Unifying preference and judgment aggregation

ABSTRACT

The paper proposes a unification of the two main frameworks commonly used for the analysis of collective decision-making: the framework of preference aggregation, developed from the seminal work of K. Arrow on social choice theory; and the more recent framework of judgment aggregation. Such unification provides several original insights on collective decision-making problems. The methods used are based on logic and, in particular, on formal semantics.

REFERENCES

• 1: K. Arrow. Social Choice and Individual Values. John Wiley, New York, 2nd edition, 1963.
• 2: S. J. Brams and P. C. Fishburn. Approval voting. The American Political Science Review, 72(3):831--847, 1978.
• 3: Yann Chevaleyre , Ulle Endriss , Jérôme Lang , Nicolas Maudet, A Short Introduction to Computational Social Choice, Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science, January 20-26, 2007, Harrachov, Czech Republic [doi>10.1007/978-3-540-69507-3_4]
• 4: G. Debreu. Representation of a preference ordering by a numerical function. In R. M. Thrall, C. H. Coombs, and R. L. Davis, editors, Decision Processes. John Wiley, 1954.
• 5: F. Dietrich and C. List. Arrow's theorem in judgment aggregation. Social Choice and Welfare, 29(19--33), 2007.
• 6: M. Dummett. A propositional calculus with denumerable matrix. Journal of Symbolic Logic, 24(2):97--106, 1959.
• 7: W. Gaertner. A Primer in Social Choice Theory. Oxford University Press, 2006.
• 8: R. Hähnle. Advanced many-valued logics. In D. M. Gabbay and F. Guenther, editors, Handbook of Philosophical Logic, 2nd Edition, volume 2, pages 297--395. Kluwer, 2001.
• 9: P. Hájek. Making fuzzy description logics more general. Fuzzy Sets and Systems, 154(1):1--15, 2005.
• 10: A. Horn. Logic with truth values in a linearly ordered Heyting algebra. Journal of Symbolic Logic, 34(3):395--408, 1969.
• 11: C. List and P. Pettit. Aggregating sets of judgments: Two impossibility results compared. Synthese, 140:207--235, 2004.
• 12: C. List and C. Puppe. Judgment aggregation: A survey. In Oxford Handbook of Rational and Social Choice. Oxford University Press, 2009.
• 13: A. K. Sen. The impossibility of a Paretian liberal. The Journal of Political Economy, 78:152--157, 1970.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
        I.2.11 Distributed Artificial Intelligence
            Subjects: Multiagent systems

General Terms:
Economics, Theory

Keywords:
collective decision-making, judgment aggregation, many-valued logic, preference aggregation, social-choice theory