Electoral fraud in Russia is not a particularly new phenomenon. The recent legislative election (450 seats of the State Duma (lower house)) held 17–19 September 2021 has been reported to be no exception, see [1–6]. The election resulted in a 49.82 % (324 seats) victory of United Russia (UR), the ruling party since 2007, whose de facto leader is Vladimir Putin.

Here we present an election forensic analysis of the recent Russian elections that clarifies to what extent voting irregularities are detectable in the outcomes of the election data on the level of voting stations and whether these irregularities were relevant for the election outcome. We use statistical forensics tests to quantify the extent to which the observed election results are compatible with specific types of electoral malpractices. In particular, we test if ballot-stuffing (multiple ballots per person during the voting process) and voter rigging (intimidation and coercion of voters) might have occurred and if yes, to what extent. We perform statistical tests to identify numerical anomalies in the election results.

For the 2021 Duma election, we find systematic and highly significant statistical support for the presence of both, ballot-stuffing and voter rigging. In about half of all voting districts different degrees of ballot-stuffing have to be assumed to explain the observed statistics. In 49 % of stations, we find signs for ballot-stuffing with a standard deviation (uncertainty of ballot-stuffing probability) of 1.6 % (30 sigma event). An inflated turnout in voting stations, in combination with an increased vote share for UR, does hint at a systematic practice of ballot-stuffing. In addition, we find that smaller voting stations contribute much stronger to statistical irregularities in the empirical vote–turnout distribution than larger stations, which strongly suggest the practice of voter rigging. Removing the ballot-stuffing- and voter rigging characteristic anomalies from the data would yield the overall outcome for UR at around 30 % instead of 50 %.