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.