It’s all about the math, dummy!

No one understands the electoral maths of the NZ electoral system including the electoral commission apparently. Last night I put the latest figures from the “Poll of Polls” into the electoral commission calculator and I discovered the calculator was broken! I put the figures in with United Future winning one electorate seat, but when it crunched the numbers it gave me a parliament without United Future in it. Hmmm… have I uncovered a conspiracy to keep Peter Dunne out of parliament, or is it just evidence that someone got their math wrong. Let’s hope it’s the latter and that they’ll get it right on the night.

Electoral Commission calculator results captured 17 September 2014

Electoral Commission calculator results captured 17 September 2014

In the meantime, let’s consider two concepts this election hangs on – the so called “Wasted vote” and the “Overhang.” The Wasted Vote is the proportion of votes that go to parties that do not make it into parliament by either crossing the 5% Party vote threshold OR by winning at least one electoral seat. The overhang is when a party or parties win more electoral seats than the proportion of their Party vote entitles them too. This means that the size of parliament would increase. Normally 120 and 1/120th of the party vote (0.83%) is equivalent to one member of a party. However, for example, if a party receives just 1% of the vote, but wins 2 electorate seats then this will increase the size of parliament to 121. The various permutations of polls have the current election resulting in a parliament ranging from 120 to 124 seats.

The number of seats in parliament is crucial because it means the effective number of seats a party of block of parties must win in order to form the majority to govern increases. 61 seats are needed for a 120 or 121 member parliament, 62 for a 122 or 123, and 63 for a 124 member parliament.

About the Wasted vote two ideas are important:

The Wasted vote supports the party already with the most votes the most

The Wasted vote could determine who governs!

Let’s assume that 61 seats are necessary in a 120 seat parliament. Ie a block needs 61/120th of the party vote (50.83%) to govern. Crucially this percentage, though, is NOT the percentage of the vote that block gain on the night (which is what the polls try and predict). What it is, is the “effective percentage” after the Wasted votes are taken into account. A scenario could help. Consider an election with two parties crossing the 5% threshold to get into parliament and all the rest being wasted votes. Let’s call the two parties the Big, Rich and Totally Selfish (BRATS*) party and the Really After Total State (RATS**) party. Consider this, there are 1 million voters. BRATS gets 450,000 votes on the night (45%). But, 10% (100,000) of the vote is Wasted. That means the proportion of votes the BRATS get out of the non-wasted votes is 450,000/900,000 giving an “effective percentage” of 50% which would give them 60 seats in parliament.  The RATS would have the same in this scenario. We can turn this question around the other way and ask how high a proportion of the total vote does the Wasted vote have to be for the BRATS “effective percentage” to cross the 50.83% threshold needed to govern? This will depend on the total proportion of votes the BRATS receive  (in our example 45%). The graph below illustrates this.

The percentage of wasted votes the BRATS need in order to govern based on the actual percentage of votes they receive

The percentage of wasted votes the BRATS need in order to govern based on the actual percentage of votes they receive

So, folks, if on the night your vote is in the waste basket, rest assured it will have an effect on the outcome of this election.  The only truly wasted vote is the one that is not cast!


*Led by Mr I.M. Wright

** Led by Mr M.Y. Tern

7 thoughts on “It’s all about the math, dummy!

  1. michaelmacaskill

    Hi John, I’d say the claim that “The Wasted vote supports the party already with the most votes the most” is a bit simplistic, and is true only in absolute arithmetical terms. In reality, the wasted vote systematically distorts the result politically even though it is just being equally redistributed arithmetically. i.e. I’d say “the wasted vote most benefits parties holding the opposite political views to those voters”.

    e.g. let’s say the election is a dead heat in left-right terms, with 50% of votes going to parties representing either end of the spectrum. But the Conservatives, say, get 4.999% and fail to get elected. Their vote is then distributed equally among the other parties. That means the right-leaning parties effectively lose 2.499% of the total vote. i.e. instead of there being a 50/50 R/L split, the effective result becomes 47.7/52.5 R/L, with a clear majority to the left.

    The redistribution is not neutral, but systematically weighted against the interests of those who “wasted” their vote.

    1. John Pickering Post author

      It’s a blog, therefore simplistic, but I take your point Michael. I was merely talking about the party with the most votes getting the biggest boost through the wasted vote. I wouldn’t got so far as to say most benefits parties holding “opposite” political views to the voters. The redistribution and the example you mention are for one particular scenario. The opposite could be argued if the Internet Mana party gets a few percent but Hone doesn’t win his seat.

      1. michaelmacaskill

        Hi John, the situation you describe would show exactly the same principle in operation, it’s just that in this case the net vote transfer would be from the left to the right. Once again, this would be the opposite of what the “wasted” Internet/Mana votes were designed to achieve. So the general principle stands: if “wasted” votes are clearly identifiable as being for the left or right, the net effect of their re-distribution will always benefit the opposite end of the spectrum. i.e. the opposite end of the spectrum gains votes that were not cast for it, while the other end loses them.

  2. Brent

    You wrote :
    “So, folks, if on the night your vote is in the waste basket, rest assured it will have an effect on the outcome of this election. The only truly wasted vote is the one that is not cast!”

    This is incorrect. A wasted vote that is cast has exactly the same effect on the results of the election as a vote that is not cast (or is invalidly cast). The only difference is in which “bucket” the non-vote sits in the official election results.

  3. John Pickering Post author

    Hi Brent, Thanks for the comment. I was just trying my hand at some rhetoric rather than anything else. Interestingly, on the surface of it your comment and Michael’s would appear to contradict each other. I think the difference is only if you can clearly distinguish which “block” a vote would have supported then by being wasted it slightly favours the other block or blocks (although my point that it favours the *party* with already the most votes still stands). On the other hand, if it does not favour one block over another (e.g. if NZ First don’t make the threshold) then it’s more like no vote cast at all. Having said that, an individual NZ First voter may have a preferred “block” option and so recognise the potential risk/reward of their vote being wasted.

    1. michaelmacaskill

      Yes, you’re right John, my reasoning only applies to wasted votes where the intentions of the voter to support one end of the spectrum are clear: it doesn’t really apply to, say, New Zealand First, or the Maori party, which can go either way. And yes, I don’t agree with Brent: wasted votes (for parties with a definite left/right identity) do not have the same effect as non-votes or invalid votes. Unlike the latter, they are systematically redistributed against the intentions of those who cast those particular votes. That is something that minor party voters have to weigh up quite carefully: they might think they are supporting a particular political view by voting for a supporting minor party, but if their vote is wasted, it will tend to be re-redistributed in a way that supports the opposite view. That is why Labour hopes the Conservatives do as well as possible without breaking 5%, and why, as you note, National would be happy for IMP to get a couple of percent as long as Hone Harawira doesn’t retain his seat.

      Anyway, good to see your blog generating some numbers-based discussion!


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