* 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.