Computing tournament solutions using relation algebra and RelView

Rudolf Berghammer, Agnieszka Rusinowska, Harrie de Swart

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.

Highlights
► We apply relational algebra and RelView to the tournament choice problem. ► We deliver the relation-algebraic specifications of several choice sets. ► RelView evaluates the relation-algebraic expressions and visualizes the results. ► The method can be very useful to many problems of social choice and game theory.
Original languageEnglish
Pages (from-to)636-645
JournalEuropean Journal of Operational Research
Volume226
Issue number3
DOIs
Publication statusPublished - 2013
Externally publishedYes

Fingerprint

Relation Algebra
Game theory
Tournament
Algebra
Specifications
Computing
Labeling
Computer systems
Visualization
Algebraic Specification
Social Choice
Game Theory
Relational Algebra
Set Covering
Prototyping
Experimentation
Immediately
Cycle
Social choice theory
Choice sets

Cite this

Berghammer, Rudolf ; Rusinowska, Agnieszka ; de Swart, Harrie. / Computing tournament solutions using relation algebra and RelView. In: European Journal of Operational Research. 2013 ; Vol. 226, No. 3. pp. 636-645.
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Computing tournament solutions using relation algebra and RelView. / Berghammer, Rudolf; Rusinowska, Agnieszka; de Swart, Harrie.

In: European Journal of Operational Research, Vol. 226, No. 3, 2013, p. 636-645.

Research output: Contribution to journalArticleScientificpeer-review

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AU - de Swart, Harrie

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AB - 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.Highlights► We apply relational algebra and RelView to the tournament choice problem. ► We deliver the relation-algebraic specifications of several choice sets. ► RelView evaluates the relation-algebraic expressions and visualizes the results. ► The method can be very useful to many problems of social choice and game theory.

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