Some of you may remember back a few weeks ago early on Qld election night, an Auspoll exit poll was released on Sky Nooz that polled Labor’s 20 most marginal seats. From that result I projected that Labor should win between 51 and 53 seats if that poll were correct. I used some simulations and regression equations for that and it seemed to do the job since it worked – but it was ridiculously complicated, having to adjust for safe vs. marginal swing behaviour before projecting a likely result across the board and then simulating an actual result using an assumed level of dispersion around a mean swing. So rather than go through that lunacy again, I’ve figured out a much easier way of getting from point A (a known result in a small number of seats of known margin) to point B (an election outcome).
One of the interesting things about Australian election results are the distributions of the two party preferred vote. If we take one of the major’s TPP results and order them from lowest to highest, we end up with an S shaped curve – a cubic polynomial (which is a very common curve in economics, representing all sorts of behaviour like technological diffusion trends for example)
For instance, the ALP TPP distribution leading into the 2009 Qld State election looked like this:
We are only looking at the 85 seats (out of 89) where the actual contest was an LNP/ALP two party race. Nearly every election result looks similar to this, be it State or Federal (although Tassie with their system of proportional representation is a different kettle of fish altogether).
We can run a cubic polynomial regression through this pre-election Qld data to get a cubic trend line with literally massive statistical significance, and we can also do the same with the post election results to compare them side by side.
So the basic shape of our cubic trend lines don’t change much in the middle – the gap between the blue and black trend lines are pretty consistent in the middle of the chart, just the level of the trend lines change.
What does change is the comparative shape of each trend line at the fringes – but for out purpose here – predicting elections from exit polling- what happens on the fringes isn’t really that important, since being a few points out for a seat that sits on 65% of the two party preferred, doesn’t make any real difference when it comes to determining whether or not that seat would change hands.
Looking again just at the results leading into the election, we had:
The blue shaded area in the above chart represents the 20 most marginal ALP seats leading into the election. So when the Auspoll came out showing the average two party preferred result in those 20 seats being 50/50, we had enough data to simply adjust the trend line according to the new results.
What we’re interested here is the way a trend line should change rather than the actual seat results that are distributed around the trend line. So Auspoll estimated the average TPP result for the 20 most marginal Labor seats was 50 when the average of the trend results for those same 20 seats was 54.4.
So if we drop that trend line by the 4.4% swing, we should end up with something approaching a realistic estimate of the new distribution – although we should expect our lines to diverge at the fringes, but again, that really doesn’t matter for what we are trying to do here.
If we know look at the old pre-election trend and compare it to the estimated election trend based on the Auspoll results, we end up with this:
From this, if we count up all the seats where the ALP has 50% + 1 of the vote, we get 53.
That’s close, but not really good enough. However, the error doesn’t come from our projections; it comes from the Auspoll polling. The actual ALP TPP average result in Labor’s most marginal 20 seats wasn’t the 50/50 that Auspoll estimated, it was actually 49.5% . Auspoll was out by half a percent – which is hardly surprising with polling uncertainty. If Auspoll were exactly right, our trend line would have been slightly different. In fact, we can compare the trend line projection based on the Auspoll exit poll, the trend line projection if the Auspoll was exactly right and the actual cubic polynomial trend of the election result itself.
As you can see, the projected numbers start to diverge at the fringes of the chart, but in the middle they are extremely close to the actual result.
If Auspoll were exactly right and estimated 49.5%, a trend projection from that number gives Labor 51 seats – the exact number they ended up winning.
So this methodology, a much, much simpler one than we used on election night, is a handy way to project ultimate outcomes from exit polls – the only trouble is the sampling error involved in the exit polls themselves. But we can simulate probabilities for that on future election nights. For instance, let’s say that we used this for the Qld election night exit poll, we could have projected the number of seats that would have fallen, and given them probabilities – so it would have been a 96% probability of a Labor victory, with a 70% probability of getting somewhere between 51 and 55 seats.
The one thing that might be worth doing between now and the next election is to slightly modify the projections to accommodate the way safe seats behave to reduce the diversion between our projections and the actual results at the fringes – which should make for better accuracy should we ever come across large swings.