Do preferential voting and similar flags interact badly?
(because I was asked about Keri Henare’s post)
Short answer: No.
As you know, we have four candidate flags. Two of them, the Lockwood ferns, have the same design with some colour differences. Is this a problem, and is it particularly a problem with Single Transferable Vote (STV) voting?
In the referendum, we will be asked to rank the four flags. The first preferences will be counted. If one flag has a majority, it will win. If not, the flag with fewest first preferences will be eliminated, and its votes allocated to their second-choice flags. And so on. Graeme Edgeler’s Q&A on the method covers the most common confusions. In particular, STV has the nice property that (unless you have really detailed information about everyone else’s voting plans) your best strategy is to rank the flags according to your true preferences.
That’s not today’s issue. Today’s issue is about the interaction between STV and having two very similar candidates. For simplicity, let’s consider the extreme case where everyone ranks the two Lockwood ferns together (whether 1 and 2, 2 and 3, or 3 and 4). Also for simplicity, I’ll assume there is a clear preference ranking — that is, given any set of flags there is one that would be preferred over each of the others in two-way votes. That’s to avoid various interesting pathologies of voting systems that aren’t relevant to the discussion. Finally, if we’re asking if the current situation is bad, we need to remember that the question is always “Compared to what?”
One comparison is to using just one of the Lockwood flags. If we assume either that there’s one of them that’s clearly more popular, or that no-one really cares about the difference, then this gives the same result as using both the Lockwood flags.
Given that the legislation calls for four flags this isn’t really a viable alternative. Instead, we could replace one of the Lockwood flags with, say, Red Peak. Red Peak would then win if a majority preferred it over the remaining Lockwood flag and over each of the other two candidates. That’s the same result that we’d get adding a fifth flag, except that adding a fifth flag takes a law change and so isn’t feasible.
Or, we could ask how the current situation compares to another voting system. With first-past-the-post, having two very similar candidates is a really terrible idea — they tend to split the vote. With approval voting (tick yes/no for each flag) it’s like STV; there isn’t much impact of adding or subtracting a very similar candidate.
If it were really true that everyone was pretty much indifferent between the Lockwood flags or that one of them was obviously more popular, it would have been better to just take one of them and have a different fourth flag. That’s not an STV bug; that’s an STV feature; it’s relatively robust to vote-splitting.
It isn’t literally true that people don’t distinguish between the Lockwood flags. Some people definitely want to have black on the flag and others definitely don’t. Whether it would be better to have one Lockwood flag and Red Peak depends on whether there are more Red Peak supporters than people who feel strongly about the difference between the two ferns. We’d need data.
What this argument does suggest is that if one of the flags were to be replaced on the ballot, trying to guess which one was least popular need not be the right strategy.
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »
I am ambivalent on the red peak flag – it reminds me too much of a shipping flag. Although it’s closest to “Z” which is in some ways appropriate.
9 years ago
There do seem to be degenerate voting outcomes which don’t seem fair.
If the swirly flag gets 49.9% of the first preference votes and the three fern flags get a) 24.9% b) 12.6% and c) 12.5% of first preference votes each and the c) flag supporters vote b) with their second preference and a) supporters vote b) with their third preference than b) will be the overall winner – on the first round c) drops out and gives second preference votes to b), on the second round a) drops out and gives it’s third preference votes to b) meaning b) beats the swirley flag.
But, it seems kinda unjust that 49.9% looses to 12.6%.
Because of the similarity between the three fern flags, the swirley flag pretty much has to get over 50% of first preference votes to win overall because it’s not likely to get many second and third preference votes off fern lovers.
STV seems to get around the problems of splitting votes but it seems to have gone too far the other way.
9 years ago
But it’s not 49.6 losing to 12.6 in your example, You have a majority of people preferring either fern to hypnoflag, so a fern should win.
9 years ago
But almost half the populations first choice gets overtaken by 1/8 of the populations first choice, 1/8 of the populations second choice and 1/4 of the populations 3rd choice.
It just seems wrong that the 3rd choices should carry equal weight to first choices – in this case the people choosing the hypnoflag only get one say while other people get more.
My thought would be that second preference votes should only count as 1/2 a vote and third preference votes should count as 1/3 a vote etc. But I haven’t really thought through the maths of that.
9 years ago
I see what you mean, but I don’t agree. I think it’s more important that when a majority prefer flag A over flag B, that flag A will win.
The system you want also has plenty of precedent. It’s a version of the Borda count method (https://en.wikipedia.org/wiki/Borda_count)
9 years ago
What if my 49.9% liking hypnoflag have a) as their second preference. It means ~75% like flag a) at the first and second preference level but still flag b) wins on third preference votes i.e. the majority prefer flag a over flag b.
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If a voter knows that the hypnoflag is leading but is not likely to make 50% on first preference vote then it doesn’t make sense to vote for hypnoflag as a first preference because then none of your preference votes will count. It would be better to vote for a fern flag straight off because you may have some influence over which fern flag wins.
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I saw Nauru use the election method as I described it above which isn’t the greatest of recommendations given what is going on there.
9 years ago