Tactical IRV

Background

Several countries, including Australia and the USA, use Instant Runoff Voting (aka IRV), which is the single-winner form of Single Transferable Vote. (Australians generally refer to STV and IRV as “preferential voting”, but that’s inadequate for voting methods experts, given that there are hundreds of preferential voting methods, from Bucklin to Borda.)

Probability

IRV is severely vulnerable to two types of strategy: compromise and push over. An example of compromise strategy would be an Australian voter voting Labor instead of Green to avoid getting Liberal. The math behind this is simple. Suppose:

S = the probability the Green is strong enough to beat Labor, but not Liberal (i.e. Labor is eliminated, then Green loses to Liberal)
W = the probability the Green is strong enough to beat Labor and beat Liberal

Both probabilities are vanishingly small, but for strategic purposes, all that matters is which is bigger? If S is bigger, then Greens are tactically motivated to vote Labor to avoid electing Liberal.

Confusion

People without mathematical expertise are often unable to understand this issue of relative probability, and get hung up on the fact that S is vanishingly small. But the relevant issue is that W is also vanishingly small. For instance, here’s an example of a long-time Australian politician repeatedly getting confused by the absolute value of S rather than the relative values of S and W.

This is further explained here with help by Warren Smith, the Princeton math PhD and voting methods expert whose work was the basis for the William Poundstone book Gaming the Vote.