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Lothar Heinrich, Friedrich Pukelsheim, Udo Schwingenschlögl

On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence

Keywords: apportionment methods, Lévy-stable distributions, proportional representation, rounding error analysis, seat bias

Stationary multiplier methods are procedures for rounding real probabilities into rational proportions, while the Sainte-Laguë divergence is a reasonable measure for the cumulative error resulting from this rounding step. Assuming the given probabilities to be uniformly distributed, we show that the Sainte-Laguë divergences converge to the Lévy-stable distribution that obtains for the multiplier method with standard rounding. The norming constants to achieve convergence depend in a subtle way on the stationary method used.

Statistics & Decisions, Oldenbourg Wissenschaftsverlag

Print ISSN: 0721-2631
Volume: 23, 02/2005
Pages: 117 - 129

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