Live Dashboard | Forensic Report
Statistical analysis of the 2025 Bundestagswahl at precinct level (95k Wahlbezirke). BSW received 4.981% — 9,529 votes short of the 5% threshold. This repo examines whether the margin justifies targeted recounts.
Included in data/ (public government data):
btw25_wbz.zip— 2025 precinct results (~95k precincts)btw21_wbz.zip— 2021 precinct resultsbtw17_wbz.zip— 2017 precinct resultsbtw13_wbz.zip— 2013 precinct resultsew24_wbz.zip— Europawahl 2024 precinct results (BSW included)btw2025_strukturdaten.csv— Sociodemographic data per Wahlkreisew24_strukturdaten.csv— EW24 Strukturdaten
Datenquelle: © Die Bundeswahlleiterin, Wiesbaden 2025 (bundeswahlleiterin.de), dl-de/by-2-0
wahlbezirk_lr.py— Ridge regression per party (GroupKFold by WKR)ridge_party_cv.py— Ridge regression (precinct-level, 2025 only)bsw_bd_decorrelate.py— BSW+BD sum decorrelation analysisbsw_forensic.py— 11-test forensic battery for missing votesbsw_claims_test.py— Tests BSW's 4 specific claims about miscountingxgb_enhanced.py— XGBoost + Europawahl 2024 + Strukturdatenbsw_evidence.py— scenario analysis for BSW crossing 5%bsw_bayesian.py— Bayesian posterior P(Δ≥9,529)bsw_power.py— Power analysis for forensic batterypanel_analysis.py— Gemeinde-level 4-election panelevidence_registry.py— Suspicious precinct registry with anomaly scoresbsw_recount_bias.py— Recount selection-bias sensitivity analysisbsw_adjacency_did.py— Ballot adjacency natural experimentbsw_generative.py— Latent-variable generative model (no double-counting)bsw_affidavits.py— Sworn statement cross-referencecalibrate_zero_model.py— Zero-vote model calibrationcalibrate_zero_betabinom.py— BB zero calibrationtriangulate_lr_xgb.py— LR vs XGB triangulationlow_tail_undercount.py— Low-tail BB undercountbsw_bd_swap.py— BSW→BD swap modelofficial_corrections.py— Prelim→final correctionsgenerate_report.py— HTML report generation
Independence-first LR (253 features):
- 2025 structural: turnout, invalid rates, log(voters)
- 2021/2017 Erst+Zweit shares (Wahlkreis-level)
- EW24 party shares (Gemeinde-level join)
- Strukturdaten demographics (Wahlkreis-level)
- Bundesland dummies (15 cols)
- No 2025 Erststimmen (avoids same-election leak)
Base LR (210 features): adds 2025 Erststimmen
95,046 precincts, 29 party models, GroupKFold(10) by Wahlkreis, Ridge(alpha=5000). BSW uses strict features (no 2025 Erststimmen); other parties use base features.
| Party | LR R² | Notes |
|---|---|---|
| CDU | 0.96 | |
| AfD | 0.96 | |
| Die Linke | 0.86 | |
| SPD | 0.85 | |
| BSW | 0.64 | strict (no e25) |
| BSW | 0.63 | base (with e25) |
| FDP | 0.59 |
BSW R²=0.64 with the strict model confirms predictions do not depend on same-election features. Leave-one-Land-out: R²=0.38 (strict model generalizes better than base R²=0.04).
| Rank | Feature | Importance |
|---|---|---|
| 1 | 2017 Die Linke Erststimme | 42.3% |
| 2 | EW24 BSW Zweitstimme | 16.8% |
| 3 | 2021 AfD Zweitstimme | 6.1% |
| 4 | Sachsen (Land dummy) | 3.2% |
| 5 | Foreigner population % | 0.9% |
BSW draws primarily from former Die Linke voters and AfD-adjacent demographics in eastern Germany.
BSW gained +4,277 Zweitstimmen (prelim→final) — 44.9% of the 9,529 deficit. BD lost −2,640.
784 precincts show fewer BSW votes than predicted. Null-calibrated excess: 5,145 votes (p=0.005).
4 powered forensic tests (skew, Benford, geographic, negative-residual fraction) have 0% power for diffuse 9,529×1 miscount. Even concentrated 953×10 patterns are only 15% detectable (skew test alone). "No evidence" ≠ "no errors exist."
Tested whether votes were swapped between them:
- Raw residual correlation: +0.028 (no anti-correlation)
- Would need ~12.5% of ALL BD votes for BSW to reach 5%
- BSW+BD pair does not stand out vs control pairs
10 of 11 tests show no BSW-specific anomaly; Benford 2nd digit deviates (p=0.0014, see report). The 4 powered tests have 0% power for diffuse errors. BSW matches controls (FDP, Die Linke) on every test.
1. Turnout–BSW correlation — Weak positive overall (r=+0.22), similar to AfD. Per-Land breakdown shows negative r in West (NI -0.26, HE -0.25) and positive in East — a normal demographic pattern matching other parties.
2. Briefwahl vs Urne — Clear East-West split: BSW is ~0.5-1.5pp higher in Urne (West) but 2-3.6pp higher in Brief (East). Die Linke shows the exact same pattern. BSW residual means are near-zero in both channels (Urne -0.006, Brief +0.013pp). No channel-specific manipulation.
