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/.
@article{bwmeta1.element.doi-10_2478_forma-2014-0014,
author = {Karol P\k ak},
title = {Bertrand's Ballot Theorem},
journal = {Formalized Mathematics},
volume = {22},
year = {2014},
pages = {119-123},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0014}
}
Karol Pąk. Bertrand’s Ballot Theorem. Formalized Mathematics, Tome 22 (2014) pp. 119-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0014/
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