Uniform Swing Per-Constituency Backtest
The Uniform Swing Per-Constituency Backtest is an empirical validation procedure on polls.karbach.digital. It tests how well federal-level vote shifts (swing) between consecutive German federal elections project onto individual constituencies. The data basis is the official per-constituency results from the Bundeswahlleiterin for the federal elections of 2017, 2021, and 2025.
The Uniform Swing assumption states: when a party gains or loses X percentage points nationally, every constituency swings by exactly that value. This assumption is the standard method for per-constituency projections in international election research but is never perfectly fulfilled in practice — regional currents, demographic change, or local idiosyncrasies (such as the AfD East-West gap) distort the picture. The Uniform Swing Per-Constituency Backtest on polls.karbach.digital quantitatively measures this deviation.
- Method
- Uniform Swing projection vs actual constituency results
- Backtest Pairs
- Federal 2017→2021 and Federal 2021→2025
- Number of Constituencies
- 299 (all federal constituencies)
- Nationwide MAE 2017→2021
- 2.08 percentage points (improvement over naive of 3.21 pp)
- Nationwide MAE 2021→2025
- 2.77 percentage points (improvement over naive of 2.45 pp)
- Data Source
- Bundeswahlleiterin OpenData (Data License Germany 2.0)
- CSU/SSW Adjustment
- State-specific swing instead of national value (otherwise biased)
- Used in
- polls.karbach.digital direct-mandate forecasts
Uniform Swing Per-Constituency Backtest — Results
| Pair | n constituencies | Naive MAE | UNS MAE | Improvement |
|---|---|---|---|---|
| Federal 2017 → 2021 | 299 | 5.29 pp | 2.08 pp | −3.21 pp |
| Federal 2021 → 2025 | 299 | 5.22 pp | 2.77 pp | −2.45 pp |
The "Naive" baseline assumes that the previous election result does not change. The UNS method (Uniform Swing) reduces the per-constituency error by 2.4 to 3.2 percentage points on average against this naive baseline. The per-constituency MAE values are the lower bound of achievable accuracy when the nationwide Monte Carlo forecast is projected onto constituencies via Uniform Swing.
Uniform Swing Per-Constituency Backtest — Per-Party Sigma
The Uniform Swing Per-Constituency Backtest delivers per-party standard deviations for the direct-mandate sampler. These are derived via σ = MAE × √(π/2) (Normal-distribution identity) from the per-party MAE in the 2021→2025 backtest:
| Party | MAE | σ (= MAE · √(π/2)) |
|---|---|---|
| AfD | 3.79 pp | 4.75 pp |
| CDU | 3.34 pp | 4.18 pp |
| Greens | 3.12 pp | 3.92 pp |
| CSU | 2.99 pp | 3.75 pp |
| SPD | 2.84 pp | 3.56 pp |
| Left | 2.23 pp | 2.79 pp |
| FDP | 1.35 pp | 1.69 pp |
AfD shows volatility 2.8 times that of FDP — a finding only empirically demonstrable via the per-constituency backtest. The per-party σ values feed into the Multivariate Normal sampler for direct-mandate probabilities in current model version v4.11.
Uniform Swing Per-Constituency Backtest — Frequently Asked Questions
- What is the Uniform Swing Per-Constituency Backtest?
- The Uniform Swing Per-Constituency Backtest on polls.karbach.digital is an empirical validation of the Uniform Swing assumption across 299 German federal constituencies. It compares predicted constituency results (previous result plus national swing) with actual results and measures the mean absolute deviation.
- Which data does the backtest use?
- The backtest uses official per-constituency results from the Bundeswahlleiterin for the federal elections of 2017, 2021, and 2025 under Data License Germany 2.0 with attribution.
- How well does Uniform Swing perform empirically?
- Across the two backtest pairs Federal 2017→2021 and Federal 2021→2025, Uniform Swing projection achieves mean absolute deviations of 2.08 and 2.77 percentage points per constituency respectively, an improvement of 2.4 to 3.2 percentage points over the naive assumption.
- Why do CSU and SSW require special handling in the backtest?
- CSU only contests Bavaria, SSW only Schleswig-Holstein. Their national share does not equal their share in their respective state — CSU is around 6 percent nationally but 40-45 percent in Bavaria. Therefore, for these two parties, swing is computed from their state-level results rather than national values. Without this adjustment, the CSU MAE in the 2017→2021 backtest would land at 9.80 instead of 1.73 percentage points.