IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v41y2013i1p169-202.html
   My bibliography  Save this article

Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings

Author

Listed:
  • Susumu Cato

    ()

Abstract

The aim of the present paper is to provide an axiomatic analysis of incomplete social judgments. In particular, we clarify the underlying power structure of Arrovian collective choice rules when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness and investigate the properties of the collection of quasi-decisive sets associated with an Arrovian collective choice rule. In the course of this, we offer a series of applications. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:41:y:2013:i:1:p:169-202
    DOI: 10.1007/s00355-012-0677-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-012-0677-z
    Download Restriction: Access to full text is restricted to subscribers.

    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. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 185-192.
    2. Campbell, Donald E. & Kelly, Jerry S., 2000. "Weak independence and veto power," Economics Letters, Elsevier, vol. 66(2), pages 183-189, February.
    3. Kaushik Basu & Tapan Mitra, 2003. "Aggregating Infinite Utility Streams with InterGenerational Equity: The Impossibility of Being Paretian," Econometrica, Econometric Society, vol. 71(5), pages 1557-1563, September.
    4. Fleurbaey, Marc & Michel, Philippe, 2003. "Intertemporal equity and the extension of the Ramsey criterion," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 777-802, September.
    5. 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.
    6. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    7. Batteau, Pierre & Blin, Jean-Marie & Monjardet, Bernard, 1981. "Stability of Aggregation Procedures, Ultrafilters, and Simple Games," Econometrica, Econometric Society, vol. 49(2), pages 527-534, March.
    8. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    9. Brown, Donald J., 1974. "An approximate solution to Arrow's problem," Journal of Economic Theory, Elsevier, vol. 9(4), pages 375-383, December.
    10. Schmitz, Norbert, 1977. "A further note on arrow's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 189-196, August.
    11. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 89(3), pages 456-469.
    12. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Consistent Rationalizability," Economica, London School of Economics and Political Science, vol. 72(286), pages 185-200, May.
    13. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
    14. David Kelsey, 1984. "Acyclic Choice without the Pareto Principle," Review of Economic Studies, Oxford University Press, vol. 51(4), pages 693-699.
    15. Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, vol. 130(1), pages 283-295, September.
    16. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, December.
    17. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
    18. Susumu Cato, 2012. "Szpilrajn, Arrow And Suzumura: Concise Proofs Of Extension Theorems And An Extension," Metroeconomica, Wiley Blackwell, vol. 63(2), pages 235-249, May.
    19. 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.
    20. Pazner, Elisha A. & Wesley, Eugene, 1977. "Stability of social choices in infinitely large societies," Journal of Economic Theory, Elsevier, vol. 14(2), pages 252-262, April.
    21. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 381-393.
    22. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    23. 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.
    24. Amartya Sen, 2012. "The reach of social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 259-272, July.
    25. 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.
    26. Grafe, F. & Grafe, J., 1983. "On arrow-type impossibility theorems with infinite individuals and infinite alternatives," Economics Letters, Elsevier, vol. 11(1-2), pages 75-79.
    27. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    28. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-1256, July.
    29. Guha, Ashok, 1972. "Neutrality, Monotonicity, and the Right of Veto," Econometrica, Econometric Society, vol. 40(5), pages 821-826, September.
    30. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
    31. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
    32. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    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. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    2. Susumu Cato, 2014. "Independence of irrelevant alternatives revisited," Theory and Decision, Springer, vol. 76(4), pages 511-527, April.
    3. Cato, Susumu, 2015. "Weak independent decisiveness and the existence of a unique vetoer," Economics Letters, Elsevier, vol. 131(C), pages 59-61.
    4. repec:eee:mateco:v:71:y:2017:i:c:p:28-35 is not listed on IDEAS

    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:41:y:2013:i:1:p:169-202. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.