ABSTRACT
Suppose, in an election, candidate A receives x votes and candidate B receives y votes, where x > y. If the votes are counted in random order, then the classical ballot theorem states that the probability that candidate A leads candidate B throughout the counting is (x - y)/(x + y). We will show how a continuous-time analog of this result can be used to answer some questions related to Brownian excursions. These questions arise in the study of a fragmentation process which was recently introduced by Aldous and Pitman.