Asymptotic bias of some election methods

2011/10/28 by Svante Janson, Janson, Svante
Mathematics · #60C05 #91B12 #91F10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60C05 #msc:91B12 #msc:91F10

paper · pdf · doi:10.48550/arxiv.1110.6369

54 pages

arxiv created 2011/10/28 · openalex publication_date 2011/10/28 · arxiv updated 2011/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider an election where N seats are distributed among parties with proportions p₁,...,p_m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a party, i.e. the difference between the number of seats given to the party and the (real) number Np_i that yields exact proportionality. Our approach is to keep p₁,...,p_m fixed and let N tend to infinity, with N random in a suitable way. In particular, we give formulas showing the bias favouring large or small parties for the different election methods.

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