[1805.08291] Seat Allocation and Seat Bias under the Jefferson--D'Hondt Method

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Physics > Physics and Society

arXiv:1805.08291 (physics)

[Submitted on 21 May 2018 (v1), last revised 4 Apr 2024 (this version, v3)]

Title:Seat Allocation and Seat Bias under the Jefferson--D'Hondt Method

Authors:Daria Boratyn, Wojciech Słomczyński, Dariusz Stolicki<br>View a PDF of the paper titled Seat Allocation and Seat Bias under the Jefferson--D'Hondt Method, by Daria Boratyn and 2 other authors

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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.

Comments:<br>24 pages, 1 figure; companion paper to J. Flis, W. Słomczyński, D. Stolicki, Pot and Ladle: A Formula for Estimating the Distribution of Seats under the Jefferson-D'Hondt Method, doi: https://doi.org/10.1007/s11127-019-00680-w

Subjects:

Physics and Society (physics.soc-ph); Probability (math.PR)

MSC classes:<br>91B12 (Primary), 91B14, 65B15 (Secondary)

Cite as:<br>arXiv:1805.08291 [physics.soc-ph]

(or<br>arXiv:1805.08291v3 [physics.soc-ph] for this version)

https://doi.org/10.48550/arXiv.1805.08291

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arXiv-issued DOI via DataCite

Journal reference:<br>Operations Research and Decisions 2025: 35(3): 1-27

Related DOI:

https://doi.org/10.37190/ord250301

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DOI(s) linking to related resources

Submission history<br>From: Dariusz Stolicki [view email]<br>[v1]<br>Mon, 21 May 2018 21:19:58 UTC (2,811 KB)

[v2]<br>Sun, 18 Nov 2018 16:10:23 UTC (4,720 KB)

[v3]<br>Thu, 4 Apr 2024 13:10:21 UTC (1,131 KB)

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