**Guest post by Dab**

I’ve noticed a number of commenters recently making reference to a party vote for ACT being worth four times a party vote for the Nats. This has been reposted on the ACT website as recently as today:

A Party Vote For ACT is worth four times a party vote for National. This is because of a little known aspect of MMP. Under MMP the electorates a party wins are deducted from the number of list MPs awarded.

On average it will take 60,000 votes to elect each National list MP. Whereas it takes just 16,000 to elect an ACT MP.

So the answer is easy. Party vote ACT for three years of stability.

Now I was intrigued, as the mathematician inside me (yes I do have a personality defect) pondered how this could be possible, so I enquired of the commentator when I first saw this and was helpfully directed to the ACT website, to see that the author was none other than Richard Prebble.

Once I saw how & what he had done, I was able to replicate his calculations, but more importantly draw my own conclusions as to whether what he was espousing is true or not. I believe the info is misleading and the 4 times’ worth is a myth.

Now to be clear I am not advocating any preference for voting for Nats over ACT; merely pointing out what certain party votes are worth, and in particular what they are not worth. Apologies if you do already get this, but as people still keep referring to Richard/ACT’s numbers I feel duty-bound to inform as widely as I can. My analysis as follows:

Q: Where does the ’60,000’ come from?

A: Based on the 2011 election result, the total number of seats gained by Nats was 59. This was based on their overall share of non-wasted part votes (i.e. subtracting votes for parties which did not either gain an electorate seat or make the 5% party vote threshold). By my calc this was 47.31% (Nat share) divided by 96.63% (100% less 3.37% wasted) then multiplied by 120 seats (overhangs not included) = 58.75.

Now of course it is not possible to have 0.75 of a list MP so 58.75 gets rounded up to 59 whole seats. (BTW this is basically what the Sainte-Laguë method does; allocating whole seats between parties and rounding up & down as required, so that all seats are divvied out based on non-wasted party vote result).

As we know, Nats also separately won a total of 42 electorate seats. As ACT correctly notes above, these are deducted from the total seats to determine how many list seats Nats won. So 59 less 42 = 17 list Nat MPs. As the total 2011 party vote for Nats was around 1,058,600, what ACT seems to have done is to take 1,058,600 and divide by 17 giving an average result of slightly over 62,000.

So far so good.

Q: Where does the ’16,000’ come from?

A: This is simpler -although I get a slightly higher answer than they did. At the end of the day it will depend on the actual number of non-wasted party votes, and of course this could vary depending on whether e.g. Conservatives, IMP get across the line (IMP by holding onto TTT electorate; Cons by getting to 5% party vote). At this stage it looks like NZF will get there, which personally stumps me, but there you go.

In 2011 total party vote excluding wasted was around 2,162,000. Dividing this by 120 gives around 18,000. Near enough for me for the purposes of this discussion.

Q: So do the Nats need to win an extra 62,000 seats to gain an extra seat?

A: NO.

Just because their average list seat “cost” was 62,000, does not mean that an additional 62,000 party votes gets them an extra seat. In fact – all based on 2011:

(1,058,600 + 62,000) / 2,162,000 = 51.8%, multiplied by 120 gives a total of just over 62 seats – an extra 3. In fact the actual extra margin gained is 62.2 – 58.75 = 3.45 (ignoring the fact that you cannot have part-seats). And 62,000 extra votes divided by 3.45 = approx. 18,000. Ah OK – the same 18,000 as above.

This, good people, is what can be referred to as marginal costing, i.e. the additional extra required, as opposed to average costing which is what ACT have used. While their calculation is arithmetically sound, it is the wrong basis on which to decide what it “costs” for the Nats to win an extra seat**. The answer IMHO is simply, once any party is ‘in the game’ so to speak; i.e. has an electorate MP or is >5% party vote, then to be sure of an additional list MP (assuming no overhang for that party) they each will need the same no of extra party votes – around 18,000 based on 2011 result**.

Q: So if say Nats had gained an extra 18,000 votes in 2011 and got this extra seat, where would it have come from? What if say 3 other parties had each lost 6,000 votes – surely this means that none of the 3 would have lost any seats?

A: Good question. However this raises another very important point to note at this juncture – the 18,000 is what it takes TO BE CERTAIN of winning – or losing – an extra seat. If a party has a result which entitles them to e.g. 10.49 “seats”:, then Sainte-Lague should give them just 10 whole seats. However if they had won enough votes to get to 10.51 “seats” then they should end up with 11; an extra one. So it is entirely possible that just a handful of extra party votes could tip a party over the threshold need to gain an extra seat, or alternatively losing those extra few votes could cost them a seat. Of course there is no way of knowing for sure how many extra votes are needed until one has an actual result!

So the answer is Sainte-Lague formula should re-divvy the seats so that the total was preserved, but with Nats having one extra, and some other party losing 1.

Q: I’m still not entirely convinced?

A: Allow me to give one more arithmetic example of why the average cost is the wrong thing to use. Let’s look forward (gulp) to Saturday. Take Labour (please do!) – if they, as has been projected by some, hold onto all the 22 electorate seats they won in 2011, plus gain another say 4 (e.g. Napier, Waimak, TTT – fingers crossed – and 1 other), but their party vote tanks and they get the 22.4% based on a recent actual poll, then this should give them a total of 27 seats, and assuming total vote of 2,162,000 would mean that roughly 484,300 people had party-voted for them.

Applying the ACT logic, to get the average party vote per list seat, we would take 27 total seats less 26 electorate seats, so 1 list MP (step forward Mr David Parker). And 484,300 / 1 = 484,300. So using ACT logic as applied previously to Nats, Labour would need another 484,300 votes (double what they would get) to gain ONE extra MP. Simply not true.

Here endeth the lesson. Party vote for ACT if you truly wish – I can see the logic in doing this assuming Epsom plays ball and there is no reason not to think so – but please don’t think you are getting 4 times the value of e.g. voting Blue.