  The Single Transferable Vote (STV) is a system of preferential voting
employed in multi-seat elections. Each vote cast by a voter is a (potentially
partial) ranking over a set of candidates. No techniques currently exist for
computing the margin of victory (MOV) in STV elections. The MOV is the smallest
number of vote manipulations (changes, additions, and deletions) required to
bring about a change in the set of elected candidates. Knowledge of the MOV of
an election gives greater insight into both how much time and money should be
spent on the auditing of the election, and whether uncovered mistakes (such as
ballot box losses) throw the election result into doubt---requiring a costly
repeat election---or can be safely ignored. In this paper, we present
algorithms for computing lower and upper bounds on the MOV in STV elections. In
small instances, these algorithms are able to compute exact margins.
