Skip to main content
SpringerLink
Log in

A generalised model of judgment aggregation

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements (“if P then Q ”) as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can be represented in it. This includes decision problems expressed in languages of standard propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bovens L, Rabinowicz W (2004) Democratic answers to complex questions – an epistemic perspective. Synthese (forthcoming)

  • Brennan G (2001) Collective coherence?. Int Rev Law Econ 21(2):197–211

    Article  Google Scholar 

  • Chapman B (1998) More easily done than said: rules, reason and rational social choice. Oxford J Legal Stud 18:293–329

    Article  Google Scholar 

  • Chapman B (2002) Rational aggregation. Polit Philos Econ 1(3):337–354

    Article  Google Scholar 

  • Dietrich F (2004) Judgment aggregation: (im)possibility theorems. J Econ Theory (forthcoming)

  • Dietrich F (2005) The possibility of judgment aggregation for network agendas. Working paper, University of Konstanz

  • Dietrich F, List C (2004a) Strategy-proof judgment aggregation. Working paper, London School of Economics

  • Dietrich F, List C (2004b) A liberal paradox for judgment aggregation. Working paper, London School of Economics

  • Dietrich F, List C (2005) Judgment aggregation by Quota Rules. Working paper, London School of Economics

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

  • Gärdenfors P (2004) An arrow-like theorem for voting with logical consequences. Working paper, Lund University

  • Gekker R (2003) A probability-based doxastic logic. Working paper, Department of Economics, NUI, Galway

  • Hintikka J (1971) Some main problems of deontic logic. In: Hilpinen R (eds). Deontic logic: introductory and systematic readings. D. Reidel, Dordrecht, pp. 59–104

    Google Scholar 

  • Kornhauser LA, Sager LG (1986) Unpacking the court. Yale Law J 96:82–117

    Article  Google Scholar 

  • Kripke S (1963) Semantical analysis of modal logic I: Normal propositional calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9:67–96

    Google Scholar 

  • Lewis D (1973) Counterfactuals. Basil Blackwell, Oxford

    Google Scholar 

  • List C (2003) A possibility theorem on aggregation over multiple interconnected propositions. Math Soc Sci 45(1):1–13

    Article  Google Scholar 

  • List C (2004a) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare (forthcoming)

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

    Article  Google Scholar 

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

    Google Scholar 

  • List C, Pettit P (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140(1–2):207–235

    Article  Google Scholar 

  • Mendelssohn E (1979) Introduction to mathematical logic. D. Van Nostrand

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

  • Nehring K (2003) Arrow’s theorem as a corollary. Econ Lett 80:379–382

    Article  Google Scholar 

  • 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

  • Nehring K, Puppe C (2004) Consistent judgement aggregation: a characterization. Working paper, University of Karlsruhe

  • Pauly M, van Hees M (2004) Logical constraints on judgment aggregation. J Philos Logic (forthcoming)

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

    Article  Google Scholar 

  • Pigozzi G (2004) Collective decision-making without paradoxes: an argument-based account. Working paper, King’s College, London

  • Priest G (2001) An introduction to non-classical logic. Cambridge University Press, Cambridge

    Google Scholar 

  • Stalnaker R (1968): A theory of conditionals. In: Rescher N. (eds). Studies in logical theory. Blackwell, Oxford

    Google Scholar 

  • van Hees M (2004) The limits of epistemic democracy. Working paper, University of Groningen

  • Wagner Decew J (1981) Conditional obligation and counterfactuals. J Philos Logic 10(1):55–72

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics, University of Maastricht, PO Box 616, Maastricht, 6200, MD, The Netherlands

    Franz Dietrich

Authors
  1. Franz Dietrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Franz Dietrich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dietrich, F. A generalised model of judgment aggregation. Soc Choice Welfare 28, 529–565 (2007). https://doi.org/10.1007/s00355-006-0187-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-006-0187-y

Keywords

Search

Navigation