An orderly algorithm for generation of Condorcet Domains

Abstract

Condorcet domains are fundamental objects in the theory of majority voting; they are sets of linear orders with the property that if every voter picks a linear order from this set, assuming that the number of voters is odd, and alternatives are ranked according to the pairwise majority ranking, then the result is a linear order on the set of all alternatives. In this paper we present an efficient orderly algorithm for the generation of all non-isomorphic maximal Condorcet domains on $n$ alternatives. The algorithm can be adapted to generate domains from various important subclasses of Condorcet domains. We use an example implementation to extend existing enumerations of domains from several such subclasses and make both data and the implementation publicly available.