Modeling Preferences: A Bayesian Mixture of Finite Mixtures for Rankings and Ratings

TL;DR

This paper introduces a Bayesian mixture model that jointly analyzes rankings and ratings to better understand heterogeneous preferences, providing a principled approach for combined preference data analysis.

Contribution

It proposes the BTL-Binomial Bayesian mixture of finite mixtures model for joint analysis of rankings and ratings, addressing a gap in preference modeling methods.

Findings

Efficiently models heterogeneous preferences in real and simulated data.

Improves decision-making accuracy by jointly analyzing rankings and ratings.

Demonstrates practical applicability in peer review and survey contexts.

Abstract

Rankings and ratings are commonly used to express preferences but provide distinct and complementary information. Rankings give ordinal and scale-free comparisons but lack granularity; ratings provide cardinal and granular assessments but may be highly subjective or inconsistent. Collecting and analyzing rankings and ratings jointly has not been performed until recently due to a lack of principled methods. In this work, we propose a flexible, joint statistical model for rankings and ratings under heterogeneous preferences: the Bradley-Terry-Luce-Binomial (BTL-Binomial). We employ a Bayesian mixture of finite mixtures (MFM) approach to estimate heterogeneous preferences, understand their inherent uncertainty, and make accurate decisions based on ranking and ratings jointly. We demonstrate the efficiency and practicality of the BTL-Binomial MFM approach on real and simulated datasets of ranking and rating preferences in peer review and survey data contexts.