Chris Keall doesn’t understand voting systems

Posted: September 25, 2015 in democracy
Tags: , , , ,

So, I stumbled across a link to National Business Review talking about the Red Peak flag being added to the referendum today. (Briefly: I support it being added, I don’t think this is the Greens playing into National’s hands, and it’s exposed that Labour is being petty to try and upset the public about how badly National has dealt with this process. But I don’t think all of that is worth a blog)

Chris Keall from NBR claims that due to what he calls “preferential voting”, (generally known in New Zealand as Single Transferable Vote or STV) that Red Peak will be disadvantaged in the first stage of the referendum, due to the fact that the three fern designs are similar. (In evaluating electoral systems, we call similar choices “clones”. Some systems split the vote with clones, disadvantaging the clones. Others allow you to stack points for clones, making it easier for a choice to win when it has many clones to pad out its score) As someone who actually follows how voting systems works and advocates for reform of our voting system, (yeah, I’m not actually perfectly happy with MMP, but it’s better than any other systems New Zealand parties have proposed) let’s go to the classroom on why that’s not the case.

The problem with this argument is that STV is not vulnerable to this flaw. (every voting system has numerous flaws and advantages, the trick is picking one that’s suited to what you want to do) Similar options generally1 neither aid nor hurt each other in a single transferable vote, unlike the plurality system where you can check only one option. STV does an “instant runoff” if no choice achieves at least 50% of the votes when it’s used in a single-winner contest like the flag referendum. With five choices and no likelihood of a landslide, we’re definitely going to have a runoff in the election. Let me show you how this works. Let’s say the first preferences are as follows:

  • Silver Fern (Black and White): 6%
  • Silver Fern (Red White and Blue): 25%
  • Silver Fern (Black Blue and White): 35%
  • Red Peak: 30%
  • Koru (Hypnoflag): 4%

No design has more than 50% of the vote yet, so STV eliminates the option with the least votes in this round. That’s the Koru design. The algorithm tallying votes then looks at how the Koru’s second preferences were set, and reallocates all its votes according to that split. Let’s say 50% of Koru voters wanted Red Peak, 25% wanted the Black and White fern, and 25% only voted for Koru with no second preferences. Koru’s 4% is reallocated according to their second preference, and round two looks like this:

  • Silver Fern (Black and White): 7%
  • Silver Fern (Red White and Blue): 25%
  • Silver Fern (Black Blue and White): 35%
  • Red Peak: 32%
  • No votes/discarded options: 1%

We still need 50% for a winner, so we eliminate the least popular option again, this time the Black and White fern. Those votes are reallocated according to the second preferences of people who voted for the fern, and the third preferences of people who voted for the Koru but had their votes transferred to the fern. Let’s say half of them were Red Peak supporters, a quarter liked the Red White and Blue fern, and a quarter didn’t express any more preferences. We proceed to the third round.

  • Silver Fern (Red White and Blue): 26.75%
  • Silver Fern (Black Blue and White): 35%
  • Red Peak: 35.5%
  • No votes/discarded options: 2.75%

We still don’t have a clear winner, so we’ll have to eliminate the Red White and Blue fern, and proceed to the final round. If we say 10% of Red White and Blue voters didn’t express any further preferences, and 45% each supported the other two designs, Red Peak wins, despite the fact that first preferences for the Ferns added up to 66%. (If you do the maths, you’ll note that Red Peak doesn’t achieve 50% to win. This is because we actually ignore the no votes in determining 50%, but that’s difficult to show)

It doesn’t matter how many people vote for similar options in the first round, it only matters whether enough of the voters for those options rank them all in a block ahead of the other options. If Red peak had polled higher than any of the ferns in the first round, then in fact, the only other proposed system would have caused the ferns to lose, even though it’s likely fern voters will normally prefer other ferns over the two remaining designs.

The other system I mentioned is the one Labour proposed it its amendment bill that was shot down- using a Plurality Vote (the same as we do for electorates) to determine the winner, and rolling both referenda into one paper. If we had done that with the above example, the Black Blue and White fern would have won instead, because the less popular desgns split the votes away from Red Peak, even though Red Peak and the Black White and Blue fern designs were the most popular overall when people’s full preferences were accounted for.

