### Clinton Boys

I am an Australian data scientist and mathematician, living in Tel Aviv.

# Australian federal election 2016 post-mortem II - third parties

Third parties in Australia have a very peculiar effect on the electoral process. Unlike in American elections, Australian third parties can have a significant effect on the electoral outcome, and can even win seats. This is mainly due to two factors

• compulsory voting, which increases the frequency of protest votes from electors who would otherwise not turnout, and
• preferential voting, which gives third parties’ votes real electoral power in all contests.

For this reason, polling Australian parliamentary elections is a priori more uncertain than in a traditional first-past-the-post contest, since third parties can introduce “chaotic” behaviour which is difficult to account for in polls.

For example, let’s imagine a pollster is trying to understand how voters in the (imaginary, future) seat of Turnbull will vote on election day.

They commission a poll of 550 voters with the following results

| Party | Votes | %  |
|-------|-------|-----|
| ALP   | 220   | 40  |
| LIB   | 130   | 24  |
| GRN   | 100   | 18  |
| ONP   |  50   |  9  |
| NXT   |  50   |  9  |


In a first-past-the-post race, as in the UK, this poll would conclude that the ALP is leading in the seat by 10 percentage points, with some margin of error that could be calculated easily, and would be fairly uncontroversial because the ALP lead is large and statistically significant.

In Australia however, this “primary vote” data is largely meaningless in modelling the predicted winner of the seat, as one must first model how the votes of candidates who did not place in the top two will have their preferences distributed. Let us suppose that 100% of NXT and ONP voters place the Coalition at #2 and then consider the three following scenarios:

• Scenario #1. Green voters split 50/50 to the ALP and the Coalition. This results in a TPP vote of 51-49 in favour of the Coalition.

• Scenario #2. Green voters split 55/45 to the ALP and the Coalition. This results in a 50-50 tied TPP vote.

• Scenario #3. Green voters split 60/40 to the ALP and the Coalition. This results in a TPP vote of 51-49 in favour of the ALP.

This means that an understanding of the second preference votes of Green voters is crucial to the outcome in this contest, which is problematic since the sample size of the subsample of Green voters is much smaller, making the margin of error significantly higher.

I think this concept is difficult to make statistically precise but in my opinion offers evidence that the margins of error quoted in Australian opinion polling are too low.