Efficient Bayesian Inference for Benter Models on Ranked Data

Michael Pearce

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arXiv · 2608.23825

Efficient Bayesian Inference for Benter Models on Ranked Data

Michael Pearce

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Abstract

The Benter model for partial and complete rankings generalizes the well-known Plackett-Luce by attaching rank-level dampening parameters that permit some ranking stages to be noisier than others. This extension is empirically important for domains ranging from horse racing to ranked-choice elections. However, model fitting is made challenging by the fractional powers these dampening parameters introduce to the likelihood, breaking the conjugacy underlying existing Plackett-Luce samplers. This paper develops an efficient Bayesian estimation procedure for the Benter model. We introduce a two-part augmentation scheme using positive $\alpha$-stable and exponential auxiliary variables that linearizes the intractable normalizers in the Benter likelihood and yields closed-form Gibbs updates. A simulation study confirms efficient estimation, accurate parameter recovery, and nominal credible-interval coverage across sample sizes and item counts. We illustrate the algorithm on complete and partial rankings from survey preference and ranked-choice election datasets.

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BibTeX RIS

Michael Pearce. 2026-08-24. Efficient Bayesian Inference for Benter Models on Ranked Data. https://arxiv.org/abs/2608.23825

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