Modeling election outcomes

So far, all our posts thus far have been set up stuff. We’ve covered

  1. self-important intros and why we’re doing this
  2. how not to use electoral probabilities
  3. a bit of talking ourselves up re the AFR article
  4. advantages and disadvantages of using electoral betting data

It’s time to look at how we use the probabilities we have from the betting markets to model the election.

What are we modeling? 

To start with, we want to predict how many seats the governing ALP will win at the next election. Dont be surprised, but the ALP will definitely win between 0 and 150 seats! The aim of our analysis is to figure out the probability of each possible outcome. So we want to figure out the probability that the ALP will win 0 seats, the probability they will win 1 seat, will win 2 seats,…, will win 150 seats. And we will then do the same for the Coalition.

We can then draw this as a nice little probability distribution, analyze the shape, and talk about the likelihood of various scenarios.

How do we go about doing this?

For each electorate, imagine there are only two relevant probabilities. The probability ALP wins, and the probability ALP loses. We can then think of the result of each electorate as a toss of an unfair coin. Some coins will favor the ALP, and some coins will favor the Coalition. We can then simulate an election by tossing each of the unfair coins. And then we can count the number of electorates won by the ALP, and not won by the ALP to make a prediction.

We repeat this process 100,000 times. The more times we do it, the better we can approximate the true probability distribution. After simulating 100,000 elections, we can then see how often certain outcomes occur. Maybe we see that the ALP winning 63 seats happens in 40,000 of the simulated elections. We’d then say the probability of the ALP winning 63 seats is 40%. We would do this for every possible outcome and then plot a probability distribution.

What do the probability distributions look like?

Below we show a probability distribution we did just before Julia Gillard was replaced. The model predicts that:

  • the probability the ALP will win government (ie. more than 75 seats) is pretty low.
  • the expected number of seats the ALP will win is 49.
  • the expected number of seats the Coalition will win is 95.

Some of these numbers were covered in the AFR last weekend. But we wanted to show the shape of the probability distribution before Gillard was replaced.

June 25 – Before Rudd

After Rudd replaced Gillard, the ALP’s probability distribution shifted to the right a bit. But the probability of them winning government (ie. winning more than 75 seats) is still not so good. The ALP increased their expected number of seats to 56, with the Coalition down to 88.

June 30 – After Rudd

As things stand, the electorate-level betting odds imply the probability of a Labor victory is still very, very small. Whether this true, or a limitation of the data, will be a focus of future posts.