Social choice theory, belief merging, and strategy-proofness

Intelligent agents have to be able to merge informational inputs received from different sources in a coherent and rational way. Several proposals have been made for information merging in which it is possible to encode the preferences of sources [5,4,19,24,25,1]. Information merging has much in common with social choice theory, which aims to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection, frameworks for information merging should provide satisfactory resolutions of problems raised in social choice theory. We investigate the link between the merging of epistemic states and some results in social choice theory. This is achieved by providing a consistent set of properties-akin to those used in Arrow's theorem [2]-for merging. It is shown that in this framework there is no Arrow-like impossibility result. By extending this to a consistent framework which includes properties corresponding to the notion of being strategy-proof, we show that results due to Gibbard and Satterthwaite [13,31,32] and others [6,3] do not hold in merging frameworks.

[1]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

[2]  Hirofumi Katsuno,et al.  Propositional Knowledge Base Revision and Minimal Change , 1991, Artif. Intell..

[3]  B. Roy,et al.  L'aide multicritère à la décision , 1989 .

[4]  Mary-Anne Williams,et al.  Iterated Theory Base Change: A Computational Model , 1995, IJCAI.

[5]  Daniel Lehmann,et al.  Representing and Aggregating Conflicting Beliefs , 2000, KR.

[6]  L. Zadeh,et al.  An editorial perspective , 1978 .

[7]  Thomas Andreas Meyer,et al.  Social Choice, Merging, and Elections , 2001, ECSQARU.

[8]  Remo Pareschi,et al.  Dynamic Worlds: From the Frame Problems to Knowledge Management , 1999 .

[9]  K. Arrow.  Social Choice and Individual Values , 1951 .

[10]  Kenneth O. May,et al.  A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision , 1952 .

[11]  Thomas Andreas Meyer,et al.  Merging Epistemic States , 2000, PRICAI.

[12]  J. Kelly.  Arrow Impossibility Theorems , 1978 .

[13]  Arunava Sen,et al.  Strategy-proof Social Choice Correspondences , 2001, J. Econ. Theory.

[14]  Sébastien Konieczny,et al.  Merging information under constraints: a qualitative framework , 2007 .

[15]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[16]  Alberto O. Mendelzon,et al.  Knowledge Base Merging by Majority , 1999 .

[17]  H. S. M. Coxeter,et al.  Foundations of Geometry , 1962, Mathematical Gazette.

[18]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[19]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .

[20]  Sébastien Konieczny,et al.  Merging with Integrity Constraints , 1999, ESCQARU.

[21]  D. Dubois,et al.  Social choice axioms for fuzzy set aggregation , 1991 .

[22]  Didier Dubois,et al.  A Practical Approach to Fusing Prioritized Knowledge Bases , 1999, EPIA.

[23]  Sébastien Konieczny,et al.  On the Logic of Merging , 1998, KR.

[24]  Richard Booth,et al.  Social contraction and belief negotiation , 2002, Inf. Fusion.

[25]  Didier Dubois,et al.  Encoding Information Fusion in Possibilistic Logic: A General Framework for Rational Syntactic Merging , 2000, ECAI.

[26]  Sébastien Konieczny,et al.  Merging Information Under Constraints: A Logical Framework , 2002, J. Log. Comput..

[27]  Thomas Andreas Meyer.  On the semantics of combination operations , 2001, J. Appl. Non Class. Logics.

[28]  Jérôme Lang,et al.  Logical representation of preferences for group decision making , 2000, KR.

[29]  Peter Gärdenfors,et al.  Belief Revision , 1995 .

[30]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

[31]  Pierre-Yves Schobbens,et al.  Operators and Laws for Combining Preference Relations , 2002, J. Log. Comput..

[32]  H. Prade,et al.  Possibilistic logic , 1994 .

[33]  Thomas Andreas Meyer,et al.  Syntactic Representations of Semantic Merging Operations , 2002, PRICAI.

[34]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[35]  Peter Z. Revesz.  On the semantics of theory change: arbitration between old and new information , 1993, PODS '93.

[36]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[37]  A. Sen,et al.  Social Choice Theory , 1980 .