Abstract: In rank-order data assessors give preference orders over choice sets. These can be thought of as permutations of the choice sets ordered by preference from best to worst. We call these permutations ``lists’’. Well known parametric models for list-data include the Mallows model and the Plackett-Luce model. These models seek a total order which is ``central’’ to the lists provided by the assessors. Extensions model the list-data as realisations of a mixture of distributions each centred on a total order. We give a model for list-data which is centred on a partial order. We give a prior over partial orders with several nice properties and explain how to carry out Bayesian inference for the unknown true partial order constraining the list-data. Model comparison favours the partial order model in all data sets we have looked at so far. However, evaluation of the likelihood costs #P. We give a model which admits scalable inference and a timeseries model for evolving partial orders. The timeseries model was motivated by queue-data informing an evolving social hierarchy, which we model as an evolving partial order.

(This is joint work with Kate Lee, Jessie Jiang, Nicholas Karn, David Johnson, Alexis Muir-Watt and Rukuang Huang.)