Second-digit Tests for Voters’ Election Strategies and Election Fraud∗

The second significant digits of precinct-level (or polling station-level) vote counts follow regular patterns when voters are acting strategically and when there are partisan imbalances of voters in districts (when there is a gerrymander). The digits often follow distinctive patterns when vote counts are affected by coercion. The patterns are illustrated by a simulation exercise that generates individual preferences that, when aggregated into precincts, have counts whose second but not first significant digits approximately satisfy Benford’s Law (2BL). Deriving sincere, strategic, gerrymandered and coerced votes from these preferences under a plurality voting rule shows that the second digits of the precinct counts are sensitive to differences in how the counts are derived. The patterns in the simulations are similar to those in real data from German Bundestag elections and from American presidential, House and state legislative elections. The strategic and gerrymandering effects are well known in both the German and American elections—the effects in the American national elections are associated with strategic party balancing between the president and the legislature—so overall I offer an inductive argument that the vote counts’ digits are diagnosing the same kinds of behavior in both the simulated and real election data. Covariates such as the margin between candidates are important, but digits can detect strategic behavior even without having any information about preferences or beliefs. The 2BL regularity is not enough, but against the more nuanced background of regular digit patterns, election fraud in the form of coercion can stand out.