Scissors beats Rock (and other failures of Transitive Models using Paired Comparisons)

Abstract

If the Utah Jazz beat the Portland Trailblazers and the Trailblazers beat the Denver Nuggets, does that mean that the Jazz are better than the Nuggets, or could the Nuggets actually be better than the Jazz? To answer this question, we investigate the assumption of transitivity. We propose a novel linear model (CRSP) whose latent bilinear fixed effect allows us to estimate deviations from our transitive model (C). Additionally, we consider extensions.