Issue: 2025/Vol.35/No.3, Pages
SEAT ALLOCATION AND SEAT BIAS UNDER THE JEFFERSON–D'HONDT METHOD
Daria Boratyn
, Wojciech Słomczyński , Dariusz Stolicki
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: D. Boratyn, W. Słomczyński, D. Stolicki. Seat allocation and seat bias under the Jefferson–D'Hondt method. Operations Research and Decisions 2025: 35(3). DOI 10.37190/ord250301
Abstract
We prove that under the Jefferson–D’Hondt method of apportionment, given certain distributional assumptions regarding mean rounding residuals, as well as absence of correlations between party vote shares, district sizes (in votes), and multipliers, the seat share of each relevant party is an affine function of the aggregate vote share, the number of relevant parties, and the mean district magnitude. We further show that the first of those assumptions follows approximately from more general ones regarding smoothness, vanishing at the extremes, and total variation of the density of the distribution of vote shares. We also discuss how our main result differs from the simple generalization of the single-district asymptotic seat bias formulae, and how it can be used to derive an estimate of the natural threshold and certain properties thereof.
Keywords: apportionment, Jefferson-D'Hondt method, seat bias, rounding
Received: 4 April 2024 Accepted: 26 January 2025
Published online: 8 February 2025