Year: 2026
Type: preprint
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 $α$-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.
Source: arXiv (Cornell University)
Author: Pearce, Michael
Institution: Reed College
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204233146
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