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Rankings and ratings are commonly used to express preferences but providedistinct and complementary information. Rankings give ordinal and scale-freecomparisons but lack granularity; ratings provide cardinal and granularassessments but may be highly subjective or inconsistent. Collecting andanalyzing rankings and ratings jointly has not been performed until recentlydue to a lack of principled methods. In this work, we propose a flexible, jointstatistical model for rankings and ratings under heterogeneous preferences: theBradley-Terry-Luce-Binomial (BTL-Binomial). We employ a Bayesian mixture offinite mixtures (MFM) approach to estimate heterogeneous preferences,understand their inherent uncertainty, and make accurate decisions based onranking and ratings jointly. We demonstrate the efficiency and practicality ofthe BTL-Binomial MFM approach on real and simulated datasets of ranking andrating preferences in peer review and survey data contexts.

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