# Statistical Models of Top-k Partial Orders

arXiv: https://arxiv.org/abs/2406.15893 · HTML: https://mlsanity.com/paper/2406.15893/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 22 Jun 2024.

## Builds on (most cited first, 4 of 4)

- [Algorithmic Monoculture and Social Welfare](https://mlsanity.com/paper/2101.05853/) (2021)
- [Modeling Assumptions Clash with the Real World: Transparency, Equity, and Community Challenges for Student Assignment Algorithms](https://mlsanity.com/paper/2101.10367/) (2021)
- [Learning Mixtures of Plackett-Luce Models from Structured Partial Orders](https://mlsanity.com/paper/1910.11721/) (2019)
- [A Distributed Method for Fitting Laplacian Regularized Stratified Models](https://mlsanity.com/paper/1904.12017/) (2019)

## Built on by (most cited first, 3 of 3)

- [Generalized Top-k Mallows Model for Ranked Choices](https://mlsanity.com/paper/2510.22040/) (2025)
- [A Differentiable Bayesian Relaxation for Latent Partial-Order Inference](https://mlsanity.com/paper/2605.06976/) (2026)
- [MoPLEx: Estimating Plackett-Luce Mixture Models for Multi-Objective Alignment](https://mlsanity.com/paper/2608.25200/) (2026)

## Abstract (arXiv)

In many contexts involving ranked preferences, agents submit partial orders over available alternatives. Statistical models often treat these as marginal in the space of total orders, but this approach overlooks information contained in the list length itself. In this work, we introduce and taxonomize approaches for jointly modeling distributions over top-k partial orders and list lengths k, considering two classes of approaches: composite models that view a partial order as a truncation of a total order, and augmented ranking models that model the construction of the list as a sequence of choice decisions, including the decision to stop. For composite models, we consider three dependency structures for joint modeling of order and truncation length. For augmented ranking models, we consider different assumptions on how the stop-token choice is modeled. Using data consisting of partial rankings from San Francisco school choice and San Francisco ranked choice elections, we evaluate how well the models predict observed data and generate realistic synthetic datasets. We find that composite models, explicitly modeling length as a categorical variable, produce synthetic datasets with accurate length distributions, and an augmented model with position-dependent item utilities jointly models length and preferences in the training data best, as measured by negative log loss. Methods from this work have significant implications on the simulation and evaluation of real-world social systems that solicit ranked preferences.