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We give a new class of models for time series data in which actors are listedin order of precedence. We model the lists as a realisation of a queue in whichqueue-position is constrained by an underlying social hierarchy. We model thehierarchy as a partial order so that the lists are random linear extensions. Weaccount for noise via a random queue-jumping process. We give a marginallyconsistent prior for the stochastic process of partial orders based on a latentvariable representation for the partial order. This allows us to introduce aparameter controlling partial order depth and incorporate actor-covariatesinforming the position of actors in the hierarchy.  We fit the model to witness lists from Royal Acta from England, Wales andNormandy in the eleventh and twelfth centuries. Witnesses are listed in orderof social rank, with any bishops present listed as a group. Do changes in theorder in which the bishops appear reflect changes in their personal authority?The underlying social order which constrains the positions of bishops withinlists need not be a complete order and so we model the evolving social order asan evolving partial order. The status of an Anglo-Norman bishop was at the timepartly determined by the length of time they had been in office. This entersour model as a time-dependent covariate. We fit the model, estimate partialorders and find evidence for changes in status over time. We interpret ourresults in terms of court politics. Simpler models, based on Bucket Orders andvertex-series-parallel orders, are rejected. We compare our results with atime-series extension of the Plackett-Luce model.

Bayesian inference for partial orders from random linear extensions: power relations from 12th Century Royal Acta