Bertrand's ballot theorem

Bertrand's ballot theorem addresses a scenario where two candidates compete in an election, with one leading in votes. It states that if candidate A receives *p* votes and candidate B receives *q* votes, with *p* > *q*, the probability that during the counting process A is always ahead of B is \(\frac{p - q}{p + q}\). This means A maintains a consistent lead throughout the count, with the probability depending on the difference in their vote counts relative to their total votes. It provides insight into the likelihood of a candidate's sustained early lead in vote counting.