IDEAS home Printed from https://ideas.repec.org/p/hit/piecis/427.html
   My bibliography  Save this paper

Decisive coalitions and coherence properties

Author

Listed:
  • Bossert, Walter
  • Suzumura, Kotaro
  • 鈴村, 興太郎
  • スズムラ, コウタロウ

Abstract

In a seminal contribution, Hansson has demonstrated that the family of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. If the population under consideration is infinite, his result implies the existence of nondictatorial social welfare functions. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We examine the structure of decisive coalitions and analogous concepts with alternative coherence properties, namely, acyclicity and Suzumura consistency, and without assuming that the social relation is complete.

Suggested Citation

  • Bossert, Walter & Suzumura, Kotaro & 鈴村, 興太郎 & スズムラ, コウタロウ, 2009. "Decisive coalitions and coherence properties," PIE/CIS Discussion Paper 427, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:piecis:427
    Note: This version: March 12, 2009
    as

    Download full text from publisher

    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/17297/pie_dp427.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
    2. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    3. Walter Bossert & Kotaro Suzumura, 2011. "Multi-profile intergenerational social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 493-509, September.
    4. Robert A. Pollak, 1979. "Bergson-Samuelson Social Welfare Functions and the Theory of Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(1), pages 73-90.
    5. repec:bla:econom:v:44:y:1977:i:173:p:81-88 is not listed on IDEAS
    6. Sen, Amartya K, 1979. "Personal Utilities and Public Judgements: Or What's Wrong with Welfare Economics?," Economic Journal, Royal Economic Society, vol. 89(355), pages 537-558, September.
    7. repec:bla:econom:v:43:y:1976:i:169:p:59-66 is not listed on IDEAS
    8. John Ferejohn & Talbot Page, 1978. "On the Foundations of Intertemporal Choice," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 60(2), pages 269-275.
    9. Robert P. Parks, 1976. "An Impossibility Theorem for Fixed Preferences: A Dictatorial Bergson-Samuelson Welfare Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 447-450.
    10. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    11. Edward Packel, 1980. "Impossibility results in the axiomatic theory of intertemporal choice," Public Choice, Springer, vol. 35(2), pages 219-227, January.
    12. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 611-630, April.
    13. Prasanta K. Pattanaik & Koichi Tadenuma & Yongsheng Xu & Naoki Yoshihara (ed.), 2008. "Rational Choice and Social Welfare," Studies in Choice and Welfare, Springer, number 978-3-540-79832-3, December.
    14. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    15. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
    16. Kotaro Suzumura, 1999. "Welfare Economics Beyond Welfarist-Consequentialism," Discussion Paper Series a382, Institute of Economic Research, Hitotsubashi University.
    17. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    18. repec:bla:econom:v:43:y:1976:i:172:p:381-90 is not listed on IDEAS
    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. Shino Takayama & Akira Yokotani, 2017. "Social choice correspondences with infinitely many agents: serial dictatorship," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 573-598, March.
    2. Walter Bossert & Kotaro Suzumura, 2012. "Quasi-transitive and Suzumura consistent relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 323-334, July.
    3. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    4. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 611-630, April.
    5. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.

    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. Bossert, Walter & Suzumura, Kotaro, 2012. "Product filters, acyclicity and Suzumura consistency," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 258-262.
    2. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    3. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    4. Walter Bossert & Kotaro Suzumura, 2011. "Multi-profile intergenerational social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 493-509, September.
    5. Walter Bossert & Kotaro Suzumura, 2012. "Multi-Profile Intertemporal Social Choice," Cahiers de recherche 09-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Susumu Cato, 2020. "Quasi-stationary social welfare functions," Theory and Decision, Springer, vol. 89(1), pages 85-106, July.
    7. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    8. Walter Bossert & Kotaro Suzumura, 2015. "Multi-Profile Intertemporal Social Choice: A Survey," Studies in Choice and Welfare, in: Constanze Binder & Giulio Codognato & Miriam Teschl & Yongsheng Xu (ed.), Individual and Collective Choice and Social Welfare, edition 127, pages 109-126, Springer.
    9. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    10. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    11. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    12. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
    13. Susumu Cato, 2013. "Alternative proofs of Arrow’s general possibility theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 131-137, November.
    14. Susumu Cato, 2022. "Stable preference aggregation with infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 287-304, August.
    15. Cato, Susumu, 2021. "Preference aggregation and atoms in measures," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    16. Noguchi, Mitsunori, 2011. "Generic impossibility of Arrow’s impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 391-400.
    17. Bossert, Walter & Cato, Susumu, 2021. "Superset-robust collective choice rules," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 126-136.
    18. Susumu Cato, 2015. "Conditions on social-preference cycles," Theory and Decision, Springer, vol. 79(1), pages 1-13, July.
    19. Kotaro Suzumura, 2020. "Reflections on Arrow’s research program of social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 219-235, March.
    20. John Weymark, 1984. "Arrow's theorem with social quasi-orderings," Public Choice, Springer, vol. 42(3), pages 235-246, January.

    More about this item

    Keywords

    Infinite-Population Social Choice; Decisiveness; Suzumura Consistency;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:hit:piecis:427. 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: Digital Resources Section, Hitotsubashi University Library (email available below). General contact details of provider: https://edirc.repec.org/data/cihitjp.html .

    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.