# The Ballot Problem

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Consider an election with two candidates A and B resulting in votes for A and votes for B. If candidate A wins the election, the ballot problem is concerned with the probability that A was in the lead throughout the entire voting process. The ballot-counting process may be interpreted as a simple one-dimensional random walk with a step of for each vote for A and for each vote for B. The ballot problem asks for the probability that a simple random walk from to is strictly positive except at the origin. This probability turns out to be .

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Contributed by: Jose Sanchez and Madina Bolat (September 2016)

(Illinois Mathematics Summer REU Program 2016)

Open content licensed under CC BY-NC-SA

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