A Generalized Model for Multidimensional Intransitivity

TL;DR

This paper introduces a probabilistic model that captures complex multidimensional intransitive preferences, improving prediction accuracy in real-world datasets by jointly learning player representations and a dataset-specific metric space.

Contribution

It proposes a novel probabilistic model for high-dimensional intransitivity that unifies and extends previous models, with extensive empirical validation.

Findings

Model outperforms existing methods in prediction accuracy

First extensive quantitative study of intransitivity in real-world data

Effectively captures complex preference cycles in high-dimensional spaces

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 dimensions is difficult to capture. In this paper, we propose a probabilistic model that jointly learns each player's d-dimensional representation (d>1) and a dataset-specific metric space that systematically captures the distance metric in Rd 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 vast existence of intransitive relationships between objects in various real-world benchmark datasets. To our knowledge, this investigation is the first of this type. The predictive performance of our proposed method on different 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.