IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v39y2012i4p855-867.html
   My bibliography  Save this article

A measure of distance between judgment sets

Author

Listed:
  • Conal Duddy
  • Ashley Piggins

Abstract

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming’s metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in $${A \cap B}$$ jointly imply that the propositions in A−B share the same truth value, then the disagreement between A and B over those propositions in A−B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings. Copyright Springer-Verlag 2012

Suggested Citation

  • Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 855-867, October.
    • Handle: RePEc:spr:sochwe:v:39:y:2012:i:4:p:855-867
    DOI: 10.1007/s00355-011-0565-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-011-0565-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00355-011-0565-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    2. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    3. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    4. Dietrich, F.K. & List, C., 2009. "Propositionwise judgment aggregation," Research Memorandum 020, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    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. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    7. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    8. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    9. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    10. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    11. 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.
    12. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    13. Kornhauser, Lewis A, 1992. "Modeling Collegial Courts. II. Legal Doctrine," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 8(3), pages 441-470, October.
    14. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 575-601, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    2. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    3. García-Bermejo, Juan Carlos, 2013. "A Non-Proposition-Wise Variant of Majority Voting for Aggregating Judgments," Working Papers in Economic Theory 2013/02, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    4. Marcel Heidemann, 2018. "Judgment aggregation and minimal change: a model of consensus formation by belief revision," Theory and Decision, Springer, vol. 85(1), pages 61-97, July.
    5. G. Laffond & J. Lainé, 2013. "Unanimity and the Anscombe’s paradox," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 590-611, October.
    6. Conal Duddy & Ashley Piggins, 2012. "The proximity condition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 353-369, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    2. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    3. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    4. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    5. Bozbay, İrem & Dietrich, Franz & Peters, Hans, 2014. "Judgment aggregation in search for the truth," Games and Economic Behavior, Elsevier, vol. 87(C), pages 571-590.
    6. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    7. repec:hal:pseose:halshs-01249513 is not listed on IDEAS
    8. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    9. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    10. Zoi Terzopoulou & Ulle Endriss, 2020. "Neutrality and relative acceptability in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 25-49, June.
    11. Franz Dietrich & Kai Spiekermann, 2021. "Social Epistemology," PSE-Ecole d'économie de Paris (Postprint) halshs-02431971, HAL.
    12. Franz Dietrich & Christian List, 2024. "Dynamically rational judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(3), pages 531-580, November.
    13. Masaki Miyashita, 2021. "Premise-based vs conclusion-based collective choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 361-385, August.
    14. 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.
    15. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part one: general agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 747-786, April.
    16. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    17. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    18. Philippe Mongin, 2011. "Judgment aggregation," Working Papers hal-00579346, HAL.
    19. Luigi Marengo & Simona Settepanella & Yan X. Zhang, 2021. "Towards a unified aggregation framework for preferences and judgments," Evolutionary and Institutional Economics Review, Springer, vol. 18(1), pages 21-44, April.
    20. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    21. Baharad, Eyal & Neeman, Zvika & Rubinchik, Anna, 2020. "The rarity of consistent aggregators," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 146-149.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:39:y:2012:i:4:p:855-867. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.