This system is actually the best suited for the kind of referendum we’re holding in the first stage. It’s simple, (you rank as many preferences as you want, and all your consecutive preferences are counted. The only way to null vote is to not write a 1 anywhere) it doesn’t suffer from vote splitting, (that is, it doesn’t punish clones) and it allows you  to relatively1 safely vote your true preferences. Everyone’s vote is counted

1 In very rare cases, you can end up in a situation where one of your less-preferred candidates needs to advance to a later round in order for your most-preferred candidate to win, and requires your vote to swing that earlier round. In these cases, voting your real preferences in order can cause your candidate to lose. This is due to the fact that STV is one of the most mathematically complicated voting systems, (It actually requires a computer to count votes and tally the winner in any practical amount of time) and the run-offs can cause unintended consequences.

The system that fixes this problem, Range Voting, is a little more complicated to vote with. (basically, you rank each option you have an opinion on between 1 and 9.  Options that are ranked by very few people are discarded, then the option with the highest average score wins) It’s generally a better system for multi-winner contests, like in local elections for Councillors or DHB members, and allows you to distinguish between not knowing enough to vote for someone (leaving that option blank) and actually wanting them to lose. (writing a 1  or similarly low number next to them) Ironically, however, Range voting is quite easy to count with- each polling station counts the number of votes and number of each preference rank for each option. Once they’re satisfied they’ve counted correctly for each option, they figure out the average for each option and communicate that average and the number of votes in. Then the central office weights the averages for each option by the number of votes from that polling place, and calculates a new average. It’s so easy to do this that you can do a running average for candidates in a similar way to the running counts for party votes, and it also has a built-in approval rating poll for each option.

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Comments
  1. IRV (Instant Runoff Voting = single-winner STV) is certainly not immune from vote splitting.

    http://www.electology.org/spoiler

    Clay Shentrup
    Co-founder, The Center for Election Science

    • It’s definitely worth noting that what New Zealand calls “Single Transferrable Vote” is an interchangeable name both for what Australia and Ireland know as STV, and also for what is often called Instant Runoff Vote (a more functional name in my opinion) and the Alternative Vote. (In New Zealand, we use IRV under the name STV to elect the local council in Wellington, and now for the first stage of our flag referendum) Apologies to international readers who might be confused- unfortunately many voting systems go by two or three names internationally, so you kind of have to pick your audience in that regard! Australia and Ireland call the multi-winner system specifically by the name STV, (In New Zealand, we use this system to elect District Health Boards) which is a multi-winner variant on the same system, with large electorates that have a multiple-winner contests using quotas and redistributing excess votes from winners as well as from eliminated candidates until they have all votes allocated to the appropriate amount of winners. (Really, if we want to be consistent with how FPP is labelled, STV and IRV ought to be interchangeable names for the single-winner system, and the multi-winner system that Australia and Ireland call STV ought to be called STV at large or IRV at large)

      What you’re talking about is not vote-splitting in the sense that it advantages candidates without similar candidates running, which is how that term is used colloquially. STV (or IRV if you prefer) neither helps nor hurts “clones”, (a technical term for candidates similar enough to appeal to similar groups of voters) but the accusation that has now for the second time been levelled at it by people who are not used to it as a voting system is that it helps clones, and that’s the specific thing I am talking about in this post. The video you linked describes a different problem, favourite betrayal, which I agree and mention in the footnotes is why STV is not ideal, as sometimes it’s not the most strategic move to rank your most favoured option first. (Range voting is the best way to hold single-winner elections, however it has no profile in New Zealand yet) That video also refers to a very specific situation that crops up with STV when you have close three-way races where which candidate wins depends on the order other candidates are eliminated. That’s very advanced electoral mathematics, and it’s also a problem with STV that happens more rarely, and it’s okay to defend STV for what it does well while not thinking it’s an ideal system.

      Favourite betrayal is unlikely to be a problem in the flag referendum, as people broadly fall into two groups for the first stage of the referendum being run using STV: Those who want a fern on the flag if we change at all, and those who want a design that’s very different to the current flag. (note that one of the designs, the Black and White fern, overlaps between these groups, however it’s not very popular and will likely be eliminated in the second round of the instant runoff)

      Because neither of the other dissimilar designs, the black and white fern or the Koru, are likely to win or even beat either of the other two fern designs in a prior round, people voting for Red Peak as a first choice (it’s the most popular design that’s a radical change from the current flag) will not have to consider whether they should rank it first or second. Thus STV (or IRV if you prefer) is unlikely to have any particular problems being used for the referendum if the vote is broadly similar to current polling.

      edit: please also note I’m not explaining terms for you. I’m sure you’re already aware of this stuff. 🙂 I’m explaining for anyone else who reads so they can follow along.

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