Bertrand's ballot theorem

ID: bertrand-s-ballot-theorem

Bertrand's ballot theorem is a result in combinatorics related to voting and elections. It can be stated as follows: Suppose that in an election, candidate A receives \( a \) votes and candidate B receives \( b \) votes, with \( a > b \). If the votes are counted one by one in a random order, the probability that candidate A is always ahead in the vote count throughout the counting process (i.e.

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