Can a Neural Network Learn the Geography of Sweden’s Local Elections?

Two different reasons for little support

In their preprint, Haodong Qi, Stefano M. Iacus, Pieter Bevelander and Derek S. Hutcheson develop a forecasting model for a difficult combination: many parties receive no votes in particular municipalities, while others attract substantial but highly variable support.

Their approach combines a neural network with a zero-inflated negative binomial model. Despite the imposing name, its central distinction is accessible. One component estimates whether a party belongs to a state of effective local absence. Another estimates vote counts outside that state, allowing more variability than a simpler count model would accommodate.

The distinction matters because organizational absence and a disappointing result are not necessarily the same phenomenon. However, the model’s absence category is a statistical interpretation, not a direct observation of party organization. Its count-generating component can also produce zero votes.

The researchers constrain the count component’s expected votes to remain below the number of eligible voters. This bounds the average prediction for an individual party; it does not mean every possible outcome in the statistical distribution is similarly bounded.

Learning local political patterns

The historical data cover Sweden’s municipal elections in 2014, 2018 and 2022. They combine official election results with candidate-list information and electorate characteristics, including age, sex, citizenship and first-time voter status.

The model also uses previous vote totals and measures of how closely candidates resemble their local electorate in age and gender composition.

Alongside these observed characteristics, the network learns numerical representations called embeddings. These summarize recurring patterns associated with parties, municipalities and particular party–municipality combinations. Think of them as learned descriptions of electoral behavior, rather than labels supplied by political experts.

The authors explicitly caution that similarities between party embeddings are not a map of ideology. Parties can show comparable geographical support patterns without the model knowing anything about their policies or coalitions.

What the historical test establishes

Instead of randomly dividing individual records, the researchers separate municipalities into training, validation and testing groups. This keeps observations from the same municipality out of both training and testing simultaneously.

On the held-out municipalities, the authors report an R-squared of 0.90 for party support measured relative to eligible voters. This indicates a strong fit across the tested observations—not that 90 percent of election outcomes were correctly predicted. They also report a calibration slope of 0.89 and some underprediction at the upper end of support.

These results test geographical generalization within the historical data. They do not establish how accurately the model predicts a later election. The supplied preprint says evaluation against actual 2026 results is reserved for a future version. It also does not report a direct performance comparison with a simpler forecasting baseline, limiting conclusions about the benefit of the added complexity.

Useful predictors are not proven causes

To investigate what the fitted model uses, the researchers remove inputs and measure the resulting increase in prediction error. Party representations and party–municipality relationships have the largest effects.

Among measured characteristics, previous electoral support, candidate-list size and candidate–electorate age similarity stand out. Removing the logarithm of previous votes increases mean absolute error by about 153 percent; removing candidate-list size increases it by about 139 percent.

The authors suggest that larger candidate lists may indicate stronger local organizations, while demographic similarity may capture local representativeness. These are interpretations, not demonstrated mechanisms. The analysis does not show that recruiting more candidates, or changing their age profile, would itself cause a party to gain votes.

Forecasts with unresolved uncertainty

After evaluation, the selected model is refitted using all three historical elections. Table 2 projects approximately 2.03 million municipal votes for the Social Democrats, 1.49 million for the Moderates and 950,000 for the Sweden Democrats. These are model forecasts, not observed results.

Care is needed with percentages: the municipal analysis measures support among eligible voters, rather than among ballots cast. The paper’s narrative aggregate percentages also differ from those printed in Table 2.

Another limitation concerns the forecast inputs. Detailed 2026 electorate demographics were unavailable when the preliminary files were collected, so those characteristics were carried forward from 2022.

The model allows uncertainty to differ between municipalities, but its uncertainty maps are not a demonstration that prediction intervals achieve their intended coverage. The study offers a promising way to represent uneven local competition; whether its advance forecasts proved reliable remains unanswered in this supplied version.