IDEAS home Printed from https://ideas.repec.org/a/spr/reecde/v10y2006i3p167-181.html
   My bibliography  Save this article

Binary effectivity rules

Author

Listed:
  • Hans Keiding
  • Bezalel Peleg

Abstract

A social choice rule is a collection of social choice correspondences, one for each agenda. An effectivity rule is a collection of effectivity functions, one for each agenda. We prove that every monotonic and superadditive effectivity rule is the effectivity rule of some social choice rule. A social choice rule is binary if it is rationalized by an acyclic binary relation. The foregoing result motivates our definition of a binary effectivity rule as the effectivity rule of some binary social choice rule. A binary social choice rule is regular if it satisfies unanimity, monotonicity, and independence of infeasible alternatives. A binary effectivity rule is regular if it is the effectivity rule of some regular binary social choice rule. We characterize completely the family of regular binary effectivity rules. Quite surprisingly, intrinsically defined von Neumann-Morgenstern solutions play an important role in this characterization.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hans Keiding & Bezalel Peleg, 2006. "Binary effectivity rules," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 167-181, December.
  • Handle: RePEc:spr:reecde:v:10:y:2006:i:3:p:167-181
    DOI: 10.1007/s10058-006-0012-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10058-006-0012-1
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10058-006-0012-1?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. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650, October.
    3. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
    4. Mueller,Dennis C. (ed.), 1997. "Perspectives on Public Choice," Cambridge Books, Cambridge University Press, number 9780521553773, October.
    5. Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
    6. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
    7. Hans Keiding & Bezalel Peleg, 2002. "Representation of effectivity functions in coalition proof Nash equilibrium: A complete characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 241-263.
    8. repec:dau:papers:123456789/13220 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. Peleg, Bezalel & Peters, Hans, 2009. "Nash consistent representation of effectivity functions through lottery models," Games and Economic Behavior, Elsevier, vol. 65(2), pages 503-515, March.
    2. Bezalel Peleg & Ron Holzman, 2017. "Representations of Political Power Structures by Strategically Stable Game Forms: A Survey," Games, MDPI, vol. 8(4), pages 1-17, October.
    3. Bezalel Peleg & Shmuel Zamir, 2014. "Representation of constitutions under incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 279-302, October.
    4. Caroline Berden & Hans Peters, 2006. "On the Effect of Risk Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 60(4), pages 359-370, June.

    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. Keiding, Hans & Peleg, Bezalel, 2006. "On the continuity of representations of effectivity functions," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 827-842, November.
    2. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic Social Choice. Stable Representations of Constitutions, Studies in choice and welfare, Springer, 2010, 154 pp," Post-Print hal-00666816, HAL.
    3. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic Social Choice. Stable Representations of Constitutions, Studies in choice and welfare, Springer, 2010, 154 pp," Post-Print hal-00666816, HAL.
    4. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 187-204.
    5. Bezalel Peleg, 2002. "Complete Characterization of Acceptable Game Forms by Effectivity Functions," Discussion Paper Series dp283, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. 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.
    7. Bezalel Peleg & Ariel Procaccia, 2010. "Implementation by mediated equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 191-207, March.
    8. Peleg, Bezalel, 2004. "Representation of effectivity functions by acceptable game forms: a complete characterization," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 275-287, May.
    9. Peleg, Bezalel & Peters, Hans, 2009. "Nash consistent representation of effectivity functions through lottery models," Games and Economic Behavior, Elsevier, vol. 65(2), pages 503-515, March.
    10. Murat R. Sertel & M. Remzi Sanver, 2004. "Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 331-347, April.
    11. Bezalel Peleg & Hans Peters, 2010. "Consistent voting systems with a continuum of voters," Studies in Choice and Welfare, in: Strategic Social Choice, chapter 0, pages 123-145, Springer.
    12. Abdou, Joseph & Keiding, Hans, 2009. "Interaction sheaves on continuous domains," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 708-719, December.
    13. Bezalel Peleg & Ron Holzman, 2017. "Representations of Political Power Structures by Strategically Stable Game Forms: A Survey," Games, MDPI, vol. 8(4), pages 1-17, October.
    14. 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.
    15. Ben McQuillin & Robert Sugden, 2011. "The representation of alienable and inalienable rights: games in transition function form," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 683-706, October.
    16. Bezalel Peleg & Ariel D Procaccia, 2007. "Mediators Enable Truthful Voting," Levine's Bibliography 843644000000000039, UCLA Department of Economics.
    17. Joseph Abdou, 2012. "Stability and index of the meet game on a lattice," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 775-789, November.
    18. Sinan Ertemel & Levent Kutlu & M. Remzi Sanver, 2015. "Voting games of resolute social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 187-201, June.
    19. Peters, H.J.M. & Schröder, M.J.W. & Vermeulen, A.J., 2013. "Ex post Nash consistent representation of effectivity functions," Research Memorandum 049, Maastricht University, Graduate School of Business and Economics (GSBE).
    20. Caroline Berden & Hans Peters, 2006. "On the Effect of Risk Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 60(4), pages 359-370, June.

    More about this item

    Keywords

    Social choice correspondences; Effectivity functions; Nakamura’s number; Von Neumann–Morgenstern solutions; D71;
    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:spr:reecde:v:10:y:2006:i:3:p:167-181. 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.