The 2017 election was followed by early elections in 2018 to directly vote for a new president who would now be head of state and government. Removing such ballot-stuffing-characteristic anomalies from the data would tip the overall balance from ‘No’ to a majority of ‘Yes’ votes. In 11% of stations we find signs for ballot stuffing with a standard deviation (uncertainty of ballot stuffing probability) of 2.7% (4 sigma event). For the 2017 Constitutional Referendum we find systematic and highly significant statistical support for the presence of both ballot stuffing and voter rigging.

Additionally, we perform tests to identify numerical anomalies in the election results. In particular, we test whether the data contains fingerprints for ballot stuffing (submission of multiple ballots per person during the vote) and voter rigging (coercion and intimidation of voters). We apply statistical forensics tests to identify the specific nature of the alleged electoral malpractices. Here we report the results of an election forensic analysis of recent Turkish elections to clarify to what extent it is plausible that these voting irregularities were present and able to influence the outcome of the referendum. However, the referendum was confronted with a substantial number of allegations of electoral misconducts and irregularities, ranging from state coercion of ‘No’ supporters to the controversial validity of unstamped ballots. By the will of the Turkish people, this referendum transferred practically all executive power to president Erdoğan. With a majority of ‘Yes’ votes in the Constitutional Referendum of 2017, Turkey continued its drift towards an autocracy. 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. For higher ranks i, an increasing number of small stations is included, giving a characteristic “hockey stick”. (B) We again rank all stations in Turkey by their size and show the cumulative vote percentages cum i( v) which are computed over all stations with a size larger than the given rank. Reference elections are shown as dotted lines.

The displacement sizes are substantially smaller than those observed in Russian or recent Venezuelan elections (shown as blue and red dashed lines). There is a significant displacement δ( p) between small and large polling stations with values that lie outside this accepted region for the 2018 parliamentary elections (full magenta line). (A) An accepted region for the displacements is constructed from the confidence interval of displacements observed in the reference set of trustworthy elections. S2 Fig: Results of the voter rigging test for the 2018 parliamentary elections.

Election 2018 results nytimes