Modeling Stochastically Intransitive Relationships in Paired Comparison Data

Abstract

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence? We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to one another twice (i.e., home and away). We propose a novel linear model (CRSP) whose latent bilinear fixed effect allows us to estimate deviations from our transitive model (C).