# On A Mallows-type Model For (Ranked) Choices

arXiv: https://arxiv.org/abs/2207.01783 · HTML: https://mlsanity.com/paper/2207.01783/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 28 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Builds on (most cited first, 2 of 2)

- [Concentric mixtures of Mallows models for top-k rankings: sampling and identifiability](https://mlsanity.com/paper/2010.14260/) (2020)
- [Learning Context-Dependent Choice Functions](https://mlsanity.com/paper/1901.10860/) (2019)

## Built on by (most cited first, 4 of 4)

- [Federated Aggregation of Mallows Rankings: A Comparative Analysis of Borda and Lehmer Coding](https://mlsanity.com/paper/2409.00848/) (2024)
- [Beyond Pairwise: Empowering LLM Alignment With Ranked Choice Modeling](https://mlsanity.com/paper/2510.23631/) (2025)
- [Mallows Model with Learned Distance Metrics: Sampling and Maximum Likelihood Estimation](https://mlsanity.com/paper/2507.08108/) (2025)
- [Joint Progression Modeling (JPM): A Probabilistic Framework for Mixed-Pathology Progression](https://mlsanity.com/paper/2512.03475/) (2025)

## Abstract (arXiv)

We consider a preference learning setting where every participant chooses an ordered list of k most preferred items among a displayed set of candidates. (The set can be different for every participant.) We identify a distance-based ranking model for the population's preferences and their (ranked) choice behavior. The ranking model resembles the Mallows model but uses a new distance function called Reverse Major Index (RMJ). We find that despite the need to sum over all permutations, the RMJ-based ranking distribution aggregates into (ranked) choice probabilities with simple closed-form expression. We develop effective methods to estimate the model parameters and showcase their generalization power using real data, especially when there is a limited variety of display sets.