# Learning Mixtures of Plackett-Luce Models

arXiv: https://arxiv.org/abs/1603.07323 · HTML: https://mlsanity.com/paper/1603.07323/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2016.

## Built on by (most cited first, 19 of 19)

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- [Learning Rich Rankings](https://mlsanity.com/paper/2312.15081/) (2023)
- [On the identifiability of mixtures of ranking models](https://mlsanity.com/paper/2201.13132/) (2022)
- [Efficient and Accurate Learning of Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/2302.05343/) (2023)
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- [Fast Learning of MNL Model from General Partial Rankings with Application to Network Formation Modeling](https://mlsanity.com/paper/2112.15575/) (2021)
- [Sharp analysis of EM for learning mixtures of pairwise differences](https://mlsanity.com/paper/2302.10066/) (2023)
- [When the Universe is Too Big: Bounding Consideration Probabilities for Plackett-Luce Rankings](https://mlsanity.com/paper/2401.11016/) (2024)
- [PLR: Plackett-Luce for Reordering In-Context Learning Examples](https://mlsanity.com/paper/2603.21373/) (2026)
- [Efficient and Accurate Top-K Recovery from Choice Data](https://mlsanity.com/paper/2206.11995/) (2022)
- [Leveraging Human Feedback for Semantically-Relevant Skill Discovery](https://mlsanity.com/paper/2604.24127/) (2026)
- [Population-Level Generative Modeling for Ranking Data](https://mlsanity.com/paper/2608.08422/) (2026)
- [MoPLEx: Estimating Plackett-Luce Mixture Models for Multi-Objective Alignment](https://mlsanity.com/paper/2608.25200/) (2026)

## Abstract (arXiv)

In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any k≥ 2, the mixture of k Plackett-Luce models for no more than 2k-1 alternatives is non-identifiable and this bound is tight for k=2. For generic identifiability, we prove that the mixture of k Plackett-Luce models over m alternatives is generically identifiable if k≤lfloorfrac m-2 2rfloor!. We also propose an efficient generalized method of moments (GMM) algorithm to learn the mixture of two Plackett-Luce models and show that the algorithm is consistent. Our experiments show that our GMM algorithm is significantly faster than the EMM algorithm by Gormley and Murphy (2008), while achieving competitive statistical efficiency.