Advanced Search
MyIDEAS: Login to save this paper or follow this series

Computing Tournament Solutions using Relation Algebra and REL VIEW

Contents:

Author Info

  • Rudolf Berghammer

    ()
    (Institut für Informatik - Universität Kiel)

  • Agnieszka Rusinowska

    ()
    (Centre d'Economie de la Sorbonne)

  • Harrie de Swart

    ()
    (Faculty of Philosophy - Erasmus University Rotterdam)

Abstract

We describe a simple computing technique for the tournament choice problem. It rests upon a relational modeling and uses the BDD-based computer system RelView for the evaluation of the relation-algebraic expressions that specify the solutions and for the visualization of the computed results. The Copeland set can immediately be identified using RelView's labeling feature. Relation-algebraic specifications of the Condorcet non-losers, the Schwartz set, the top cycle, the uncovered set, the minimal covering set, the Banks set, and the tournament equilibrium set are delivered. We present an example of a tournament on a small set of alternatives, for which the above choice sets are computed and visualized via RelView. The technique described in this paper is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other problems of social choice and game theory.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2011/11067.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 11067.

as in new window
Length: 21 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:mse:cesdoc:11067

Contact details of provider:
Postal: 106-112 boulevard de l'Hôpital 75 647 PARIS CEDEX 13
Phone: + 33 44 07 81 00
Fax: + 33 1 44 07 83 01
Web page: http://centredeconomiesorbonne.univ-paris1.fr/
More information through EDIRC

Related research

Keywords: Tournament; relational algebra; REL VIEW; Copeland set; Condorcet non-losers; Schwartz set; top cycle; uncovered set; minimal covering set; Banks set; tournament equilibrium set.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Rudolf Berghammer & Agnieszka Rusinowska & Harrie de Swart, 2009. "Applying Relation Algebra and RelView to Measures in a Social Network," Working Papers 0902, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  2. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2009. "An Interdisciplinary Approach to Coalition Formation," Post-Print halshs-00406460, HAL.
  3. Bolus, Stefan, 2011. "Power indices of simple games and vector-weighted majority games by means of binary decision diagrams," European Journal of Operational Research, Elsevier, vol. 210(2), pages 258-272, April.
  4. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
  5. Elizabeth Penn, 2006. "Alternate Definitions of the Uncovered Set and Their Implications," Social Choice and Welfare, Springer, vol. 27(1), pages 83-87, August.
  6. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
  7. repec:hal:cesptp:halshs-00308741 is not listed on IDEAS
  8. repec:hal:cesptp:hal-00515878 is not listed on IDEAS
  9. Agnieszka Rusinowska & Harrie de Swart & Jan-Willem van der Rijt, 2005. "A new model of coalition formation," Social Choice and Welfare, Springer, vol. 24(1), pages 129-154, 09.
  10. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
  11. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
  12. John Duggan, 2011. "Uncovered Sets," Wallis Working Papers WP63, University of Rochester - Wallis Institute of Political Economy.
  13. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2007. "Applying relational algebra and RelView to coalition formation," European Journal of Operational Research, Elsevier, vol. 178(2), pages 530-542, April.
  14. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
  15. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
  16. repec:hal:journl:halshs-00308741 is not listed on IDEAS
  17. Deb, Rajat, 1977. "On Schwartz's rule," Journal of Economic Theory, Elsevier, vol. 16(1), pages 103-110, October.
  18. Nicolas Houy, 2009. "Still more on the Tournament Equilibrium Set," Social Choice and Welfare, Springer, vol. 32(1), pages 93-99, January.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:11067. 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: (Lucie Label).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.