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On the basis of a formula for calculating seat shares and natural thresholdsin multidistrict elections under the Jefferson-D'Hondt system and aprobabilistic model of electoral behavior based on P\'{o}lya's urn model, wepropose a new model of the relationship between the district magnitude and thenumber / effective number of relevant parties. We test that model on bothelectoral results from multiple countries employing the D'Hondt method(relatively small number of elections, but wide diversity of politicalconfigurations) and data based on hundreds of Polish local elections (largenumber of elections, but much higher degree of parameter uniformity). We alsoexplore some applications of the proposed model, demonstrating how it can beused to estimate the potential effects of electoral engineering.

A Formal Model of the Relationship between the Number of Parties and the District Magnitude