A general definition is proposed for the margin of victory of an election contest. That definition is applied to Instant Runoff Voting (IRV) and several estimates for the IRV margin of victory are described: two upper bounds and two lower bounds. Given round-by-round vote totals, the time complexity for calculating these bounds does not exceed O(C2 log C), where C is the number of candidates. It is also shown that calculating the larger and more useful of the two lower bounds can be viewed, in part, as solving a longest path problem on a weighted, directed, acyclic graph.
Worst-case analysis shows that neither these estimates, nor any estimates based only on tabulation round-by-round vote totals, are guaranteed to be within a constant factor of the margin of victory. These estimates are calculated for IRV elections in Australia and California. Pseudo code for calculating these estimates is provided.
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