  This paper considers elections in which voters choose one candidate each,
independently according to known probability distributions. A candidate
receiving a strict majority (absolute or relative, depending on the version)
wins. After the voters have made their choices, each vote can be inspected to
determine which candidate received that vote. The time (or cost) to inspect
each of the votes is known in advance. The task is to (possibly adaptively)
determine the order in which to inspect the votes, so as to minimize the
expected time to determine which candidate has won the election. We design
polynomial-time constant-factor approximation algorithms for both the
absolute-majority and the relative-majority version. Both algorithms are based
on a two-phase approach. In the first phase, the algorithms reduce the number
of relevant candidates to $O(1)$, and in the second phase they utilize
techniques from the literature on stochastic function evaluation to handle the
remaining candidates. In the case of absolute majority, we show that the same
can be achieved with only two rounds of adaptivity.
