Multi-district preference modelling

Generating realistic artificial preference distributions is an important part of any simulation analysis of electoral systems, for example in trading off decisiveness and proportionality, or in the study of gerrymandering. While preference generation has been discussed in some detail in the context of a single electoral district, many electoral systems of interest are based on multiple districts. Neither treating preferences between districts as independent nor ignoring the district structure yields satisfactory results. We present a model based on a multi-urn extension of the classic Eggenberger-Pólya urn, in which each district is represented by an urn and there is correlation between urns. We show in detail that this procedure has a small number of tunable parameters, is computationally efficient, and produces “realistic-looking" distributions. We present several applications to retrospective analysis and forecasting of real elections.