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Judgment aggregation without full rationality

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  • Dietrich Franz
  • List Christian

    (METEOR)

Abstract

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only independent (i.e., propositionwise) aggregation rules generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain (strong) oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of rationality (compatible even with empty judgment sets). We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinstein''s group identification problem.

Suggested Citation

  • Dietrich Franz & List Christian, 2006. "Judgment aggregation without full rationality," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2006032
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    References listed on IDEAS

    as
    1. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    2. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    3. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, vol. 23(03), pages 269-300, November.
    4. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    5. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
    6. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    7. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    8. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    9. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    10. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    11. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
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    Keywords

    mathematical economics;

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