IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v116y2012i1p46-48.html
   My bibliography  Save this article

A note on the extension of a binary relation on a set to the power set

Author

Listed:
  • Cato, Susumu

Abstract

This paper is concerned with the problem of extending an antisymmetric binary relation on a set to a linear order on the power set. A necessary and sufficient condition is offered.

Suggested Citation

  • Cato, Susumu, 2012. "A note on the extension of a binary relation on a set to the power set," Economics Letters, Elsevier, vol. 116(1), pages 46-48.
    • Handle: RePEc:eee:ecolet:v:116:y:2012:i:1:p:46-48
    DOI: 10.1016/j.econlet.2011.12.074
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176511005970
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2011.12.074?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. Fishburn, Peter C., 1984. "Comment on the Kannai-Peleg impossibility theorem for extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 176-179, February.
    2. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    3. Eric S. Maskin, 2008. "Mechanism Design: How to Implement Social Goals," American Economic Review, American Economic Association, vol. 98(3), pages 567-576, June.
    4. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
    5. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, Spring.
    6. Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
    7. Barbera, Salvador & Pattanaik, Prasanta K., 1984. "Extending an order on a Set to the power set: Some remarks on Kannai and Peleg's approach," Journal of Economic Theory, Elsevier, vol. 32(1), pages 185-191, February.
    8. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    9. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    10. Holzman, Ron, 1984. "An extension of Fishburn's theorem on extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 192-196, February.
    11. 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. 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. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Ritxar Arlegi, 2001. "Rational Evaluation of Actions Under Complete Uncertainty," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0114, Departamento de Economía - Universidad Pública de Navarra.
    3. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 729-741, October.
    4. Bossert, Walter, 1997. "Uncertainty aversion in nonprobabilistic decision models," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 191-203, October.
    5. Bossert, Walter, 2000. "Opportunity sets and uncertain consequences1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 475-496, May.
    6. Walter Bossert & Kotaro Suzumura, 2012. "Revealed preference and choice under uncertainty," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 247-258, March.
    7. Walter Bossert, 1998. "Opportunity Sets and the Measurement of Information," Discussion Papers 98/6, University of Nottingham, School of Economics.
    8. Banerjee A., 1996. "Choice between opportunity sets: A characterization of welfarist behaviour," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 56-56, February.
    9. Ballester, Miguel A. & de Miguel, Juan R. & Nieto, Jorge, 2004. "Set comparisons in a general domain: the Indirect Utility Criterion," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 139-150, September.
    10. Nicolas Gravel & Thierry Marchant, 2022. "Rank Dependent Weighted Average Utility Models for Decision Making under Ignorance or Objective Ambiguity," Working Papers hal-03817362, HAL.
    11. Baharad, Eyal & Nitzan, Shmuel, 2003. "Essential alternatives and set-dependent preferences--an axiomatic approach," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 121-129, April.
    12. Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
    13. Walter Bossert & Marc Fleurbaey, 2015. "An Interview with Kotaro Suzumura," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 179-208, January.
    14. KayI, Çagatay & Ramaekers, Eve, 2010. "Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems," Games and Economic Behavior, Elsevier, vol. 68(1), pages 220-232, January.
    15. BOSSERT, Walter & SLINKO, Arkadii, 2004. "Relative Uncertainty and Additively Representable Set Rankings," Cahiers de recherche 2004-13, Universite de Montreal, Departement de sciences economiques.
    16. Kaushik Basu, 1996. "Bargaining with set-valued disagreement," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 61-74, January.
    17. Podinovski, Vladislav V., 2010. "Set choice problems with incomplete information about the preferences of the decision maker," European Journal of Operational Research, Elsevier, vol. 207(1), pages 371-379, November.
    18. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    19. Nieken, Petra & Schmitz, Patrick W., 2012. "Repeated moral hazard and contracts with memory: A laboratory experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1000-1008.
    20. Stefan Maus & Hans Peters & Ton Storcken, 2006. "Strategy-proof voting for single issues and cabinets," Public Choice, Springer, vol. 126(1), pages 27-43, January.

    More about this item

    Keywords

    Extension theorem; Power set; Suzumura consistency; Strategy-proofness;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:eee:ecolet:v:116:y:2012:i:1:p:46-48. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.