Votes and a half-binomial |
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Authors: | J.S. Frame Dennis C. Gilliland |
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Affiliation: | Dept. of Mathematics and Dept. of Statistics and Probability, Michigan State University, Wells Hall, East Lansing, MI 48824, USA |
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Abstract: | In two party elections with popular vote ratio , a theoretical model suggests replacing the so-called MacMahon cube law approximation , for the ratio of candidates elected, by the ratio of the two half sums in the binomial expansion of (p+q)2k+1 for some k. This ratio is nearly when k = 6. The success probability for the power law is shown to so closely approximate , if we choose , that for . Computationally, we avoid large binomial coefficients in computing for k>22 by expressing as the sum , whose terms decrease by the factors . Setting K = 4k+3, we compute ak for the large k using a continued fraction derived from the ratio of π to the finite Wallis product approximation. |
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