Bayesian aggregation

Now that we have enough data (around 40 national polls since the last election), we can start looking at a Bayesian aggregation using a Gaussian random walk to estimate voting intention from day to day.  I will tease with the chart that intrigues me the most: the rise of the One Nation Party since the 2025 election.

A Gaussian Random Walk

I describe the Gaussian Random Walk model in some detail on the Bayesian Aggregation page. If you are not familiar with the model, you should read the Bayesian Aggregation page first. 

Here I want to take a look at the complete set of charts I produce using this model, and explain some of the diagnostic charts. You should note: I only produce diagnostic plots if something looks unusual relative to the model's assumptions. The production of a diagnostic plot doesn't automatically mean there is a problem, just that we may need to make further model specifications to handle the observed anomaly.

For some reason, the Blogger software inserted these charts in reverse chronological order to how I generated them, so we are going backwards, starting with the primary votes before moving to the two-party preferred (2PP) voting intention polling.

Also, I only explain the key features of a specific chart once. Because similar charts are produced for all series, you might need to refer back to an earlier chart for the detailed explanation.

Primary vote - other parties

A note on interpretation: With all of the voting intention charts, the model is more reliable for showing the direction of travel and the scale of movement over time than for pinpointing the exact level of voting intention. House effects shift the entire trend line up or down, and while the median house-effect = zero constraint anchors pollsters relative to each other, it doesn't guarantee the aggregate is centred on truth. If one methodology is systematically closer to reality, the constraint won't know. Trust the shape of the trend more than the precise numbers. 

In past elections, the Coalition has historically been the upside surprise more often than not - until 2025, which was a dramatic reversal. Historically, there's been a persistent pro-Labor bias in Australian polls that 2025 spectacularly contradicted. 

I have considered constraining polls by the best performers at previous elections. But this is complicated. Some pollsters are relatively new, with a limited track record. Many pollsters may also have changed their methodology after the 2025 election to address their performance at that election, making reference to prior performance less relevant. On balance, the zeroed median of the regular pollsters at least tells you what the polling industry collectively believes is happening, even if that collective belief turns out to be wrong.

sigma_likelihood (median: 1.06): This is the observation noise - how much individual polls scatter around the true underlying voting intention after accounting for house effects. A value of ~1.06 percentage points means that even after removing systematic pollster biases, about two thirds of the polls are within about ±1 point of the true value (one standard deviation). This is consistent with effective sample sizes of around 1,000-1,500 respondents, which is smaller than reported sample sizes - reflecting the "design effects" from quota sampling and weighting that reduce the effective information in each poll. Note: the percentage rules you learnt with normal distributions become less accurate with Student-t distributions, especially when nu is small (below 10). With nu around 11, as here, 'about two thirds' is still approximately correct.

nu/100 (median: 0.111, so ν ≈ 11.1): This is the degrees of freedom parameter for the Student-t distribution divided by 100 for display purposes. We use a Student-t likelihood distribution to account for the distribution of polls (including the pollster's house effect) around the population voting intention. A value of ν ≈ 11 puts us in the "moderate tails" regime - the model is finding that the polling data is reasonably well-behaved but benefits from some outlier protection. The Student-t distribution with ν ≈ 11 has slightly heavier tails than a Normal distribution, meaning occasional outlier polls get automatically down-weighted rather than dragging the trend line toward them. If the data were perfectly Normal, ν would be much larger (30+). If there were severe outliers, ν would be smaller (<10). In plain terms: the polls are fairly clean but not perfectly so, and the model is providing a modest amount of insurance against anomalous results distorting the aggregate.

Primary vote - One Nation (ONP)

This chart shows how Redbridge's One Nation Party (ONP) primary vote polling has deviated from what the model expected over time, after accounting for their overall house effect. The green shaded area on the chart is the plus or minus three standard deviations zone. For a Student-t distribution with ν = 19.5 (see the scalar posteriors chart for One Nation below, each series is modelled independently and will have a different value for ν), approximately 99.3% of the distribution falls within ±3 standard deviations. Compare this to the Normal distribution, where ±3σ covers 99.7%.

What it's showing: Each blue dot is a residual - the difference between what Redbridge actually reported and what the model predicted for that day (latent voting intention + Redbridge's house effect). If Redbridge were perfectly consistent with their estimated house effect and the changes noted by the other pollsters collectively, these points should scatter randomly around zero.

The problem: The residuals aren't random. There's a clear upward drift - Redbridge's early polls (June, August) came in below the model's expectation, while their recent polls (November, December) came in above it. In effect, Redbridge saw a larger swing to One Nation over this period than the other pollsters on average.

The red dashed trend line makes this visible. The annotation "mean shift +2.15 (p=0.024)" quantifies this: the average residual in the second half of their polls is 2.15 percentage points higher than in the first half, and this shift is statistically significant (p < 0.05).

What it might mean: Redbridge's house effect for One Nation doesn't move in line with the other pollsters. It is possible that something has changed - possibly their panel composition, weighting scheme, question wording, or how they prompt for minor parties. Their earlier polls suggested One Nation support was lower than the consensus; their recent polls suggest it's higher. The model has estimated a single average house effect across all their polls, but that average may be masking a methodological drift.

The caveat: With only 6 polls, this observation could just be noise. It could also mean that my linear assumptions are wrong, some pollsters might have a non-linear bias, capturing more or less of any movement than other pollsters do (a compressed or exaggerated sensitivity to changes in voting intention). At the moment, I am not concerned. But, it is worth watching - if the pattern continues, I might want to treat early-Redbridge and late-Redbridge polls as separate series.

Primary vote - Greens (GRN)

Primary vote - the Liberal / National Parties (L/NP) Coalition

Primary vote - Australian Labor Party (ALP)

These two charts show opposite "mean shift" patterns for Labor's primary vote:

Roy Morgan (mean shift -1.85, p=0.010): Residuals drift downward—their early polls came in above the consensus, their recent polls below. Roy Morgan is seeing a larger decline in ALP support than other pollsters on average.

Newspoll (mean shift +1.06, p=0.042): The reverse pattern—early polls below expectation, recent polls above. Newspoll is seeing less decline in ALP support than other pollsters.

The fact that two established pollsters are drifting in opposite directions is worth noting. It could reflect different sensitivities to real movement, or methodology drift, or simply noise from small samples (6-9 polls each). It also means the effects partially cancel out in the aggregate, which is some comfort - but it suggests the uncertainty around the ALP trend line may be understated if pollster behaviour isn't as stable as the model assumes.

Two-party preferred vote - the Liberal / National Parties Coalition

Resolve shows a different pattern in the above chart - one significant outlier rather than systematic drift. The August poll (red circle) came in over 3σ below expectation for Coalition 2PP, well outside the normal range. With only 6 polls, that single outlier means 17% of all their polls fall outside ±3σ (compared with an expectation of less than one percent).

The remaining polls cluster reasonably close to zero. The upward-sloping trend line is largely driven by that one early outlier pulling down the left side rather than genuine drift. This is exactly the kind of situation where the Student-t likelihood earns its keep - that August poll gets down-weighted rather than dragging the entire aggregate toward an implausibly low Coalition 2PP estimate.

Two-party preferred vote - Labor

Because two-party preferred voting intention sums to one (or 100%), the Labor 2PP charts mirror the Coalition charts around 50%. The same Resolve outlier appears here, just in the opposite direction - their August poll showed Labor implausibly high rather than the Coalition implausibly low.