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Synthese

, Volume 173, Issue 2, pp 199–210 | Cite as

Ranking judgments in Arrow’s setting

  • Daniele Porello
Open Access
Article

Abstract

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit (Synthese 140(1–2):207–235, 2004). Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments proved in List and Pettit (Economics and Philosophy 18:89–110, 2002) and Arrow’s theorem (Arrow, Social choice and individual values, 1963). I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit (Synthese 140(1–2):207–235, 2004) to the conditions on the aggregation procedure.

Keywords

Arrow’s theorem Conodorcet’s paradox Discursive dilemma Aggregation of ranking judgments First order logic 

Notes

Acknowledgments

I wish to thank Valeria Ottonelli for the invaluable discussions. I also thank an anonymous referee for the very helpful comments on notation.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Arrow K. (1963) Social choice and individual values. Wiley, New YorkGoogle Scholar
  2. Dietrich F. (2007) A generalized model of judgment aggregation. Social Choice and Welfare 28(4): 529–565CrossRefGoogle Scholar
  3. Dietrich F., List C. (2007) Arrow’s theorem in judgment aggregation. Social Choice and Welfare 29(1): 19–33CrossRefGoogle Scholar
  4. Dryzek J., List C. (2003) Social choice theory and deliberative democracy: A reconciliation. British Journal of Political Science 33(1): 1–28CrossRefGoogle Scholar
  5. Kornhauser L.A. (1992) Modelling collegial courts. II. Legal doctrine. Journal of Law, Economics and Organization 8: 441–470Google Scholar
  6. Kornhauser L.A., Sager L.G. (1986) Unpacking the court. Yale Law Journal 96: 82–117CrossRefGoogle Scholar
  7. Kornhauser L.A., Sager L.G. (2004) Group choice in paradoxical cases. Philosophy and Public Affairs 32(3): 249–276CrossRefGoogle Scholar
  8. List C., Elsholtz C. (2005) A simple proof of Sen’s possibility theorem on majority decisions. Elemente der Mathematik 60: 45–56Google Scholar
  9. List C., Pettit P. (2002) Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18: 89–110Google Scholar
  10. List C., Pettit P. (2004) Aggregating sets of judgments: Two impossibility results compared. Synthese 140(1–2): 207–235CrossRefGoogle Scholar
  11. Ottonelli V. (2005) Errore deliberativo e legittimità democratica. Networks 5: 32–51Google Scholar
  12. Ottonelli, V. (2009). What does the discursive paradox really mean for democracy? Political Studies (forthcoming).Google Scholar
  13. Pauly M. (2007) Axiomatizing collective judgment sets in a minimal logical language. Synthese 158(2): 235–250CrossRefGoogle Scholar
  14. Pauly M., van Hees M. (2006) Logical constraints on judgment aggregation. Journal of Philosophical Logic 35: 569–585CrossRefGoogle Scholar
  15. Pettit, P. (2001). Deliberative democracy and the discursive dilemma. Philosophical Issues (supplement to Nous 39), 11, 268–299.Google Scholar
  16. Pigozzi G. (2006) Belief merging and the discursive dilemma: An argument-based account to paradoxes of judgment aggregation. Synthese 152(2): 285–298CrossRefGoogle Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Institute for Logic, Language and Computation (ILLC)University of AmsterdamAmsterdamThe Netherlands

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