Thursday, 24 September 2015

Manipulating an STV vote

Ok, so the Internets are all a-twitter about how strategic voters should behave in the coming flag vote, and whether it's possible to vote strategically.

Recall that there are now 5 options: 3 with ferns, monkey-butt, and the red peak thing. Let's denote these A, B, and C for the ferns; M and R for Monkey-butt and Red-peak, respectively.

Suppose there are five different basic types of voters. This is just a constructed example; I have no clue what the actual preference distributions are. But suppose that red-peak is the second choice of a lot of fern-lovers who have strong preference for their most-preferred fern as compared to the others. And that one of the ferns - nobody much likes that fern. You all know which one.

And so:
10 voters7 voters5 voters3 voters4 voters

Everyone votes for most preferred candidate.  If no majority, the one with the fewest first-choice votes is dropped and the second choice moves up for those voters. And so on until there is a majority.

  • C has no first-place votes and is dropped in the first round. 
  • Then, R is dropped because it has only 3 first-place votes.
  • Then, M is dropped because it has only 9 first-place votes (to 10/10 for A&B)
  • Then, B wins 15 to 14 in the final round.
Suppose that the four monkey-butt supporters in the last column don't like this. Their least preferred option wins. What happens if they lie and say that they prefer red-peak to monkey-butt?

10 voters7 voters5 voters3 voters4 voters

And the sequence:

  • C is dropped in the first round.
  • M is dropped in the second round, having only 5 first-place votes.
  • B is dropped in the third round, with only 7 votes.
  • R wins in the fourth round, 19 to 10 against A.
By lying about their preference ordering, 4 of 29 voters flipped the outcome from their last choice to their second choice. If you think this isn't fair or somehow bad, they've also made sure that the Condorcet Winner actually won:
  • R>A 19:10
  • R>B 22:7
  • R>C (unanimous)
  • R>M 20:9
If they hadn't lied, B would have won: an outcome that 22/29 people would not have liked. So are they so bad?

Again, this is just a trivial constructed example. It is not easy in the real world to tell what actual preference orderings are. And knowing what they are is important for figuring out strategy. At the same time, since no one vote will ever change the outcome of an election, neither will any one strategic vote.

But, in general, if you think that fern-supporters are divided across ferns, and that a non-fern option might be a strong second choice, you might want to list that second choice as your first choice if you fear winding up with a fern you don't like. Similarly, if you're a big fern-supporter and you're scared that splitting your first choice options across the field will let somebody else sneak up the middle, well, maybe go with the fern you think most others like best.

This isn't something unique to STV - all systems are manipulable (other than dictatorship). That's the Gibbard-Satterthwaithe theorem. It may take more information to run properly than is feasible in a lot of cases, but it's possible. 

Perhaps a better bottom line: voting is irrational if you think you're going to change the outcome; it's even more irrational to put a ton of thought into strategy where you're not likely to change the outcome. Do you run complicated strategies when picking lotto numbers?

1 comment:

  1. But if I pick lotto numbers that haven't come up as often in the past, I'm more likely to won due to reversion to the mean right? Right?