<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: <italic>A</italic> that receives <italic>n</italic> votes and <italic>B</italic> that receives <italic>k</italic> votes, and additionally <italic>n ≥ k</italic>. Then this theorem states that the probability of the situation where <italic>A</italic> maintains more votes than <italic>B</italic> throughout the counting of the ballots is equal to (<italic>n − k</italic>)/(<italic>n</italic> + <italic>k</italic>).</p><p>This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.</p></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/.

Bertrand’s Ballot Theorem

Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

{"article-title":"Bertrand\u2019s Ballot Theorem"}

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...

Bertrand’s Ballot Theorem

Publié en ligne: 30 juin 2014

Pages: 119 - 123

Reçu: 13 juin 2014

DOI: https://doi.org/10.2478/forma-2014-0014

Mots clés
ballot theorem, probability

© 2014 Karol Pąk

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Bertrand’s Ballot Theorem

Publié en ligne: 30 juin 2014

Pages: 119 - 123

Reçu: 13 juin 2014

DOI: https://doi.org/10.2478/forma-2014-0014

Mots clésballot theorem, probability

© 2014 Karol Pąk

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Mots clés
ballot theorem, probability