3. Second-digit Benford's Law — BSW deviates (p=0.0014), but FDP is worse and AfD far worse. Die Linke passes cleanly. Not a BSW-specific anomaly. (See report for current computed χ² values.)
4. Precinct-size stratification — BSW residuals have a weak positive trend with precinct size (Spearman +0.066): larger precincts have slightly more BSW than predicted. Opposite of the fraud hypothesis (larger = easier to manipulate). FDP and Die Linke show negligible patterns.
5. Invalid vote correlation — BSW residual–invalid rate correlation is 0.0000 overall. Per-Land values are small and mixed-sign. No evidence of BSW ballots being invalidated.
6. Multimodality — KDE of BSW residuals shows a single peak at -0.21. FDP and Die Linke also unimodal. No hidden "depleted" subpopulation.
7. Kurtosis & skewness — BSW has slightly positive right tail skew. Missing votes would produce negative skew (left tail). Leptokurtic (heavier tails than normal). Not consistent with systematic undercounting. (See report for computed values.)
8. Geographic clustering — Only 5/299 Wahlkreise have BSW mean residual z < -2. In those 5, FDP residuals are positive (+0.08) and Die Linke slightly negative (-0.08). Pattern reflects model limitations, not coordinated fraud.
9. Zero-vote deep dive — 60 suspicious BSW zeros (model predicts >3%, >100 valid votes, Poisson P<0.01). Mostly in BY (22) and NI (10). But FDP also has 10 suspicious zeros despite being well-established. 60 out of 95k precincts is within normal variance.
10. Gaussian Mixture Model — 2-component GMM fits better for all three parties equally (BSW ΔBIC=9258, Die Linke ΔBIC=12757). BSW components: 67% with μ=-0.2pp, 33% with μ=+0.4pp. Die Linke nearly identical. Reflects demographic heterogeneity, not a "depleted" fraud subpopulation.
11. Feature importance — BSW residuals correlate with essentially nothing (all |r| < 0.02). The model already captures all systematic variation; remaining errors are noise.
68% Jaccard overlap between LR and XGB suspicious sets. Spearman ρ=0.878. Top-20 overlap: 70%, Top-50: 94%. Both models flag the same precincts.
BSW got 4.981%, missing 5% by 9,529 votes (0.019pp).
Claim 1: Ballot confusion — r=+0.028, no systematic swap detected. Would need ~12.5% of BD votes.
Claim 2: Zero-vote precincts — 784 low-tail precincts. Null-calibrated excess: 5,145 votes (p=0.005).
Claim 3: Recount extrapolation — 50 BSW-selected recounts. Selection bias limits extrapolation.
Claim 4: Official corrections — BSW +4,277 (44.9% of deficit) through normal verification.
The 9,529-vote deficit is small enough that targeted recounts are justified:
- Official corrections already recovered 44.9%
- 5,145 excess missing votes (p=0.005)
- 4 powered forensic tests lack power for diffuse errors
- All 3 publicly specified affidavit cases matched to anomaly registry
- Strict BSW model (no e25) confirms R²=0.64
3,578 flagged precincts by 4 criteria (BB P(0), BD rank). Uses Beta-Binomial p0 via bb_utils. BB-calibrated excess: HE +20.6, NI +28.7, BY +52.1. All 3 publicly specified affidavit cases matched (8 filed total; precinct IDs for remaining 5 not yet public).
Rate θ=0.304 [0.18, 0.48]. If recounts represent only the 81 BB-suspicious precincts: ~25 votes (P=0%). Need f≥20% representativeness for any chance. f=30%: P=35.5%.
Anomalies lower where BSW has Erst (ratio 0.43). Logistic regression with controls: has_erst OR=1.12, p=0.50 (not significant). FDP placebo: OR=1.54, p=0.04. BSW=0 concentrates in small precincts (471/517 in Q0).
Swap + zero-out channels. Conservative: med=3,089, P=0%. Bias-adjusted Beta(1,9): med=8,385, P=41%. Results are highly sensitive to π prior — treat as scenario exploration, not proof.
# Step 1: generates data/wahlbezirk_lr_predictions.csv (125 MB, gitignored)
# All downstream scripts depend on this file.
# Alternatively: make all
python3 wahlbezirk_lr.py # LR prediction models
python3 xgb_enhanced.py # XGBoost + EW24 + Strukturdaten
python3 bsw_bd_decorrelate.py # decorrelation analysis
python3 bsw_forensic.py # forensic battery
python3 bsw_claims_test.py # BSW's specific claims
python3 bsw_evidence.py # scenario analysis
python3 bsw_bayesian.py # Bayesian posterior
python3 bsw_power.py # power analysis
python3 panel_analysis.py # Gemeinde panel analysis
python3 evidence_registry.py # build precinct registry
python3 bsw_recount_bias.py # recount bias analysis
python3 bsw_adjacency_did.py # adjacency DiD
python3 bsw_generative.py # generative model
python3 bsw_affidavits.py # affidavit cross-reference
python3 calibrate_zero_model.py # zero-vote calibration
python3 recount_targets.py # triage funnel → top 100
python3 generate_casefiles.py # per-precinct case files
Quick paths:
make reproduce-core # predictions → report → tests
make recount # evidence → targets → case files
make all # everything