Computing Tournament Solutions using Relation Algebra and REL VIEW
AbstractWe 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.
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Bibliographic InfoPaper 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.
Length: 21 pages
Date of creation: Oct 2011
Date of revision:
Tournament; relational algebra; REL VIEW; Copeland set; Condorcet non-losers; Schwartz set; top cycle; uncovered set; minimal covering set; Banks set; tournament equilibrium set.;
Find related papers by JEL classification:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-14 (All new papers)
- NEP-CMP-2011-11-14 (Computational Economics)
- NEP-GTH-2011-11-14 (Game Theory)
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.:
- Michel Grabisch & Agnieszka Rusinowska, 2008.
"A model of influence in a social network,"
Documents de travail du Centre d'Economie de la Sorbonne
b08066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00308741, HAL.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00344457, HAL.
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- Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
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