[Reading Science] The Secret Behind 'Twin Vote Counts': 3,030 and 1,440 in Songdo, 1,401 and 120 in Gwangju and Jeonnam (Comprehensive)

The 'Illusion' Created by Thousands of Combinations: Why Numbers Deceive Us

Identical Vote Counts and the Birthday Paradox: A Central Limit Theorem Perspective

In the early voting within Songdo 1-dong, Incheon, candidate Park Chan-dae received 3,030 votes, while candidate Yoo Jeong-bok received 1,440 votes. Remarkably, in Songdo 2-dong as well, the two candidates received exactly the same number of votes—3,030 and 1,440, respectively.

A similar phenomenon occurred in Gwangju and Jeonnam. In Songjeong 1-dong, Gwangsan-gu, Gwangju, candidate Min Hyung-bae received 1,401 votes and candidate Lee Junghyun received 120 votes. The exact same numbers were recorded in Geumsan-myeon, Goheung-gun, Jeonnam. As these so-called "twin polling stations," where candidates’ vote counts match perfectly, continued to emerge, some social networking service (SNS) users even claimed that such a coincidence is "almost statistically impossible."

On June 3rd, the local election day, election clerks are opening early voting boxes at the counting center set up in the gymnasium of Seoul National University, Gwanak-gu, Seoul. Photo by Yonhap News

However, statisticians interpret this phenomenon quite differently. While the numbers are eye-catching, mathematically they are well within the realm of possible chance events.

"Probability is Not Zero... Estimated at 0.6–0.9%"

Lee Yoon-dong, a professor at Sogang University's School of Business, explained in an expert commentary for the Korea Science & Technology Media Center (SMCK), "The important thing is not to compare any two random districts, but to calculate the probability of identical vote counts occurring between regions with similar voting tendencies and numbers of voters."

For example, as in the Songdo case, if the total number of voters is about 4,470 and the two candidates’ vote share is roughly at a 2-to-1 ratio, the results will cluster in a particular range. This means that rather than any random number emerging from among thousands of possibilities, similar numbers will appear repeatedly.

Professor Lee analyzed, "In such a scenario, the probability that a candidate receives exactly the same number of votes in two districts is approximately between 0.6% and 0.9%, which is significantly higher than most people would intuitively expect."

The Principle Behind the Birthday Paradox

Jang Wonchul, a professor at Seoul National University's Department of Statistics, described this phenomenon using the well-known statistical example, the "Birthday Paradox."

At a gathering of 100 people, it may seem intuitively unlikely that two people share the same birthday. However, in reality, the probability is not 0.1% but close to 99%. This is because, while people might focus on just two individuals, statistics considers all possible pairings.

Professor Jang used the last three digits of phone numbers as another example. At first glance, the probability that two out of 100 people share the same last three digits looks like one in a million. In fact, since there are 4,950 possible pairings among 100 people, the probability that at least one pair shares the same number is about 99.3%.

The Songdo case follows the same logic. While people focus on the specific numbers "3,030 and 1,440," in reality, all possible vote count combinations—from 0 to 4,470 and vice versa—should be considered.

Professor Jang stated, "Calculating the probability based on just the specific result of 3,030 and 1,440 votes is not appropriate. When considering all possible vote combinations and similar-sized polling stations, the likelihood of identical vote counts is much higher than most would expect."

On June 3rd, the day of the local elections, election clerks were counting valid votes at the counting center set up at the Seoul National University Gymnasium in Gwanak District, Seoul. Photo by Yonhap News.

The 'Illusion' Created by Thousands of Combinations

In statistics, the focus is not on individual incidents but on the total number of possible cases.

Heo Myunghoe, a professor in the Department of Statistics at Korea University, explained that when two people each toss a coin 4,470 times, the probability that they get exactly the same number of heads, as calculated by a computer simulation, is about 0.9%.

The issue is that there isn’t just a single pair being compared. Assuming there are 137 administrative districts in Incheon, the number of possible combinations between districts is 9,316. Given these thousands of combinations, it is actually natural for some of them to yield identical results.

In Gwangju and Jeonnam, the likelihood of this phenomenon is even greater. With some candidates enjoying support rates close to 90% and a total of 393 towns, townships, and neighborhoods, the number of possible combinations exceeds 70,000. In fact, five pairs of "twin polling stations" with identical vote counts were found in Gwangju and Jeonnam.

Numbers Can Be More Convincing Than Facts

Experts point out that this controversy is less about the election results themselves and more about the interpretation of data.

Park Hanwoo, a professor at Yeungnam University, stated in an expert commentary for the Korea Science & Technology Media Center (SMCK), "It is not scientifically valid to conclude wrongdoing simply because a phenomenon is rare. Instead of focusing on a particular number, we must look at the entire data structure and context."

He also warned, "If numbers labeled as probabilities are spread without a clear basis for calculation, it can fuel public distrust. Therefore, the transparency of data disclosure, expert verification, and the probability calculation process is crucial."

3,030 and 1,440 votes, and then 1,401 and 120 votes—at first glance, these might seem like inexplicable coincidences. Yet, statisticians see this as a phenomenon similar to the birthday paradox: while individual cases may appear extremely rare, considering the thousands or tens of thousands of possible combinations, identical vote counts are, in fact, a statistically plausible occurrence.

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