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What it would take to steal a seat in the special votes

Update: I’ve uploaded the spreadsheet I used to make these calculations—a link is at the bottom of the post.

While the two million ordinary votes have been counted, there are still around 220,000 special votes left. We won’t know the effects of these votes until final results are released on 10 December. In the past, they’ve changed the provisional results: last election, they saw the Greens take a seat from National. What would it take for that to happen again in 2011?

Summary

  • Greens need a 2.23-point swing on National in the special votes (alone) to take a seat from them.
  • Greens need a 2.27-point swing on Labour (in the special votes alone) to take a seat from them.
  • To gain two more seats, the Greens would need to almost double their vote in the specials (i.e. get 20.23%).
  • NZ First is closest to picking up another seat. They only need a 0.43-point swing on National, or a 0.54-point swing on Labour (though the latter is more complicated).
  • It’s impossible for NZ First to lose a seat.
  • National would take a seat off Labour with a 3.73-point swing. Labour would do the same to National with a 4.5-point swing. Both situations require NZ First to lose a little as well.
  • Maori, ACT, Mana and United Future would need to quintuple, double, triple and decuple their votes in the specials respectively, so their seat counts won’t be budging.

Explanation of model

This analysis works as follows. As a starting point, we assume that special votes follow the same proportions as ordinary votes. We then transfer votes from a “losing party” to a “gaining party”. When this happens, their quotients (under the Sainte-Laguë method, see Elections NZ, Wikipedia) fall and rise respectively. The idea is to find the point where the last quotients of the parties gaining and losing seats are equal. This is the minimum vote transfer needed to steal the seat.

When I talk about “losing”, “gaining” or “transferring” votes, I mean relative to the assumption that the special votes are in proportion to the ordinary votes. A “swing” means the difference in percentage points between the special votes (not the total votes) and the ordinary votes.

We try not to touch the votes of other parties. This means that this analysis is a bit simplistic but shows the absolute minimum vote gains necessary, like a best-case scenario. (You need fewer votes if you’re only stealing from one party.) In some cases, though, a vote transfer between two parties results in a seat being picked up by a third party, so we adjust that party’s votes accordingly too.

Greens to take a seat from National

Party Provisional result Special required Swing Total required Change
National 47.99% < 45.76% -2.23% < 47.77% -0.22%
Greens 10.62% > 12.84% +2.22% > 10.84% +0.22%

Given the Greens’ history with special votes, this is the most likely scenario. For the Greens to take a seat from National, they need to get 12.84% of the special votes. (That is, of the 220,720 special votes, 12.84% need to be cast for the Greens, all at National’s expense—a “vote transfer” of 4,863 votes or 2.23 percentage points.) This would take the Greens’ total party vote from 10.62% to 10.84%, enough to see Mojo Mathers (14th on Greens list) replace Aaron Gilmore (53rd on National list).

This will probably happen: the Green co-leaders think they will hit 11 per cent. Based on a comparison to the special vote effect of 2008, Graeme Edgeler on the Legal Beagle finds similarly. I think it’s a good bet that, even if they don’t hit 11 per cent, they’ll pick up enough to get seat number 14.

Because National was allocated the 120th seat (using the Sainte-Laguë method), it’s the easiest to steal seats from. It’s theoretically possible for the Greens to steal from Labour though.

Greens to take a seat from Labour

  Provisional result Special required Swing Total required Change
Labour 27.13% < 24.86% -2.27% < 26.91% -0.22%
Greens 10.62% > 12.89% +2.27% > 10.84% +0.22%

If the Greens take their extra votes from Labour rather than National, they can see Labour’s last quotient (8,967) slip past National’s (8,930) to be lost to the Greens at 8,893. In this case, they would need 12.89% of the special votes, or a transfer of 4,971 votes, slightly more than what they would need stealing from National. At time of writing, iPredict’s live parliament projection had this scenario happening.

The current deadlock in Christchurch Central means that the exiting Labour MP could be either Raymond Huo (21st on list) or Rajen Prasad (20th), depending on whether Brendon Burns wins.

Note that if the Greens pull that same number of votes (just under 5,000) from both National and Labour, but split between them, they would not gain an extra seat. This is because National’s and Labour’s last quotients would both go down, but neither by as much—so the increase in the Greens’ last quotient won’t meet either. It works best for the Greens if their extra support in specials comes “from” a single major party.

It’s not possible for the Greens to steal from any other party: that would require the losing party to get a negative number of special votes.

