### Ballot Experiment

Walk graph
Distribution graph

#### Description

The ballot experiment concerns an election in which candidate $$A$$ receives $$a$$ votes and candidate $$B$$ receives $$b$$ votes, where $$a \gt b$$. The votes are assumed to be randomly ordered. The first graph shows the difference between the number of votes for $$A$$ and the number of votes for $$B$$, as the votes are counted. This process is a random walk in which the initial point $$(0, 0)$$ and terminal point ($$a + b, a - b)$$ are fixed.

The event of interest is that $$A$$ is always ahead of $$B$$ in the vote count, or equivalently, that the graph is always above the horizontal axis (except of course at the origin). The indicator variable $$I$$ of this event is recorded in the first table on each update. The probability density function of $$I$$ is shown in blue in the distribution graph and is recorded in the distribution table. On each update, the empirical density function of $$I$$ is shown as red in the distribution graph and recorded in the distribution table. The parameters $$a$$ and $$b$$ can be varied with the input controls.