1. Liberals' Lost Incumbency Advantage

With the departure of the outgoing Liberal leader Sussan Ley—an eight-term incumbent in a rural electorate—the party loses an estimated 3.9% personal vote advantage. This penalty is calculated by comparing the party’s primary vote in the House of Representatives against their Senate vote (as Senate voting is heavily party-based, it provides a clean baseline free from local candidate effects). While the 2025 data was clouded by a strong independent candidate (Michelle Milthorpe), the 2022 election provides a perfect real-world check: without a major independent on the ballot, Sussan Ley's personal vote gap was a very close 4.3%.

2. Entering & Exiting the Field

Twelve candidates are contesting the Farrer by-election, up from nine in 2025. To account for this larger field, the model uses 2025 Senate results to reallocate votes away from non-contesting parties TOP and establish baselines for new minor party entrants LCPSAP . For the major new additions to the ballot, the NAT vote is carved directly out of the broader Coalition baseline, while the two new independents are injected as 'generic' independents via a separate model.

3. Choosing the Right Polling Swing

Applying national polling shifts to a single electorate requires the right tool:

• Uniform Swing applies the flat shift in national polls since the last election (e.g., ON shifting from 6.4% to 23.8%), but it fails to account for a party's local strength. In Farrer, the COAL baseline (38.4%) is substantially higher than their 31.8% national vote in 2025, while GRNandLAB are much lower.
• Proportional Swing respects the local baseline through scaling it by the national swing, but it breaks the fundamental reality that total swings must sum to exactly zero (meaning the final vote total won't be 100%).
• The Additive Log-Ratio ( ALR ) transformation solves both problems. It scales shifts relative to Farrer's local baseline while mathematically locking the final total to exactly 100%. This methodology was accurate in capturing how One Nation's surge during the recent South Australian election translated to their votes in individual seats.

4. Labor Voters' Strategic Reallocation

Labor is not fielding a candidate in the Farrer by-election, so their adjusted baseline vote is shattered and redistributed into the remaining parties. Similar cases from historical by-elections suggest the primary beneficiary is the leading independent, absorbing an estimated 56% of the orphaned vote. On average, 21% cascades to ideologically aligned minor parties GRNLCPSAP. These estimates rely on only 6 by-elections since 1990 without a Labor candidate, but with a prominent Independent, meaning Labor's reallocation is incorporated with significant uncertainty.

5. The Final Projection: Blending National and Seat Polls

The final projection blends the information from the national polling trend with that of recent seat polls of Farrer using dynamic Bayesian weighting:

• Historical Calibration: How much should we trust a local poll over the national polling trend? By testing the model against a decade of past elections and by-elections to minimize historical prediction errors, the model is tuned to an optimal blend. This blend is used to inject polling error uncertainty using multivariate normal distributions in ALR space, specifically accounting for historical by-election polling errors being ~14% greater than those in general elections.
• The Farrer Blend: Currently, Farrer has two published seat polls, and the latest national poll was taken 14 days prior to the by-election. The historical calibration gives the local seat polls a dominant average weight of 56% in the final calculation, leaving 44% for the National-polling-based model. The weights differ per party, which is why some parties' final average is closer to that of the seat polls than others.
• Minor Party Allocation: Pollsters don't prompt respondents for every minor party. To fill these gaps, the model uses Dirichlet distributions to split the 'Other' vote into its constituent parties, as well as the 'Coalition' vote between LIB and NAT. Here, the model applies a probabilistic mix: 52% of the simulations draw their split from the seat polls, while the other 48% draw from the historical baseline.

6. Simulating the Winner

In our preferential voting system, the winner is determined by sequentially eliminating the lowest-polling candidate and reallocating their voters to the remaining parties. To avoid modelling each possible order of elimination - with 12 candidates there are over 479 million of them! - the model assumes the two parties with the highest first preference vote will form the final Two-Candidate Preferred (TCP) matchup.

There is one important exception: if neither the Liberals nor the Nationals place in the top two. Because their voters typically heavily preference one another, the model checks if reallocating 70% of the smallest Coalition party's vote to the other would mathematically push them into the top two. If so, they replace the initial second-placed party.

Finally, significant shifts in the political landscape since the 2025 election mean historical preference flows may be inaccurate. The model augments Farrer's baseline TCP flows with recent data from the 2026 South Australian Election.

Limitations of the Model

This by-election model is at its core probabilistic: it aims to describe the uncertainty inherent to the by-election outcome rather than to 'predict' an exact result. When tested on historical elections/by-elections, its average error (MAE) is ~3% per party - that's how much you should expect each party's average to be wrong by! Its real power is its ability to interpret which kinds of extreme outcomes are plausible.

Some aspects are captured imperfectly:

• National polling constraints:National polling poorly captures Independent vote intentions. With the combined minor/IND vote dropping from 15% to 11% since 2025, applying this swing directly would artificially suppress the vote of a prominent local Indendent, Michelle Milthorpe. There are no perfect solutions: the model fixes the IND baseline at 7.2% (as in 2025), forcing the remaining minor parties to brunt the swing. If this forces the minor party total below a crude 4.5% threshold, a small rebalancing adjustment is applied to all parties to stabilize the simulation.
• Use of Senate results: A fully Bayesian probabilistic model would incorporate uncertainty about each component being estimated. The current model takes some shortcuts in the early stages, with Senate results used for reallocating votes to new parties being accepted as direct fill-ins for votes in the House. While it could be claimed that these newly-contesting parties should be treated with greater uncertainty, the model is none the wiser.
• Deterministic parameters: The model uses several sub-models to estimate its components, such as incumbency advantage, polling error covariance matrices, or the vote ratio between the Coalition parties. Ideally, the uncertainty in the estimation should be incorporated to make the estimated parameters themselves random. At present, most of these are taken to be deterministic, although the primary election-specific sources of uncertainty in polling error and minor-party splits are rigorously dealt with.
• ALR transformation bias: Using an ALR transformation to apply polling swings solves many mathematical problems, but carries a subtle statistical cost: one party must be chosen as the 'reference' category - in this case COAL - and made to suffer an artificial slight reduction in its simulated uncertainty. Hence, it is possible that the model is underestimating the variability of the Coalition parties' vote, however my impression is that the effect is on the scale of less than 1% in win probability.

The polling data fed to the Farrer by-election model (adjusted for undecideds) can be downloaded here: Seat Poll (CSV), National Polls (CSV).

See the projections for Farrer at the 2025 election