🔎 What Was the Problem?

Digit-based election forensics (DBEF) typically depends on null-hypothesis significance testing, which can distort substantive conclusions and leave practitioners with hard-to-interpret results.

🧩 How the New Framework Works

The approach decomposes the observed numeral distribution into two latent classes—"no fraud" and "fraud"—by identifying the smallest fraction of numerals that must be removed or reallocated to attain a perfect fit to the "no fraud" model. That fraction is directly interpretable as a measure of fraudulence.

• Two specific procedures are described:
• Removing numerals until the remainder perfectly fits the "no fraud" model (a removal-based measure).
• Reallocating numerals to achieve a perfect fit (a reallocation-based measure).
• These two procedures map onto established fit measures: the π* (pi-star) mixture index of fit and the Δ (Delta) dissimilarity index, respectively.

⚙️ Relaxing Distributional Assumptions

Independently of the latent-class decomposition, the distributional assumptions that standard DBEF methods require can be relaxed in some contexts. Either alone or together, the latent-class framework and these relaxed assumptions permit decomposition and model-fitting that are more flexible than existing DBEF approaches.

📊 Reanalysis of Existing Data

Application of the method to Beber and Scacco (2012) data demonstrates that the latent-class approach can produce different substantive conclusions than prior analyses, illustrating its practical implications for forensic inference.

⚖️ Why It Matters

The framework avoids overreliance on hypothesis-testing heuristics, yields an interpretable fraud measure (the minimal fraction of problematic numerals), and expands the modeling toolkit for digit-based election forensics, enabling clearer, more nuanced assessments of suspicious numeral patterns.