Coalition By 32 On Sept 7

Using implied probabilities from Sportsbet and Centrebet odds to simulate the result of all 150 federal seats, I estimate the Coalition will gain a 32 seat majority in the House of Representatives on Sep 7.

Both bookmakers give odds on every federal seat. One can use the payouts to estimate the probabilities of each candidate winning in each seat. The method I used is discussed here. Then it is a matter of calculating a probability distribution for the election outcome by running many simulations of the result of all 150 seats simultaneously. In this model, the most probable outcomes are 91 or 92 seats for the Coalition, 56 or 57 for Labor and 2 or 3 for independents.

Interestingly, when I first ran the simulation on Friday night, the most likely results were the Coalition 90 or 91, Labor 57 or 58 and 2 or 3 independents. However, the odds for the Coalition have shortened in many seats over the past few days, especially in Queensland. In particular, the Liberals are now favourites in Brand and Eden-Monaro. On Friday night, the ALP were.

There will almost certainly be at least two independents in the lower house after Sep 7. Bob Katter is an overwhelming favourite to retain Kennedy and Andrew Wilkie is paying $1.15 on Sportsbet and $1.10 on Centrebet to win Denison. That implies an 85% probability of winning the seat. The other independent could either be strong local candidate and rural consultant, Cathy McGowan in Indi or the Greens’ Adam Bandt in Melbourne. The betting on both of these has lengthened in the past week, but it is possible one will get in. There are a couple of other seats with a strongly rated third candidate: Clive Palmer in Fairfax and former Gosford mayor Lawrie McKinna in Robertson, although these two are paying $8 - $10. Between the four candidates, there is a significant chance at least one could get up (though I believe, less than 50%).

Here is how the simulation works:

1.      For each of the 150 electorates, get the payouts from Sportsbet and Centrebet, then separately calculate the implied probability distributions as per my article.

2.      Average the two implied probability densities. I grouped all candidates other than the Coalition and ALP into a single “third outcome”, or fourth outcome in the three Lib – Nat – ALP three cornered contests: Mallee, Durack and O’Connor. These three seats will all be won by the Coalition anyway.

3.      For each run of the simulation, draw 150 random numbers between 0 and 1. For any particular seat, suppose the calculated probability in Step 2 of the Coalition winning is P₁, the ALP winning is P₂ and someone else winning is 1 – P₁ – P₂. Then if the random number R < P₁, the Coalition wins the seat. If P₁ < R < P₂, the ALP wins the seat. Otherwise the shortest priced other candidate wins. This gives us the distribution of seats in the lower house for this particular simulation run.

4.      Run Step 3 many times. I used 1,000,000. The frequency of each possible make-up of parliament is an estimate of its probability.

A brief note on generating the 150 random numbers:

Generating them independently assumes the events and voter decisions which will lead to each candidate winning or losing are independent between seats. This is clearly not the case. Between now and Sep 7, local issues will combine with an overall “electoral mood” to decide the results. The changes in electoral mood (currently swinging toward the Coalition) will influence seats toward either Coalition or ALP candidates and thus produce correlations in outcomes.

The way to model this is to generate a single random number R₀ in the interval (0, C) for the mood, then 150 independent random numbers, R_k in the interval (0, 1-C), representing local factors.

The random number in Step 3 for electorate k is then R₀ + R_k. The common factor R₀ in all 150 random numbers represents the overall electoral mood in that particular simulation. Raising the value of C increases the correlation of outcomes.

I used C = 0.1. Lower values of C favour the independents. A higher value than 0.1 may even be justified: I have no data on which to calibrate a choice, so have decided to err on the conservative side (scientific, not political).

It is important to understand that C does not reprsent the correlation between current voting intentions in different seats. That is provided by the correlations between the current payouts.

What C reprsents is the correlation between changes in voting intentions in different seats between now and the election date. Higher values mean changes in the overall electoral mood will have a stronger influence on the outcomes in each seat.

A run just prior to this post gave Coalition – Labor – Independents 91 – 57 – 2 as the most likely outcome. Last Friday night, it was 90 – 58 – 2.

Even though the Coalition has moved ahead in the betting in both Brand and Eden-Monaro in the past few days, the most probable outcome is still that they will pick up one of these seats, although there is a significant chance they could win both.

Nate Silver had great success forecasting the 2012 US presidential election using betting and polling data. The latter was easier to obtain than polling data by individual seat here, because in the US presidential election, the “seats” are actually the states, with the winner of a state taking all allotted electors.

I don’t really have the time to get such data and probably couldn’t anyway, unless I was embedded in one of the major parties’ campaigns. I’m assuming the changes in betting odds will correlate highly with changes in local polls, even though they are actually determined more by the amounts bet on each candidate.

Anyway, given the data currently available, my call is an easy victory to the Coalition, with a 32 seat majority in the House of Representatives. I strongly doubt they will get control of the Senate.

I'll run an update on the night of Friday Sep 6 to see how much things have changed.