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Fluctuations in the ratio of scores in counting a ballot

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Columbia University, New York
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Extract

Suppose that in a ballot candidate A scores a votes and candidate B scores b votes and that all the possible voting records are equally probable. Denote by α r and β r, the number of votes registered for A and B respectively among the first r votes recorded. Let µ, be a nonnegative integer. Denote by Pj(a, b) the probability that the inequality holds for exactly j subscripts r=1,2,..,a + b.

Type
Short Communications
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 393 - 396
Copyright
Copyright © Applied Probability Trust 

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References

[1] Aeppli, A. (1924) Zur Theorie verketteter Wahrscheinlichkeiten. Thèse, Zürich.Google Scholar
[2] Andre, D. (1887) Solution directe du problème résolu par M. Bertrand. C. R. Acad. Sci. Paris 105, 436–437.Google Scholar
[3] Andersen, , Sparre, E. (1953) On sums of symmetrically dependent random variables. Skand. Aktuartidskr. 36, 123–138.Google Scholar
[4] Barbier, É. (1887) Généralisation du problème résolu par M. J. Bertrand. C. R. Acad. Sci. Paris 105, 407.Google Scholar
[5] Bertrand, J. (1887) Solution d'un problème. C. R. Acad. Sci. Paris 105, 369.Google Scholar
[6] Feller, W. (1959) On combinatorial methods in fluctuation theory. Probability and Statistics, The Harald Cramér Volume. 75–91. Almqvist and Wiksell, Stockholm.Google Scholar
[7] TakáCs, L. (1961) The probability law of the busy period for two types of queuing processes. Operat. Res. 9, 402–407.Google Scholar
[8] TakáCs, L. (1963) The distribution of majority times in a ballot. Z. Wahrscheinlichkeitstheorie 2, 118–121.Google Scholar