Social Choice Theorists are going to see an experiment in action as San Francisco votes for a new mayor using rank-order voting.  Here is how it works:

Each voter lists up to three candidates in ranked order: First, second and third choice.
If one candidate gets more than 50 percent of the first-place votes in the first round of counting, he’s the winner and there’s no need to look at the second and third choices.
But if no one has a majority, the candidate with the fewest number of votes is eliminated from the future count and his second-choice votes are distributed to the remaining candidates.
If still no one cracks the 50 percent mark, then the candidate with the second-lowest vote total is eliminated and his second-place votes are distributed. If the voters’ second choice already was eliminated, it’s the third-choice vote that goes back into the pool.
This continues until one candidate has a majority of the remaining votes. Last November, it took 20 rounds before Malia Cohen finally was elected as supervisor from San Francisco’s District 10.

There are two strategic issues.  First, there must be an incentive for strategic voting via Gibbard-Satterthwaite/Arrow.  Hence, sincere voting and strategic voting will differ.  Second, the candidate positions and in fact the issue of who enters as a candidate is a key factor in the rationale for switching to rank order voting in the first place.  Some voters must hope that third party candidates can now enter and have a chance of winning.  Others must hope that more centrist policies are adopted by the candidates in the hope of being voters’ second or third choice.

I assume there are many formal theory papers in political science on this but am not familiar with them…anyone have any ideas?