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Abstract Arrowian aggregation

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  • Nehring, Klaus
  • Puppe, Clemens

Abstract

In a general framework of abstract binary aggregation, we characterize aggregation problems in terms of the monotone Arrowian aggregators they admit. Specifically, we characterize the problems that admit non-dictatorial, locally non-dictatorial, anonymous, and neutral monotone Arrowian aggregation, respectively. As a consequence of these characterizations, we also obtain new results on the possibility of strategy-proof social choice and the "concrete Arrowian" aggregation of preferences into a social ordering on generalized single-peaked domains.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 2 (March)
Pages: 467-494

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:2:p:467-494

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Judgement aggregation Social choice Non-dictatorship Local non-dictatorship Anonymity Neutrality Median spaces Median points Intersection property Conditional entailment Critical family;

References

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  1. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Series Working Papers 2002-W15, University of Oxford, Department of Economics.
  2. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  3. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
  4. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
  5. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  6. Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer, vol. 22(1), pages 45-62, 08.
  7. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  8. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  9. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
  10. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  11. Elad Dokow & Ron Holzman, 2009. "Aggregation of binary evaluations for truth-functional agendas," Social Choice and Welfare, Springer, vol. 32(2), pages 221-241, February.
  12. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  13. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
  14. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
  15. 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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Citations

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Cited by:
  1. Mongin, Philippe, 2011. "Judgment aggregation," Les Cahiers de Recherche 942, HEC Paris.
  2. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
  3. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Levine's Working Paper Archive 661465000000000006, David K. Levine.
  4. Mongin, Philippe, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," MPRA Paper 37752, University Library of Munich, Germany.
  5. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
  6. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.
  7. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
  8. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
  9. Dietrich, Franz, 2012. "Judgment aggregation and the discursive dilemma," MPRA Paper 36772, University Library of Munich, Germany.
  10. Dietrich, Franz, 2011. "Scoring rules for judgment aggregation," MPRA Paper 35657, University Library of Munich, Germany.
  11. Pivato, Marcus & Nehring, Klaus, 2010. "The McGarvey problem in judgement aggregation," MPRA Paper 22600, University Library of Munich, Germany.

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