Skip to content

Posts tagged ‘special votes’

A growing swing to the left in the special votes

The Greens and Labour have been doing increasingly well in the special votes, and National increasingly poorly.

I did a projection, based on the 2011 results, that the Greens probably wouldn’t pick up the extra seat they often do from special votes. But I didn’t call it a prediction, partly because I didn’t intend it to be, but also because the numbers had the Greens only narrowly missing out on that 14th seat. So if the Greens had pushed just a tad further and made it over the line, I wouldn’t have been surprised. I said it was going to be close.

As it happened, it wasn’t close. The Greens had nearly 5,000 votes to spare.

Party Preliminary Projected final Project vs prelim Actual final Actual vs project Actual vs prelim
% Seats % Seats % Seats
National 48.06% 61 47.36% 61 -0.69% 47.04% 60 -0.33% -1.02%
Labour 24.69% 32 25.11% 32 +0.42% 25.13% 32 +0.02% +0.44%
Greens 10.02% 13 10.52% 13 +0.50% 10.70% 14 +0.18% +0.67%
NZ First 8.85% 11 8.54% 11 -0.30% 8.66% 11 +0.12% -0.19%
Māori 1.29% 2 1.38% 2 +0.09% 1.32% 2 -0.06% +0.04%
Act 0.69% 1 0.69% 1 -0.00% 0.69% 1 +0.01% +0.00%
UF 0.22% 1 0.21% 1 -0.00% 0.22% 1 +0.01% +0.00%
Conservative 4.12% 0 3.93% 0 -0.19% 3.97% 0 +0.04% -0.15%
IM 1.26% 0 1.39% 0 +0.12% 1.42% 0 +0.03% +0.16%

To be more specific: The Greens saw their 14th seat shoot not just past National’s 61st, but also past its 60th, to become the 119th quotient. This meant the Greens had room to spare: 4,873 votes less (with no redistribution) and they would’ve stayed on 13, or National would have needed 21,836 more to get to 61. (This is more than the ~18,800 “votes per seat” because National also has the 120th quotient.) For comparison, my projection had the Greens needing 1,139 more than projected to pick up a 14th seat.

Changes in context
What happened? I suggested there were reasons why the specials might swing further left in my projection post:

  • The number of overseas voters doubled this election compared to 2011.
  • Some universities had on-campus polling booths, where a lot of students would have cast advance special votes.

Further on the second point, as Jonathan Marshall suggested on Twitter, unlike 2011’s, this election was during the university semester so more students would have been outside their electorates in the first place.

But I certainly didn’t expect any combination of these effects to add to 5,000 more votes for the Greens alone, so I suspect there’s something else. Also, those reasons are just speculation. For all we know, it could even be related to migration patterns (including domestic migration), though I don’t know that those have actually been changing. The full statistics that the Electoral Commission will release in about two weeks might offer a bit more insight, but it’s hard to discern.

A growing swing since 2008
Beneath this swing, there might be an underlying trend. The Greens have traditionally done well on special votes, of course. But they’re doing increasingly better on specials than they used to, at least since 2008. (I couldn’t easily find preliminary results for 2005.)

special-votes-trend-2

The first set of columns is the special vote percentage divided by the preliminary result (so < 1 means a drop), and the second set is the difference between the specials (not total) and preliminary result in percentage points.

Now, take the sparklines with a grain of salt. The scales aren’t consistent between cells, and they each only have three data points anyway.* Also, the two sets of columns are just different measures for the same phenomenon, so the fact that it happens twice adds no weight. (I did both while trying to find a more consistent predictor of special vote impact, and couldn’t.)

But they do broadly indicate an improving trend for Labour and the Greens, and the opposite for National. And the trend isn’t small. In 2008, National lost 0.52 points from specials; this year, they lost 1.02 points. The Greens have gone from gaining 0.29 points to 0.67 points. One seat’s “worth of votes” is roughly 0.83 per cent, a bit less if you allow for wasted votes.

If I were in the National Party, I’d be concerned about this trend. As it stands, National is generally expected to lose a seat to the Greens on specials. But the Greens are getting increasingly good at this, and are picking up the seat even when the numbers suggest the increase won’t be enough.

Spreadsheet
For people who like numbers, here’s the spreadsheet I used for these calculations: Special vote impact projection 2014. It’s an extended version of the projection spreadsheet I posted earlier.


*Although there are only three data points, they are reliable since they are true by definition, not a sample. (Turnout is interesting for other reasons, but it’s the final result that matters here.) I’d be more worried about short-term circumstances giving the illusion of a long-term trend. The value of adding anything before 2005 might be questionable though, since the situation a decade ago might lose relevance to today.

