# 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.

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 1/120

^{th}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 61/120^{th} 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.

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!*

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*Led by Mr I.M. Wright

** Led by Mr M.Y. Tern

Tagged: Election, electoral commission, electoral maths, mathematics, Overhang, Party vote, Vote2014NZ, Wasted vote

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Update: It looks like the electoral commission have now fixed their online calculator