Transitive convex subsets in large tournaments

A convex subset of vertices of a tournament T is such that any vertex not in the subset either dominates or is dominated by all of the vertices in the convex subset. Given a large tournament T, we explore the structure of T by looking for its transitive convex subsets. In a majority voting tournament some isolated inconsistencies may appear in such subsets. We propose a way to reveal such “nearly” transitive convex subsets. They are the subsets of a partition which optimizes the inertia of a geometrical embedding of T.