Projection of special votes for the 2014 election

On my projection for the 2014 special votes, based on the 2011 impact, the Greens will miss out on a 14th seat by a whisker and National will retain its outright majority. Maybe.

I crunched some numbers to project (I didn’t say “predict”) the impact of special votes. I suspect most of you will just want to know the answer, so I’ll cut to the chase first, then give a bit of analysis, then give a bit more details, and I’ll talk about my method fourth.

Special votes include, among other things, overseas votes and votes cast for a different electorate to the polling place location. They aren’t counted on election night; they’re just set aside for the full count released two weeks later. And they’re not normally representative of the vote as a whole. Historically, special votes have favoured the Greens significantly—they have often picked up an extra seat from it, as they did in 2011.

The most fundamental assumption I make is that you can use the 2011 impact of the special votes as a guide to the 2014 impact. Some other minor assumptions will become apparent in the method description at the end.

Summary
Basically, on my projection, the results would stay the same. The Greens will get closer to a 14th seat, but because on the preliminary results they only just got their 13th one, special votes won’t propel them far enough for a 14th. However, they will be tantalisingly close, moving their 14th seat to the 121st quotient.

Party Preliminary results Projected final results Gain/loss
Votes % Seats Vote % Seats
National Party 1,010,464 48.06% 61 1,136,155 47.37% 61 -0.69%
Labour Party 519,146 24.69% 32 602,304 25.11% 32 +0.42%
Green Party 210,764 10.02% 13 252,394 10.52% 13 +0.50%
New Zealand First Party 186,031 8.85% 11 204,919 8.54% 11 -0.30%
Māori Party 27,074 1.29% 2 33,134 1.38% 2 +0.09%
ACT New Zealand 14,510 0.69% 1 16,685 0.70% 1 +0.01%
United Future 4,533 0.22% 1 5,098 0.21% 1 -0.00%
Conservative 86,616 4.12% 0 94,357 3.93% 0 -0.19%
Internet MANA 26,539 1.26% 0 32,826 1.37% 0 +0.11%
Aotearoa Legalise Cannabis Party 8,539 0.41% 0 10,894 0.45% 0 +0.05%
Ban1080 4,368 0.21% 0 4,992 0.21% 0 +0.00%
Democrats for Social Credit 1,609 0.08% 0 1,983 0.08% 0 +0.01%
The Civilian Party 906 0.04% 0 1,035 0.04% 0 +0.00%
NZ Independent Coalition 895 0.04% 0 1,023 0.04% 0 +0.00%
Focus New Zealand 677 0.03% 0 774 0.03% 0 +0.00%

I project the Green gain to be 0.50%, and the National loss to be 0.69%. In a lot of cases, this can be enough to win and lose a seat, respectively: one seat is roughly 0.8% of the vote (0.83% if you ignore “wasted” votes), so it’s easy to imagine that another 0.5% might push you over.

But in this election, it wouldn’t be enough. The reason is that, in the preliminary results, the Greens only just made their 13th seat: it was the 118th quotient, i.e., the 118th seat to be allocated. National, on the other hand, has some room to slack before losing a seat—in fact, it would have picked up the 121st quotient, if there was one. In effect, the Greens would need to pick up to nearly a “whole seat” worth of votes to pick up seat number 14.

In my projection, the Greens nearly get there, but not quite. They move their 14th seat from the 127th quotient to the 121st. So if there was one more seat in Parliament, it would be theirs. And they’re very close: with 1,129 votes more (all other vote counts staying the same), they would steal the 120th quotient from National. Conversely, if National had had 5,058 votes less (all other counts staying the same), they would give up the 120th quotient to the Greens.

What does this mean?
In practice, what this tell us is not necessarily that Steffan Browning won’t make back in at Maureen Pugh’s expense. It’s that he might—but it’ll be very close. Certainly, the Greens shouldn’t be expecting another seat from specials, like they could in 2011.

There are, however, reasons to believe the wind might blow in the Greens’ favour. Firstly, advance votes were way up on previous elections. This was partly due to a concerted effort from parties to promote advance voting this election, and (I think) more so from the left than the right. Now, ordinary advance votes are counted on election night. But special advance votes—which include votes cast in advance outside the voter’s electorate—are not. And, as @annagrammatiste pointed out to me on Twitter, a lot of those special advance votes will have been cast at universities, some of which had advance voting booths on campus this year. University students, on average, lean left.

Secondly, estimated overseas votes doubled in this election, from 19,500 in 2011 to 38,500 in 2014. Overseas voters are known for being particularly Green-heavy.

Without those reasons, I would have said that it’s more likely that the seat allocations will stay put, but not enough to put money on it. But these weaken that likelihood. My instinct is that it probably won’t be enough, but objectively, I’m not really sure. It’ll be super close.

That’s basically the gist of this post. If you like voting systems, read on.

