Judgment aggregation without full rationality

Abstract

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions 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 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.

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References

  1. Alchourron CE, Gärdenfors P, Makinson D (1985) On the logic of theory change: partial meet contraction and revision functions. J Symbolic Logic 50:510–530

    Article  Google Scholar 

  2. Dietrich F (2006) Judgment Aggregation: (Im)Possibility Theorems. J Econ Theory 126(1):286–298

    Article  Google Scholar 

  3. Dietrich F (2007) A generalised model of judgment aggregation. Soc Choice Welfare 28(4):529–565

    Article  Google Scholar 

  4. Dietrich F, List C (2007a) Arrow’s theorem in judgment aggregation. Soc Choice Welfare 29(1):19–33

    Article  Google Scholar 

  5. Dietrich F, List C (2007b) Judgment aggregation by quota rules: majority voting generalized. J Theor Polits 19(4) (in press)

  6. Dietrich F, List C (2007c) Strategy-proof judgment aggregation. Econ Philos (in press)

  7. Dokow E, Holzman R (2005) Aggregation of binary evaluations. Working paper, Technion Israel Institute of Technology

  8. Dokow E, Holzman R (2006) Aggregation of binary evaluations with abstentions. Working paper, Technion Israel Institute of Technology

  9. Gärdenfors P (2006) An Arrow-like theorem for voting with logical consequences. Econ Philos 22(2):181–190

    Article  Google Scholar 

  10. Kasher A, Rubinstein A (1997) On the Question “Who is a J?”: a social choice approach. Log Anal 160:385–395

    Google Scholar 

  11. Konieczny S, Pino-Perez R (2002) Merging information under constraints: a logical framework. J Logic Comput 12:773–808

    Article  Google Scholar 

  12. Kornhauser LA, Sager LG (1986) Unpacking the Court. Yale Law J 96(1):82–117

    Article  Google Scholar 

  13. List C (2004) A model of path-dependence in decisions over multiple propositions. Am Polit Sci Rev 98(3):495–513

    Article  Google Scholar 

  14. List C (2007) Which worlds are possible? A judgment aggregation problem. J Philosophical Logic (in press)

  15. List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18:89–110

    Google Scholar 

  16. List C, Pettit P (2004) Aggregating Sets of Judgments: Two Impossibility Results Compared. Synthese 140(1–2):207–235

    Article  Google Scholar 

  17. List C, Pettit P (2006) Group agency and supervenience. Southern J Philos XLIV (Spindel Supplement):85–105

    Article  Google Scholar 

  18. Mongin P (2005) Factoring out the impossibility of logical aggregation. Working paper, CNRS, Paris

  19. Nehring K (2003) Arrow’s theorem as a corollary. Econ Lette 80(3):379–382

    Article  Google Scholar 

  20. Nehring K, Puppe C (2002) Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between. Working paper, University of California at Davies

  21. Nehring K, Puppe C (2005) Consistent judgment aggregation: a characterization. Working paper, University of Karlsruhe

  22. Pauly M, van Hees M (2006) Logical constraints on judgment aggregation. J Philos Logic 35:569–585

    Article  Google Scholar 

  23. Pettit P (2001) Deliberative democracy and the discursive dilemma. Philos Issues 11:268–299

    Article  Google Scholar 

  24. Rubinstein A, Fishburn P (1986) Algebraic aggregation theory. J Econ Theory 38:63–77

    Article  Google Scholar 

  25. Samet D, Schmeidler D (2003) Between liberalism and democracy. J Econ Theory 110:213–233

    Article  Google Scholar 

  26. van Hees M (2007) The limits of epistemic democracy. Soc Choice Welfare 28(4):649–666

    Article  Google Scholar 

  27. Wilson R (1975) On the theory of aggregation. J Econ Theory 10:89–99

    Article  Google Scholar 

Download references

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Correspondence to Christian List.

Additional information

This paper was circulated in August 2006 and presented at the Yale workshop on Aggregation of Opinions, September 2006, at the Centre interuniversitaire de rechere en économie quantitative, Montreal, October 2006, and at the 1st International Workshop on Computational Social Choice, Amsterdam, December 2006. We are grateful to the participants at these occasions and the anonymous referees for comments. We also thank Ton Storcken for discussion. Elad Dokow and Ron Holzman have independently proved closely related results, which were also presented at the Yale workshop in September 2006, and circulated in the December 2006 paper (Dokow and Holzman 2006).

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Dietrich, F., List, C. Judgment aggregation without full rationality. Soc Choice Welfare 31, 15–39 (2008). https://doi.org/10.1007/s00355-007-0260-1

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Keywords

  • Aggregation Function
  • Full Rationality
  • Agenda Condition
  • Impossibility Result
  • Judgment Aggregation