Searching for Electoral Irregularities in an Established Democracy: Applying Benford’s Law Tests to Bundestag Elections in Unified Germany
Bibliographic record
Abstract
This article investigates electoral irregularities in the 1990 to 2005 Bundestag elections of unified Germany. Drawing on the Second-Digit Benford Law (2BL) by Mebane (2006), the analysis consists of comparing the observed frequencies of numerals of candidate votes and party votes at the precinct level against the expected frequencies according to Benford’s Law. Four central findings stand out. First, there is no evidence for systematic fraud or mismanagement with regard to candidate votes from districts where fraud would be most instrumental. Second, at the state level (Bundesland), there are 51 violations in 190 tests of the party list votes. Third, East German states are not more prone to violations than Western ones. This finding refutes the notion that the East’s more recent transition to democracy poses problems in electoral management. Fourth, a strong variation in patterns of violation across Bundesländer exists: states with dominant party control are more likely to display irregularities. The article concludes by hypothesizing and exploring the notion that partisan composition of nominees involved in the counting may produce a higher likelihood of violation and be a cause of Länder variation. This may especially be the case when a party dominates in a Bundesland or opponents to the former socialist regime party are involved in the counting.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.032 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".