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Description: 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 a multi-urn extension of the classic Eggenberger-Polya 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 applications to retrospective analysis and forecasting of real elections, and intend to use the methodology to help set optimal parameters for electoral systems.
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