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

Stationary multiplier methods are procedures for rounding real probabilities into rational proportions, while the Sainte-Lague 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-Lague divergences converge to the Levy-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.

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