Results of the statistical test for voter manipulation.

(A) The displacement δ(p) between small and large units for the first (solid dark magenta line) and second (solid light magenta line) round of the 2023 elections is very narrowly outside the accepted range for a restricted set of size thresholds, similar as it was in 2018 (solid black line). These displacements are much smaller displacements in the Russian or Venezuelan elections (dashed lines); the reference elections are shown as dotted lines. (B) Units in the 2023 and 2018 Turkish elections are ranked according to their electorate size. We show the cumulative vote share, cum_i(v), calculated over all units with a size greater than the given rank. As in 2018, we observe a characteristic “hockey stick” in 2023, meaning that units with high rank (low electorate size) show a clear tendency to favour Erdoğan.