Multi-district preference modelling

Generating realistic artificial preference distributions is an important part of any simulation analysis of electoral systems. While this 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 an extension of the classic Eggenberger-P\'olya 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 intend to use it in further studies of electoral systems.