Benford's Law and the 2025 Philippine Senate Election: A Forensic Statistical Analysis of Official Results

This study applies both the first- and second-digit Benford’s Law (1BL and 2BL) tests to the 2025 Philippine Senate election results to assess the statistical integrity of the official vote counts. Using a precinct-level dataset aggregated to the city/municipal level, we analyzed vote distributions per candidate across 112,698 city-candidate pairs. In absolute percentage terms, the results showed that first-digit frequencies deviated by no more than ±0.5 percentage points from theoretical expectations, and second-digit frequencies by ±0.2 percentage points. The overall distributions closely followed the expected Benford patterns, with particularly strong alignment observed in the second-digit test. Although the chi-squared test for the first-digit distribution indicated a statistically significant deviation, this is likely attributable to the large sample size amplifying minor differences. Taken together, the results suggest a pattern consistent with naturally occurring electoral data, providing a baseline for validating electoral processes in the Philippines through statistical forensics.