IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v51y2018i3d10.1007_s00355-018-1129-1.html
   My bibliography  Save this article

Restricting the domain allows for weaker independence

Author

Listed:
  • Justin Kruger

    (Université Paris-Dauphine, PSL Research University, CNRS, UMR 7243, LAMSADE)

  • M. Remzi Sanver

    (Université Paris-Dauphine, PSL Research University, CNRS, UMR 7243, LAMSADE)

Abstract

Arrow’s classical axiom of independence of irrelevant alternatives may be more descriptively thought of as binary independence. This can then be weakened to ternary independence, quaternary independence, etc. It is known that under the full domain these are not real weakenings as they all collapse into binary independence (except for independence over the whole set of alternatives which is trivially satisfied). Here we investigate whether this still happens under restricted domains. We show that for different domains these different levels of independence may or may not be equivalent. We specify when and to what extent different versions of independence collapse into the same condition.

Suggested Citation

  • Justin Kruger & M. Remzi Sanver, 2018. "Restricting the domain allows for weaker independence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 563-575, October.
    • Handle: RePEc:spr:sochwe:v:51:y:2018:i:3:d:10.1007_s00355-018-1129-1
    DOI: 10.1007/s00355-018-1129-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-018-1129-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-018-1129-1?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    2. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, September.
    3. repec:bla:econom:v:38:y:1971:i:152:p:413-20 is not listed on IDEAS
    4. Rothstein, Paul, 1991. "Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
    5. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    6. Ugur Ozdemir & M. Sanver, 2007. "Dictatorial domains in preference aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 61-76, January.
    Full references (including those not matched with items on IDEAS)

    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. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    2. Donald Wittman, 2005. "Valence characteristics, costly policy and the median-crossing property: A diagrammatic exposition," Public Choice, Springer, vol. 124(3), pages 365-382, September.
    3. Guillaume Cheikbossian, 2016. "The political economy of (De)centralization with complementary public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 315-348, August.
    4. Martínez-Mora, Francisco & Puy, M. Socorro, 2014. "The determinants and electoral consequences of asymmetric preferences," European Journal of Political Economy, Elsevier, vol. 33(C), pages 85-97.
    5. Marco Bassetto & Jess Benhabib, 2006. "Redistribution, Taxes and the Median Voter," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 211-223, April.
    6. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    7. John Duggan, 2016. "Preference exclusions for social rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 93-118, January.
    8. Slinko, Arkadii & Wu, Qinggong & Wu, Xingye, 2021. "A characterization of preference domains that are single-crossing and maximal Condorcet," Economics Letters, Elsevier, vol. 204(C).
    9. Kruger, Justin & Remzi Sanver, M., 2018. "Which dictatorial domains are superdictatorial? A complete characterization for the Gibbard–Satterthwaite impossibility," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 32-34.
    10. Fan-chin Kung, 2005. "Formation of Collective Decision-Making Units: Stability and a Solution," Game Theory and Information 0505002, University Library of Munich, Germany, revised 21 Jun 2005.
    11. Puppe, Clemens & Slinko, Arkadii, 2024. "Maximal Condorcet domains. A further progress report," Games and Economic Behavior, Elsevier, vol. 145(C), pages 426-450.
    12. Puppe, Clemens & Slinko, Arkadii, 2022. "Maximal Condorcet domains: A further progress report," Working Paper Series in Economics 159, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    13. Clemens Puppe & Arkadii Slinko, 2019. "Condorcet domains, median graphs and the single-crossing property," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 285-318, February.
    14. Muhammad Mahajne & Oscar Volij, 2019. "Condorcet winners and social acceptability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 641-653, December.
    15. John Duggan, 2016. "Preference exclusions for social rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 93-118, January.
    16. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    17. Lê Nguyên Hoang, 2017. "Strategy-proofness of the randomized Condorcet voting system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 679-701, March.
    18. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    19. Martínez-Mora Francisco & Puy M. Socorro, 2012. "Asymmetric Single-peaked Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-26, December.
    20. Maurice Salles, 2006. "La théorie du choix social : de l'importance des mathématiques," Economics Working Paper Archive (University of Rennes & University of Caen) 200617, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.

    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:51:y:2018:i:3:d:10.1007_s00355-018-1129-1. 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.