# Non-Parametric Bayesian Inference for Partial Orders with Ties from Rank Data observed with Mallows Noise

arXiv: https://arxiv.org/abs/2408.14661 · HTML: https://mlsanity.com/paper/2408.14661/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [Hierarchical Partial-Order Models for Ranking](https://mlsanity.com/paper/2606.25062/) (2026)

## Abstract (arXiv)

Partial orders may be used for modeling and summarising ranking data when the underlying order relations are less strict than a total order. They are a natural choice when the data are lists recording individuals' positions in queues in which queue order is constrained by a social hierarchy, as it may be appropriate to model the social hierarchy as a partial order and the lists as random linear extensions respecting the partial order. In this paper, we set up a new prior model for partial orders incorporating ties by clustering tied actors using a Poisson Dirichlet process. The family of models is projective. We perform Bayesian inference with different choices of noisy observation model. In particular, we propose a Mallow's observation model for our partial orders and give a recursive likelihood evaluation algorithm. We demonstrate our model on the 'Royal Acta' (Bishop) list data where we find the model is favored over well-known alternatives which fit only total orders.