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Judgement aggregation functions and ultraproducts

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  • Herzberg, Frederik S.

Abstract

The relationship between propositional model theory and social decision making via premise-based procedures is explored. A one-to-one correspondence between ultrafilters on the population set and weakly universal, unanimity-respecting, systematic judgment aggregation functions is established. The proof constructs an ultraproduct of profiles, viewed as propositional structures, with respect to the ultrafilter of decisive coalitions. This representation theorem can be used to prove other properties of such judgment aggregation functions, in particular sovereignty and monotonicity, as well as an impossibility theorem for judgment aggregation in finite populations. As a corollary, Lauwers and Van~Liedekerke's (1995) representation theorem for preference aggregation functions is derived.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10546.

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Date of creation: 22 Jul 2008
Date of revision: 10 Sep 2008
Handle: RePEc:pra:mprapa:10546

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Keywords: Judgment aggregation function; ultraproduct; ultrafilter;

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  1. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, Elsevier, vol. 2(1), pages 103-106, March.
  2. Christian Klamler & Daniel Eckert, 2009. "A simple ultrafilter proof for an impossibility theorem in judgment aggregation," Economics Bulletin, AccessEcon, vol. 29(1), pages 319-327.
  3. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
  4. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, Elsevier, vol. 5(2), pages 267-277, October.
  5. G Rdenfors, Peter, 2006. "A Representation Theorem For Voting With Logical Consequences," Economics and Philosophy, Cambridge University Press, vol. 22(02), pages 181-190, July.
  6. Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 57-59, February.
  7. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 512-543, March.
  8. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
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Cited by:
  1. Christian Klamler & Daniel Eckert, 2009. "A simple ultrafilter proof for an impossibility theorem in judgment aggregation," Economics Bulletin, AccessEcon, vol. 29(1), pages 319-327.

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