IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v47y2004i1p51-68.html
   My bibliography  Save this article

On two new social choice correspondences

Author

Listed:
  • Borm, Peter
  • van den Brink, Rene
  • Levinsky, Rene
  • Slikker, Marco

Abstract

Preferences of a set of n individuals over a set of alternatives can be represented by a preference profile being an n-tuple of preference relations over these alternatives.A social choice correspondence assigns to every preference profile a subset of alternatives that can be viewed as the `most prefered' alternatives by the society consisting of all individuals.Two new social choice correspondences are introduced and analyzed.Both are Pareto optimal and are refinements of the well known Top cycle correspondence in case the corresponding simple majority win digraph is a tournament.One of them even is such a refinement for arbitrary preference profiles.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract wa
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Borm, Peter & van den Brink, Rene & Levinsky, Rene & Slikker, Marco, 2004. "On two new social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 51-68, January.
    • Handle: RePEc:eee:matsoc:v:47:y:2004:i:1:p:51-68
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(03)00070-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gernot Grabher & Walter W. Powell (ed.), 2004. "Networks," Books, Edward Elgar Publishing, volume 0, number 2771.
    2. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
    3. Laffond G. & Laslier, J. F. & Le Breton, M., 1996. "Condorcet choice correspondences: A set-theoretical comparison," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 59-59, February.
    4. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    5. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2001. "Measuring the Power of Nodes in Digraphs," Discussion Paper 2001-72, Tilburg University, Center for Economic Research.
    6. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    7. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
    8. Gilbert Laffond & Jean Lainé & Jean-François Laslier, 1996. "Composition-consistent tournament solutions and social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 75-93, January.
    9. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2001. "Measuring the Power of Nodes in Digraphs," Tinbergen Institute Discussion Papers 01-096/1, Tinbergen Institute.
    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. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
    2. Marco Slikker & Peter Borm & René Brink, 2012. "Internal slackening scoring methods," Theory and Decision, Springer, vol. 72(4), pages 445-462, April.
    3. Marieke Quant & Peter Borm & Hans Reijnierse & Mark Voorneveld, 2003. "On a compromise social choice correspondence," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 311-324, December.
    4. Marieke Quant & Peter Borm & Hans Reijnierse & Mark Voorneveld, 2006. "A note on theβ-measure for digraph competitions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 167-176, June.
    5. Ayllon Aragon, Grisel, 2013. "On Weak Condorcet Winners: Existence and Uniqueness," MPRA Paper 53272, University Library of Munich, Germany.
    6. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & Voorneveld, M., 2002. "Characterizations of Solutions in Digraph Competitions," Other publications TiSEM f8406395-a31f-47b0-ab62-d, Tilburg University, School of Economics and Management.
    7. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & Voorneveld, M., 2006. "On the Beta measure for digraph competitions," Other publications TiSEM 214590f7-5605-42d6-8353-6, Tilburg University, School of Economics and Management.

    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. Laslier, Jean-Francois, 1996. "Rank-based choice correspondences," Economics Letters, Elsevier, vol. 52(3), pages 279-286, September.
    2. Laffond, Gilbert & Laine, Jean, 2000. "Representation in majority tournaments," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 35-53, January.
    3. Amer, Rafael & Gimenez, Jose Miguel & Magana, Antonio, 2007. "Accessibility in oriented networks," European Journal of Operational Research, Elsevier, vol. 180(2), pages 700-712, July.
    4. De Donder, Philippe & Le Breton, Michel & Truchon, Michel, 2000. "Choosing from a weighted tournament1," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 85-109, July.
    5. Scott Moser & John W. Patty & Elizabeth Maggie Penn, 2009. "The Structure of Heresthetical Power," Journal of Theoretical Politics, , vol. 21(2), pages 139-159, April.
    6. Mark Fey, 2008. "Choosing from a large tournament," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 301-309, August.
    7. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
    8. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    9. Marco Slikker & Peter Borm & René Brink, 2012. "Internal slackening scoring methods," Theory and Decision, Springer, vol. 72(4), pages 445-462, April.
    10. van den Brink, J.R. & Borm, P.E.M. & Hendrickx, R.L.P. & Owen, G., 2008. "Characterizations of the beta- and the degree network power measure," Other publications TiSEM 101ef139-cc05-4b30-bef5-1, Tilburg University, School of Economics and Management.
    11. Begoña Subiza & Josep Peris, 2005. "Condorcet choice functions and maximal elements," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 497-508, June.
    12. Josep E. Peris & Begoña Subiza, 2023. "Rational stability of choice functions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 580-598, September.
    13. Encarnacion Algaba & René van den Brink & Chris Dietz, 2015. "Power Measures and Solutions for Games under Precedence Constraints," Tinbergen Institute Discussion Papers 15-007/II, Tinbergen Institute.
    14. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    15. Daniel R. Carroll & Jim Dolmas & Eric Young, 2015. "Majority Voting: A Quantitative Investigation," Working Papers (Old Series) 1442, Federal Reserve Bank of Cleveland.
    16. Vincent Anesi, 2012. "A new old solution for weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 919-930, October.
    17. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    18. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    19. Daniel Carroll & Jim Dolmas & Eric Young, 2021. "The Politics of Flat Taxes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 174-201, January.
    20. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.

    More about this item

    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:eee:matsoc:v:47:y:2004:i:1:p:51-68. 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/inca/505565 .

    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.