~

Some more detail
To dive in a little deeper, here’s a quick primer on how the Sainte-Laguë method works. This is the method used in New Zealand to proportionally allocate seats. The easiest way to think of it (in my opinion) is that you allocate the seats one by one, to the party with the highest “quotient” at the time. Every party’s initial quotient is their total number of votes, so the first seat effectively goes to the party with the most votes. Then, every time you allocate a seat, you divide that party’s total votes by their next divisor to get their new quotient (leaving the rest untouched). The first divisor for each party is 1, then it goes 3, 5, 7, and so on. You repeat till you’ve allocated all 120 seats.

How are quotients relevant? Well, here are the quotients near 120 for the preliminary results:

Quotient National Labour Greens NZ First Māori ACT UF
118 8350.9 8240.4 8430.6 8088.3 5414.8 4836.7 4533.0
119 8350.9 8240.4 7806.1 8088.3 5414.8 4836.7 4533.0
120 8215.2 8240.4 7806.1 8088.3 5414.8 4836.7 4533.0
121 8215.2 7986.9 7806.1 8088.3 5414.8 4836.7 4533.0
122 8083.7 7986.9 7806.1 8088.3 5414.8 4836.7 4533.0
123 8083.7 7986.9 7806.1 7441.2 5414.8 4836.7 4533.0

As I said, the Greens got the 118th quotient, and won’t pick up another one until 127. National’s getting quotients more often because it has more votes, and the gap between dividing by 121 and 123 is “smaller” than between 25 and 27 (Greens), so to speak.

Here is the same for my projected results:

Quotient National Labour Greens NZ First Māori ACT UF
118 9547.5 9560.4 9347.9 8909.5 6626.7 5561.7 5098.4
119 9547.5 9266.2 9347.9 8909.5 6626.7 5561.7 5098.4
120 9389.7 9266.2 9347.9 8909.5 6626.7 5561.7 5098.4
121 9237.0 9266.2 9347.9 8909.5 6626.7 5561.7 5098.4
122 9237.0 9266.2 8703.2 8909.5 6626.7 5561.7 5098.4
123 9237.0 8989.6 8703.2 8909.5 6626.7 5561.7 5098.4

The Green’s 14th quotient is just 41.8 away from National’s 61st. So we find a rudimentary “margin” for the Greens by multiplying this difference by the 14th divisor: 41.8 × 27 = 1,129. For National, we use the 61st divisor: 41.8 × 121 = 5,058.

Method
Okay, now for the exciting part. (Heh.) There are lots of ways to do this projection; Graeme Edgeler has one that basically gives the same outcome. This is how mine works.

I took the preliminary results for 2011 and subtracted them from the final results to get the “special vote addition”. I use quote marks because it’s not actually all special votes: it also includes votes cast at polling places with fewer than 6 votes (these aren’t counted on election night) and any corrections. But anyway, I compare the preliminary percentages to the “special vote addition” percentages, by division, to get a “multiplier” for each party. This multiplier represents a relationship between the preliminary votes and the special votes for each party.

I apply this multiplier to the preliminary vote percentages for each party in 2014. If a party didn’t contest the 2011 election, I just use 1 (i.e., no adjustment). Now, after doing this, the percentages won’t add up to 100, so I scale them so that they do.

The next part is the complication. The preliminary total vote count includes informals (ballots where you can’t tell who they voted for); obviously the sum of parties’ votes don’t. And the preliminary special vote estimate (I take the figure that includes overseas votes and fewer-than-6 places) includes ballots that might later be ruled invalid, because the statutory declaration wasn’t completed correctly or something like that. So I use 2011 ratios of preliminary to final counts to project how many valid special votes there will be in 2014. It doesn’t end up making much of a difference (0.4%), but hey, I wouldn’t know unless I tried.

The last step is to use the projected special vote percentages and the projected valid special vote count, to project the “special vote addition” for each party, add those to the preliminary count and that’s the projected result.

If you get excited by numbers like I do, here’s the spreadsheet I used to figure this out: Special vote impact projection 2014. The actual Sainte-Laguë stuff is in a different spreadsheet, but I’ve pasted the borderline quotients into that spreadsheet.

A Parliament based on the special votes only

Parliament would have looked incredibly different if the country voted the same way that the special voters did.  Note that this is not the “results including special votes”; it’s a hypothetical “special” Parliament that would have existed if tabulated based on the special votes only.

Major differences from the actual Parliament
  1. The Greens would have had 19 seats and the Mana Party two seats.
  2. New Zealand First would not have made it back to Parliament.
  3. Labour would most likely have formed government.

