Strict (m,1)-Ferrers properties

The transitivity of a preference relation is a traditional tenet of rationality in economic theory. However, several weakenings of transitivity have proven to be extremely useful in applications, giving rise to the notions of interval orders and semiorders among others. Strict (m, 1)-Ferrers properties go in this direction, classifying asymmetric preferences on the basis of their degree of transitivity, which becomes generally weaker as m gets larger. We show that strict (m, 1)-Ferrers properties can be arranged into a poset contained in the reverse ordering of the natural numbers. Our main result completely describes this poset. Although this paper has a combinatorial flavor, the topic of Ferrers properties is suited to applications in economics and psychology, for instance in relation to money-pump phenomena.