Saturday 2 October 2010

STV isn't subject to manipulation? Ahem.

Kiwiblog points to Graeme Edgeler, below, and advises sincere voting in the STV local body elections.
But is it a good idea to rank everyone?


But if I give someone I don't like a rank, couldn't this hurt the chances of candidates I like more?


Your lower preferences cannot ever harm the election prospects of anyone you rank higher than them.

But some of my vote could still go to someone I'm not a fan of?

Yes. But only if all the people you ranked higher than them have already been elected, or cannot possibly win.

By ranking a candidate lowly, you're not helping them beat people you like more than them, you're only helping them against people you hate more.

In the 2002 French Presidential election, there was a vote-off between the top two candidates, the right wing incumbent Jacques Chirac, and far right National Front leader Jean-Marie Le Pen. Many left-wing voters did something they never thought they would do, and voted for Chirac. They weren't using STV, but the principle is identical. In Australian Senate Elections, and some state elections – which do use STV – the Labor Party has advised its supporters to rank the right-wing Liberal Party above Pauline Hanson's One Nation Party. Voting this way doesn't hurt the Labor Party, but it makes it as unlikely as possible that One Nation gets anyone in.

Like the French voters who "voted for the crook, not the fascist", ranking all the candidates helps ensure that what you might consider "the greater of two evils" won't be elected.
Let's consider a contest for a single member district: one candidate will be elected.

There are five types of voters.

Group 1, 10 people, prefer candidate A over C over B over D: A>C>B>D
Group 2, 7 voters, prefer: B>C>A>D
Group 3, 5 voters, prefer: D>C>B>A
Group 4, 3 voters, prefer: C>B>D>A
Group 5, 4 voters, prefer: D>C>A>B

Everyone votes sincerely. In the first round, nobody meets the quota of 15 first choices. So the candidate who is the least preferred is dropped. Candidate C is the first choice of only 3 voters and so is dropped. Again, nobody meets the quota of 15 first choices: B and A now tie at 10 first choices, D has 9 and is dropped. In the third round, B reaches the quota of 15 first choices and is elected.

Suppose, though, that Group 5 votes strategically. B is that group's last choice and was the outcome of the STV election. If they had instead reported their preference ordering as having been C>D>A>B, the selection would have run as follows: D would have been dropped in the first round as the first choice of only 5 voters. In the second round, C would be the first choice of 12, A of 10 and B of 7 so B would have been dropped. In the third round, C makes quota with 19 votes; C is the winner.

So can your placing a candidate lower down the ordering ever hurt the chances of someone you've ranked higher? That's been proven above. Now, it may be very very difficult in the real world because nobody has access to the kind of information we've used in this example. But in a single-candidate district, a non-crazy rule of thumb might be that if your first choice is a candidate who is hated by lots of other folks (like D, above, who was the first choice of 9 but the last choice of 17), you may do better by listing as your first choice somebody a bit further down your preference ordering who's more likely to win (like C, above, who was the second choice of lots of folks) if your last choice otherwise has reasonable support.

I don't think that kind of a rule is computationally hard.

Let's look now to Graeme's precise scenario: he argues you can never hurt the chances of someone higher up by ranking lower order candidates rather than leaving them blank. I think he's right about that: your lower preferences are never checked unless your higher preferences have been eliminated. But you can sometimes do better by lying about your preference ordering than by reporting things sincerely. So Farrar's line at Kiwiblog is, I think, incorrect:
Don’t try and be strategic and working out who is most popular and hence I will rank them lower as they don’t need my vote etc. Just rank candidates in order of your true actual preference.
Farrar is right that you won't waste your vote in a multimember election by keeping a popular guy as your first choice if he is your first choice; any votes in excess of quota are allocated to your lower order preferences. But that doesn't mean you can't do better by being strategic if your first choice is a bit of an odd one.


  1. I do not dispute that tactical voting is possible under STV. Indeed, I voted tactically in the 2007 local elections.

    I considered that my favoured ward candidate was obviously going to win, and what I wanted to ensure was that one person - a current councillor - was not returned. So I gave my first preference to my third favoured candidate, whom I - rightly as it turns out - considered would be the one contesting for the last spot against the guy I didn't want.

  2. @Graeme: It was Kiwiblog's interpretation of your post that I think was wrong.