A Generalized Model for Multidimensional Intransitivity

Abstract

Intransitivity is a critical issue in pairwise preference modeling. It refers to the intransitive pairwise preferences between a group of players or objects that potentially form a cyclic preference chain, and has been long discussed in social choice theory in the context of the dominance relationship. However, such multifaceted intransitivity between players and the corresponding player representations in high dimension are difficult to capture. In this paper, we propose a probabilistic model that joint learns the d-dimensional representation ($d > 1$) for each player and a dataset-specific metric space that systematically captures the distance metric in $\mathbb {R}^d$ over the embedding space. Interestingly, by imposing additional constraints in the metric space, our proposed model degenerates to former models used in intransitive representation learning. Moreover, we present an extensive quantitative investigation of the wide existence of intransitive relationships between objects in various real-world benchmark datasets. To the best of our knowledge, this investigation is the first of this type. The predictive performance of our proposed method on various real-world datasets, including social choice, election, and online game datasets, shows that our proposed method outperforms several competing methods in terms of prediction accuracy.