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Ballot Theorems, Old and New

  • L. Addario-Berry
  • B. A. Reed
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 17)

Abstract

We begin by sketching the development of the classical ballot theorem as it first appeared in the Comptes Rendus de 1’Academie des Sciences. The statement that is fairly called the first Ballot Theorem was due to Bertrand: Theorem 1 ([8]). We suppose that two candidates have been submitted to a vote in which the number of voters is μ. Candidate A obtains n votes and is elected; candidate B obtains m = μ − n votes. We ask for the probability that during the counting of the votes, the number of votes for A is at all times greater than the number of votes for B. This probability is (2nμ)/μ = (nm)/(n + m).

Keywords

Random Walk Random Measure Strong Markov Property Real Random Variable Fair Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2008

Authors and Affiliations

  • L. Addario-Berry
    • 1
  • B. A. Reed
    • 2
    • 3
  1. 1.Department of StatisticsUniversity of OxfordUK
  2. 2.School of Computer ScienceMcGill UniversityCanada
  3. 3.Projet Mascotte, I3S (CNRS/UNSA)-INRIASophia AntipolisFrance

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