In the 2011 San Francisco Mayor's Election (election day is this November, but early voting has already begun), there are 12 "major" candidates... from the LOWV debate:
There are four others running: Ascarrunz, Currier, Lawrence, and Pang, but I think it's safe to say none of these four candidates is in the running, given their lack of representation in the debates so far.
San Francisco switched this mayor's election to Instant Runoff Voting. The way this works is each virtual "round" the candidate receiving the least non-zero number of first-place votes is eliminated, along implicitly with those receiving no first-place votes. Votes lower than first place on the ballots of those who voted for this eliminated candidate are then promoted until either there are no votes left on the ballot (the ballot is "exhausted") or the new first place vote on the ballot is still in the race. The idea is to allow voters to vote their preference, rather than to worry about which candidates are most viable. I really like this system, as long as the number of exhausted ballots remains relative small.
The problem is if a voter ends up with an exhausted ballot, then in the final "round" that voter's preference is no longer being heard. If the number of votes per voter is no more than one less than the number of "legitimate" candidates, then no ballot becomes exhausted. However, fewer votes, and on some ballots the final two candidates remaining may be the two candidates omitted from a ballot and that ballot will be exhausted before this final selection. These voters tend to feel bitter that their preference among these candidates is being ignored.
In the San Francisco election, with 16 candidates on the ballot, there are three slots available for voters to select their preference. The election commission argues this is due to a technological limitation of the voting process here. Errr.... I simply refuse to accept this, especially in the presence of many counter-examples throughout the world, for example Ireland, where voters get more selections.
The result is in the San Francisco election, voters are forced to engage, at least a little, in game theory. Since they don't want their ballots to become exhausted before the final round, they feel compelled to vote for at least one candidate who is likely to make the final round. I think pretty much everyone agrees that Lee will likely make it there, as Lee is the sitting mayor; he was appointed by the Board of Supervisors to take over when Gavin Newsom took the seat of the state Attorney General. So suppose a lot of voters wouldn't place Lee in their top three, but they prefer Lee to some other candidate who might have a long-shot chance to win, so they would be tempted to put Lee in their #3 vote as a safety net in case their first two choices don't make it.
So maybe every single voter has Lee as their mid-rank choice, say 6th or 7th (of the 12 candidates with "a chance"). But a majority of these voters put Lee in the #3 slot because doing so essentially blocks out the 6 or 7 candidates they really don't want to see in office. It's a good strategic move, they may feel.
The issue is now there's only two slots left for their true preferences. These two spots will get split between the 5 or so candidates they'd all prefer to see than Lee. Many of these voters will thus have their top two votes eliminated, in which case Lee gets their top vote. This gives Lee the election. Add in those voters who out of inertia and laziness will just vote for the person in office at the time and it becomes exceptionally challenging for anyone to beat Lee. This puts Lee in a very comfortable position.
There have been major questions about Lee, most recently with campaign contributions getting laundered through low-income voters to avoid campaign contribution limits, but also because he oversaw a police crack-down on cyclists in which cyclists were ticketed for trivial offenses (or non-offenses) like not "putting a foot down" at stops or riding during the day without reflectors, neither of which is illegal. Previously he canned an agreed-upon lane reduction on Cesar Chavez to improve cyclist safety after lobbying from the teamsters (although an alternate plan removing parking is moving forward). I really don't trust him to be the city's mayor at a time when hard decisions about city budgets, decisions which are going to cost people money, need to be made. We can't have the mayor's office going to the highest bidder.
So I really hope the city changes its ranked-choice voter scheme. The number of options should depend on the number of candidates. For example, during the District 10 Board of Supervisor's election, with 21 candidates and no incumbent, I proposed the following:
choices = floor[sqrt(N)] + 1
This formula would yield 1 choice for no candidates, two for up to 3 candidates, 3 for up to 8 candidates, 4 for up to 15 candidates, and 5 for up to 24 candidates. In the San Francisco Mayor's race, as with that Board of Supervisor's election, there would thus be 5 choices available. I feel this formula is the absolute lower-limit of what I'd want to see given Lee's presence in the race. For example, the following might be even better:
choices = floor[N2/3] + 1
This revised formula would yield one choice for no candidates, two for up to 2 candidates, three for up to 5 candidates, four for up to 8 candidates, five for up to 11 candidates. six for up to 14 candidates, seven for up to 18 candidates, and eight for up to 22 candidates. Thus we'd get seven votes for this election. I'd have no problem ranking seven candidates here.
The idea in these formulas is that all candidates aren't equally likely to get votes. In any election, some candidates are going to be more popular than others, so you don't need the number of spots on the ballot to be equal to the number of candidates or even one less, unless there is a very small number of candidates. In a 16-candidate field, the huge majority of voters will have one of the two final candidates among their seven top choices; the number of exhausted ballots need not be zero, just less than the number which could have swung the final result with reasonable probability. But fixing the number at three is clearly woefully inadequate to the democratic process. Voting should be about expressing real preferences, not engaging in game theory.