Candidate strategies with Instant Runoff Voting

In a recent email to her supporters, San Francisco District 5 supervisor candidate Hope Johnson outlines a strategy for the upcoming Instant Runoff Voting election.

Johnson and Resignato are launching The People's Ticket to give voters a better choice than the big-money downtown and progressive machine candidates who are constantly at odds with each other.  They are asking D5 constituents to vote for them in either the first and second or first and third positions, in any order, on November 6’s ranked choice ballot.

A friend asks, "Does this make sense, from a strategic voting perspective?" The answer is, it's complicated. Say you have these hypothetical preferences:

35% X > Johnson > Resignato
32% Johnson > X > Resignato
33% Resignato > X > Johnson

Johnson has only 32% of the first-place rankings, so she's the first eliminated, which causes 32% of the votes to be transferred to X in the next round. X then trounces Resignato 67% to 33%.

But say Johnson and Resignato successfully convince their supporters to adopt the strategy. Then it would look like this:

35% X > Johnson > Resignato
32% Johnson > Resignato > X
33% Resignato > Johnson > X

Johnson is still eliminated first (indeed, this strategy cannot possibly affect the election prior to the elimination of the first of the two colluders). But now Resignato trounces X 65% to 35%. So the strategy worked.

But things aren't so simple! The strategy helped one of the candidates, but it also caused 32% of voters to get their 3rd choice instead of their 2nd. So from their point of view, it was the opposite of strategic. While the Johnson supporters certainly want the Resignato supporters to help Johnson, they don't want to help Resignato, particularly within the privacy of the voting booth. And vice versa. This is the classic prisoners' dilemma.

History has disproved the notion that voters care more about loyalty to their favorite candidates than about getting what's best for themselves. Consider that exit polls in the 2000 U.S. presidential election showed that 90% of Nader-favoring voters claimed to have voted for someone other than Nader. Obviously a Nader supporter who preferred Gore to Bush was maximizing his expected value by voting for Gore instead of Nader. Likewise, we expect that Johnson and Resignato would have a hard time convincing people to vote against their own best interests.

There's also some interesting game theory related to which partner you should pick, if engaging in this strategy. Notice that if X were to team up with Johnson in the last example, that would lift X one ranking up (above Resignato) on 32% of the ballots. The same deal with Resignato would create a one-rank lift on 33% of ballots, but above Johnson. Which strategy makes sense? In this case, it doesn't matter, because X loses head-to-head against any rival. But in general, the strategy is to team up with someone whom you think will be ranked higher than your greatest rival, by a lot of voters. But you also want to pick someone whom you believe will be eliminated before you, otherwise you don't benefit from the strategy.

I'll leave the more complicated analysis to my math Ph.D. associates at The Center for Election Science.