Posts Tagged ‘plurality voting’

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

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