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Summary
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.
Keywords: apportionment methods; Lévy-stable distributions; proportional representation; rounding error analysis; seat bias; stationary divisor method; success-value bias; uniform distribution
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Published Online: 2009-09-25
Published in Print: 2005-02-01
© R. Oldenbourg Verlag, München
