As some claimed that identical early voting tallies for ruling and opposition candidates in certain areas, including Incheon and Gwangju, during the 9th nationwide local elections (June 3 local elections) were evidence of vote rigging, Heo Myeong-hoe, an emeritus professor in the Department of Statistics at Korea University, countered that it is a mathematically natural phenomenon. Heo, the emeritus professor, is the father of Fields Medalist Heo Joon-yi.
Heo, the emeritus professor, on the 9th and 10th presented on his social media (SNS) the results of a simulation analysis related to the so-called "twin tallies." First, in the Incheon mayoral race early voting during the June 3 local elections, in Songdo 1-dong and Songdo 2-dong, the vote counts for Democratic Party of Korea candidate Park Chan-dae (3,030 votes) and People Power Party candidate Yoo Jeong-bok (1,440 votes) were exactly the same.
Heo likened it to coin flips. He examined the probability that the number of heads would be exactly the same when two people each flipped a coin 4,470 times (3,030 votes + 1,440 votes). He assumed the probability of heads as 67.79%, the vote share of Incheon Mayor-elect Park Chan-dae.
Heo, the emeritus professor, said, "Based on 1 billion computer simulations, the probability that the two people's number of heads matches is 0.00903, roughly 1%," and added, "Viewed as a single event, 1% may look a bit small, but that's not the case when looking at Incheon as a whole."
That is because the number of cases increases. Using Incheon's 137 administrative dongs as the basis, Heo calculated 9,316 possible pairings of two dongs.
Even if we assume a 1% chance among the 9,316 combinations that there are two dongs with similar numbers of voters and similar political leanings, there would be 93 similar pairs (9,316 × 1%). Since the probability of a match in each pair is also 1%, the expected number of twin tallies is 0.84 (93 × 0.00903). The point is that it wouldn't be unusual for at least one matching case to appear.
Heo said, "Do you suspect vote rigging just because two dongs were found where the two candidates' vote counts match perfectly?" and added, "From a statistical standpoint, that suspicion is not reasonable."
In early voting for the Gwangju–Jeonnam special mayor, there were five places where Democratic Party of Korea candidate Min Hyung-bae's vote count (1,401 votes) and People Power Party candidate Lee Jung-hyun's vote count (120 votes) were the same, which Heo, the emeritus professor, likewise explained is possible under statistical probability.
Likewise, comparing it to coin flips, the number of coin trials for the two candidates in the Gwangju–Jeonnam special mayor race is 1,521 (1,401 votes + 120 votes), fewer than the Incheon case (4,470). The fewer the trials, the higher the probability of a match.
Conversely, based on vote share, the probability of heads in the Gwangju–Jeonnam special mayor case is 92.11%, higher than the Incheon case (67.79%). The closer it is to 100%, the more the probability of a match inevitably rises.
Also, there are 393 eup, myeon and dong within the Gwangju–Jeonnam special city constituency. The number of two-dong pairings is 77,028, more than the Incheon case (9,316). Put simply, it means more "twin tallies" are bound to appear.
Heo, the emeritus professor, said, "Are you very surprised that as many as five twins appeared?" and added, "Mathematically, it is a phenomenon that is naturally understood."
The National Election Commission also called the twin tallies "the result of coincidence." The commission said observers recommended by parties and candidates participate throughout the counting process, and that results tallied by different locations and personnel happened to match by chance.
The commission urged, "Please refrain from raising or spreading unfounded suspicions about fairly tallied election results solely because they are statistically rare."