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Nationwide inclusion and exclusion thresholds of representation

Abstract

The theoretical inclusion and exclusion thresholds are, respectively, the vote shares below which a party cannot possibly win a seat, and above which it cannot possibly fail to do so. They are important in evaluating how hospitable electorcal systems are to small parties. Previously, they have been calculated at the district level. Here the theory is extended to the national level. Surprisingly, the inclusion thresholds depends on the smallest district in the country-not the largest. The exclusion threshold depends on all districts. The theoretical results are compared to empirical observations for 23 electoral systems. The inclusion threshold is indeed close to the minimal vote share that ever led to a seat in the national assembly. In stark contrast, the exclusion threshold is much higher than the maximal vote share that ever failed to produce a seat in practice. The total number of districts emerges as a significant.

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