Computing tournament solutions using relation algebra and RelView

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.