A hypothetical “special-votes” Parliament

Party

% special votes

Electorate seats*

List seats

Total seats

Difference from prelim
National Party
41.76%
41
13
54
-6
Labour Party
30.41%
23
17
40
+6
Green Party
14.67%
0
19
19
+6
Maori Party
2.11%
3
0
3
† 0
ACT New Zealand
1.13%
1
0
1
0
Mana
1.65%
1
1
2
+1
United Future
0.53%
1
0
1
0
New Zealand First Party
4.84%
0
0
0
-8
Conservative Party
1.72%
0
0
0
0
Aotearoa Legalise Cannabis Party
0.92%
0
0
0
0
Democrats for Social Credit
0.12%
0
0
0
0
Libertarianz
0.08%
0
0
0
0
Alliance
0.06%
0
0
0
0
Total
100.00%
70
 50
120
-1
* I didn’t take note of the preliminary electorate vote counts, so I’m just using final electorate results here.
† The Maori Party’s seat allocation would have increased by one, from two to three, but because they got three electorate seats this would have just removed the overhang seat.

Special votes have historically favoured the left-wing parties, and it’s quite evident from these numbers: Labour and the Greens had seven percentage points between them more in the special votes than the preliminary results (27.13% and 10.62% respectively).

The biggest change, though, is New Zealand First.  Less than five per cent of special votes ticked New Zealand First, so the special voters would have had NZ First miss out on Parliament altogether.  This, combined with a 6.2-point loss for National, would have seen Labour and the Greens six seats stronger each.

Labour and the Greens would then have had 59 seats between them, just short of a 61-seat majority.  National, ACT and United Future (assuming Mr Dunne still chose to favour National) would have had 56.

The two-seat Mana Party was ruled out by both Mr Key and Mr Goff.  That only leaves the Maori Party.  Even if they did favour National, their three seats wouldn’t have been enough to push National over the 61-seat line.  So it’s a fair bet to say that, whoever the Maori Party talked to first, they would have ended up with Labour.

So basically the special voters voted for a left-wing government.  Labour, the Greens and the Maori Party would have between them commanded 62 seats, enough to govern.  That is very fascinating given how certain it’s always seemed (and still seems) that National had this election in the bag.

Impact of special votes on the final election result

This is a follow-up to my earlier post, What it would take to steal a seat in the special votes.

Party

% votes in prelim count

% special votes

Swing from prelim

Prelim total seats

Final total seats

Gain/loss
National Party
47.99%
41.76%
-6.2%
60
59
-1
Labour Party
27.13%
30.41%
+3.3%
34
34
 
Green Party
10.62%
14.67%
+4.1%
13
14
+1
New Zealand First Party
6.84%
4.84%
-2.0%
8
8
 
Maori Party
1.35%
2.11%
+0.8%
2
2
 
ACT New Zealand
1.07%
1.13%
+0.1%
1
1
 
Mana
1.00%
1.65%
+0.7%
1
1
 
United Future
0.61%
0.53%
-0.1%
1
1
 
Conservative Party
2.76%
1.72%
-1.0%
0
0
 
Aotearoa Legalise Cannabis Party
0.48%
0.92%
+0.4%
0
0
 
Democrats for Social Credit
0.07%
0.12%
+0.05%
0
0
 
Libertarianz
0.07%
0.08%
+0.008%
0
0
 
Alliance
0.05%
0.06%
+0.004%
0
0
 
Total
100.00%
100.00%
0.0%
121
121
0

I said in my earlier post that the Greens would need a 2.23-point swing on National in order to take a seat from them in the actual results. With a 4.1-point swing, they did that with ample room to spare.  Because Labour also gained 3.3 points while National lost ground, the Greens steal from National rather than Labour, even though Labour was more “at risk” of losing their last seat.

The Greens were obviously well short of the 9.6-point swing they would have needed to get two more seats.

As predicted, NZ First had a negative swing—so they lose their position of being the “closest” to another seat.  That 121st seat now belongs to the Labour Party, and NZ First’s next seat would be number 124.  It was impossible for NZ First to lose a seat, so they stay on eight seats.

Labour sort of got close-ish to the 3.73-point swing required to draw a seat from National, but the swings in the other parties would have raised this bar even further for Labour anyway.  They do, however, now claim the first non-qualifying quotient (a.k.a. seat 121, previously held by NZ First).  With another 5,906 votes at the expense of National (a 2.4-point swing in the special votes, or a 0.26-point swing nationally), they could have taken another seat of National.  That would have reduced the National-ACT-United Future total from 61 to 60—just short of a majority.

So, to paraphrase, if Labour had pulled another 5,906 all at National’s expense, they would have forced National to get the support of at least one party other than ACT and United Future (most likely the Maori Party) in order to pass legislation.

It was impossible for all minor parties to lose a seat, and none of them close to doubling their vote, let alone tripling or decupling as required for Mana and United Future.  So they all stayed put.

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.