Pot and ladle: a formula for estimating the distribution of seats under the Jefferson-D'Hondt method

摘要

We propose a simple yet new formula for estimating national seat shares and quantifying seat biases in elections employing the Jefferson-D'Hondt (JDH) method for seat allocation. It is based solely on the national vote shares and fixed parameters of the given electoral system. The proposed formula clarifies the relationship between seat bias on the one hand, and the number of parties and the number of districts on the other. We demonstrate that the formula provides a good estimate of seat allocations in real-life elections even in the case of minor violations of the underlying assumptions. With that aim in mind, we have tested it for all nine EU countries that employ the JDH method in parliamentary elections. Moreover, we discuss the applications of the formula for modeling the effects of vote swings, coalition formation and breakup, spoiler effects, electoral engineering, artificial thresholds and political gerrymandering. By not requiring district-level vote shares, our formula simplifies electoral simulations using the JDH method.