Results for the statistical test for voter rigging.

(A) An accepted region for the displacements is constructed from the confidence interval of displacements observed in the reference set of trustworthy elections. There is a significant displacement δ(p) between small and large polling stations with values that lie outside this accepted region for Turkey 2017 (full dark magenta line) and 2018 (full light magenta line). The displacement sizes are substantially smaller than those observed in Russian or recent Venezuelan elections (shown as blue and red dashed lines). Reference elections are shown as dotted lines. (B) We rank all stations in the Turkish elections by their size and show the cumulative vote percentages cumi(v) which are computed over all stations with a size larger than the given rank. For higher ranks i, an increasing number of small stations is included, leading to a characteristic “hockey stick”. In 2017 it is the addition of small units with inflated votes and turnouts that pushes the results over the 50% line and leads to a majority of Yes’ votes (highlighted by a red circle). In the insets, we show the same relationship for other elections that (left) show significant displacements or (right) belong to the set of reference elections.