Bertrand’s Ballot Theorem

Karol Pąk

Formalized Mathematics (2014)

  • Volume: 22, Issue: 2, page 119-123
  • ISSN: 1426-2630

Abstract

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In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

How to cite

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Karol Pąk. "Bertrand’s Ballot Theorem." Formalized Mathematics 22.2 (2014): 119-123. <http://eudml.org/doc/268859>.

@article{KarolPąk2014,
abstract = {In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.},
author = {Karol Pąk},
journal = {Formalized Mathematics},
keywords = {ballot theorem; probability},
language = {eng},
number = {2},
pages = {119-123},
title = {Bertrand’s Ballot Theorem},
url = {http://eudml.org/doc/268859},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Karol Pąk
TI - Bertrand’s Ballot Theorem
JO - Formalized Mathematics
PY - 2014
VL - 22
IS - 2
SP - 119
EP - 123
AB - In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.
LA - eng
KW - ballot theorem; probability
UR - http://eudml.org/doc/268859
ER -

References

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