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?
Cheap Talk 
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October 24, 2011 at 1:06 pm
Evan
This sounds like a variation on the preferential voting system that is used in (almost) all elections in Australia. Antony Green’s blog (http://blogs.abc.net.au/antonygreen/) is probably a good place to start. He’s a journalist, not an academic, but he has a very good understanding of voting systems from a practical viewpoint.
October 24, 2011 at 1:10 pm
Evan
Also, from a strategic viewpoint, the Australian system has one particularly interesting feature.
Candidates can ‘recommend’ to their supporters how they should order the other candidates, and a large and relatively stable proportion of voters blindly follow the recommendation of their preferred candidate. Thus the bargaining of ‘preference deals’ before the election adds an extra stage to the voting game. The election of Senator Steve Fielding a few years ago is one case where preference deals caused a very bizarre result.
October 24, 2011 at 6:13 pm
Michael Webster
Single transferable vote schemes are designed to avoid the messy looking deals which take place on the convention floor when the last place candidate is dropped and there is a flurry for his or her votes.
These schemes are not monotonic – which gives rise to controversy as to their value.
November 4, 2011 at 10:57 am
Owen Rooney
Australian elections (like parliamentary elections here in Ireland), are PR-STV. That is, they are multiple-winner elections. What Sandeep is describing is single-winner STV, usually known as IRV or (in the recent UK referendum) AV, although San Francisco seem to be implementing it with a maximum of three preferences. It’s far from an experiment, though, as Ireland have been running our Presidential elections under STV since 1938. In fact, just three days after you posted this we held a presidential election under STV with 7 candidates and 1.8 million votes. (For reference it required 4 counts, which took the best part of 2 days)
It’s true that these schemes exhibit monotonicity violations, and these are particularly prevalent in multiple-winner elections, where tactical voting is quite common. However, in single-winner STV, any attempt to exploit monotonicity violations by voting tactically would require exceptionally detailed knowledge of other people’s voting intentions, in particular much more detailed than any poll would provide. This means that, for 99.9% of voters, it’s an optimal strategy to simply vote according to your true preferences.
As far as impact on candidates, it is the case in Ireland that candidates in Presidential elections adopt rather centrist platforms, although this is more likely to be because of the popular perception of the President as apolitical, than any feature of the electoral system.