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Horizons of Combinatorics pp 9–35Cite as

Ballot Theorems, Old and New

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Part of the book series: Bolyai Society Mathematical Studies ((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 (2n − μ)/μ = (n − m)/(n + m).

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Oxford, UK

    L. Addario-Berry

  2. School of Computer Science, McGill University, Canada

    B. A. Reed

  3. Projet Mascotte, I3S (CNRS/UNSA)-INRIA, Sophia Antipolis, France

    B. A. Reed

Authors
  1. L. Addario-Berry
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  2. B. A. Reed
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Editor information

Editors and Affiliations

  1. Alfréd Rényi Inst. of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Ervin Győri , Gyula O. H. Katona  & Gábor Sági ,  & 

  2. Institute of Mathematics, Eötvös University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary

    László Lovász

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© 2008 János Bolyai Mathematical Society and Springer-Verlag

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Addario-Berry, L., Reed, B.A. (2008). Ballot Theorems, Old and New. In: Győri, E., Katona, G.O.H., Lovász, L., Sági, G. (eds) Horizons of Combinatorics. Bolyai Society Mathematical Studies, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77200-2_1

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