Computing Tournament Solutions using Relation Algebra and RelView

Autor: Agnieszka Rusinowska, Rudolf Berghammer, Harrie de Swart
Přispěvatelé: Institut für Informatik, Christian-Albrechts-Universität zu Kiel (CAU), Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Department of Philosophy, Erasmus University Rotterdam, Ce travail a bénéficié d'une aide de l'Etat gérée par l'Agence Nationale de la Recherche au titre du programme ' Investissements d'avenir ' portant la référence ANR-10-LABX-93-01. This work was supported by the French National Research Agency, through the program Investissements d'Avenir, ANR-10--LABX-93-01., European Science Foundation EUROCORES Programme - LogICCC, Erasmus School of Philosophy
Rok vydání: 2013
Předmět:
Mathematical optimization
Information Systems and Management
Theoretical computer science
General Computer Science
Computer science
Management Science and Operations Research
Schwartz set
Industrial and Manufacturing Engineering
Set (abstract data type)
RelView
JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation Modeling
0502 economics and business
JEL: C - Mathematical and Quantitative Methods/C.C8 - Data Collection and Data Estimation Methodology • Computer Programs/C.C8.C88 - Other Computer Software
Tournament
050207 economics
relational algebra
Copeland set
Condorcet non-losers
top cycle
uncovered set
minimal covering set
Banks set
tournament equilibrium set
05 social sciences
Covering set
Relation algebra
JEL: D - Microeconomics/D.D7 - Analysis of Collective Decision-Making/D.D7.D71 - Social Choice • Clubs • Committees • Associations
[SHS.ECO]Humanities and Social Sciences/Economics and Finance
Modeling and Simulation
050206 economic theory
Game theory
Social choice theory
Tournament
relational algebra
RelView
Copeland set
Condorcet non-losers
Schwartz set
top cycle
uncovered set
minimal covering set
Banks set
tournament equilibrium set
Zdroj: European Journal of Operational Research
European Journal of Operational Research, Elsevier, 2013, 226 (3), pp.636-645. ⟨10.1016/j.ejor.2012.11.025⟩
European Journal of Operational Research, 3(226), 636-645. Elsevier
ISSN: 0377-2217
DOI: 10.1016/j.ejor.2012.11.025⟩
Popis: International audience; We describe a simple computing technique for the tournament choice problem. It rests upon 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.
Databáze: OpenAIRE
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