Judgment aggregation functions and ultraproducts
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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- 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.
- Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
- 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.
- Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
- Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
- Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
- 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.
- Franz Dietrich & Christian List, 2010.
"Majority voting on restricted domains,"
LSE Research Online Documents on Economics
27902, London School of Economics and Political Science, LSE Library.
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