Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T14:30:44.224Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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