactic representations of semantic merging operations. In IJCAI’01 Workshop on Inconsistency in Data and Knowledge, 2001.
Mark Satterthwaite. The Existence of a Strategy Proof Voting Procedure: a Topic in Social Choice Theory. PhD thesis, University of Wisconson, 1973.
Mark Satterthwaite. Strategy-proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions. Journal of Economic Theory, 10(2):187–217, 1975.
Amartya Sen. Social choice theory. In K. J. Arrow and M. D. Intriligator, editors, Handbook of Mathematical Economics, volume III, chapter 22, pages 1073–1181. Elsevier Science Publishers, 1986.
Wolfgang Spohn. Ordinal conditional functions: A dynamic theory of epistemic states. In William L. Harper and Brian Skyrms, editors, Causation in Decision: Belief Change and Statistics: Proceedings of the Irvine Conference on Probability and Causation: Volume II, pages 105–134, Dordrecht, 1988. Kluwer Academic Publishers.
Mary-Anne Williams. Iterated theory base change: a computational model. In IJCAI-95. Proceedings of the 14th International Joint Conference on Artificial Intelligence, volume 2, pages 1541–1547, San Francisco, CA, 1995. International Joint Conference on Artificial Intelligence, Morgan Kaufmann.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meyer, T., Ghose, A., Chopra, S. (2001). Social Choice, Merging, and Elections. In: Benferhat, S., Besnard, P. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Lecture Notes in Computer Science(), vol 2143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44652-4_41
Download citation
DOI: https://doi.org/10.1007/3-540-44652-4_41
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42464-2
Online ISBN: 978-3-540-44652-1
eBook Packages: Springer Book Archive