Greens to take two extra seats from National or Labour

Since this would get James Shaw (15th on Greens list) into Parliament, I feel compelled to include this. The easiest way for the Greens to gain two seats is to take one from each of National (who got the 120th seat) and Labour (who got the 119th seat):

  Provisional result Special required Swing Total required Change
National 47.99% < 42.73% -5.26% < 47.47% -0.52%
Labour 27.13% < 23.03% -4.10% < 26.73% -0.40%
Greens 10.62% > 20.23% +9.61% > 11.57% +0.95%
NZ First 6.81% < 6.51% -0.27% < 6.78% -0.03%

This would also require NZ First to lose a little to prevent them getting one of the vacated seats first. Unfortunately, though, this situation does require the Greens to almost double their party vote (10.62% to 20.23%) in the specials, which for supporters of Mr Shaw is rather wishful thinking.

The Greens could also gain two seats off National or two off Labour with just a bit more (20.97% or 21.02% respectively).

New Zealand First to take a seat from National

  Provisional result Special required Swing Total required Change
National 47.99% < 47.56% -0.43% < 47.94% -0.05%
NZ First 6.81% > 7.23% +0.42% > 6.85% +0.04%

It’s actually easier for NZ First to take a seat from National than it is for the Greens to. That’s because NZ First, in the provisional results, is “next in line” for a seat: its next quotient of 8,867 is the highest of the non-qualifying quotients. So it just needs to catch up to National’s last quotient of 8,930, which it can do with a 0.43-point swing.

This isn’t likely to happen. NZ First is more likely to suffer from the special votes than pull 7.23% of them. But it’s not a foregone conclusion.

New Zealand First to take a seat from Labour

  Provisional result Special required Swing Total required Change
National 47.99% > 48.37% +0.38% > 48.02% +0.03%
Labour 27.13% < 26.20% -0.93% < 27.04% -0.09%
NZ First 6.81% > 7.35% +0.54% > 6.86% +0.05%

For this to happen, both National and NZ First have to gain votes at the expense of Labour. This is because when we transfer votes from Labour to NZ First, their quotients (originally 8,967 and 8,867) meet at 8,947, which is higher than National’s 8,930. Then NZ First wins the seat off Labour, who in turn wins it back off National—hence the need for National to gain votes too. The number of votes switching hands is still just 2,025, less than what the Greens need. But for NZ First it probably won’t happen.

New Zealand First to lose a seat to anyone: NZ First’s Asenati Taylor (8th on list) is safe. NZ First’s eighth seat sits at a quotient of 10,050, well ahead of the 120th quotient of 8,930. For them to lose a seat they would effectively need to get less than zero special votes. Sorry to disappoint you.

National to take from Labour or Labour to take from National: For either of these to happen, NZ First would need to lose 299 votes to the gaining party to stop it from getting the seat first. Including those votes, a 3.73-point swing towards National would do the trick for them, as would a 4.5-point swing towards Labour.

Maori Party to gain a third seat: Note that this wouldn’t actually gain the Maori Party a seat—they have three electorates but are only allocated two seats, so a third seat just means no overhang for Parliament. They would need at least 7.87% of the special votes to take the 120th seat from National and prevent NZ First from getting there first. They weren’t far over the bar for two seats with ordinary votes (1.35%) so their next quotient is down on 5,966, well short of 8,930. It’s also impossible for the Maori Party to lose a seat, but only just.

The one-seat parties (ACT, Mana and United Future): The ACT Party would need to get 2.41%, the Mana Party 3.10% and United Future 6.54% to benefit from special votes. Since this is doubling, tripling and decupling their votes respectively, it’s fair to say these parties won’t be affected by special votes. They can’t lose their party vote seat allocation (to create an overhang) either, even if they get zero special votes.

Spreadsheet
Update: The spreadsheet I did to figure out these “minimum vote transfers” can be found here (XLSX format). It’s a little esoteric but hopefully it’s followable.
Update 2: It appears that that spreadsheet doesn’t work in Excel 2007 and earlier, so you need Excel 2010, because I used the FLOOR() function with negative numbers but positive significance.
Update 3: Uploaded new version, that spreadsheet should now work in Excel 2007 and earlier.

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2 Comments Post a comment
  1. IanS #

    Interesting. But I suspect that more of the voting for specials (o’seas) were counted in the early votes than last time.

    29 November 2011

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  1. The minimum swing needed in the special votes for the Greens to steal that seat | Trying to Reason

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