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A Statistics-Related Approach to the Legislative Apportionment Problem…and also, a Second One

Summary We investigate global optimization methods in the Apportionment Problem, using objective functions which arise rather naturally from the field of Probability and Statistics. Minimizing the Chi-Square statistic (and also, minimizing the variance in seat-share per person) is equivalent to using Webster’s method. Meanwhile, finding a mode of the multinomial distribution (hence maximizing the P-value in an Exact Test) is equivalent to using Jefferson’s method.