# Did The 2020 Election Follow Benford’s Law?

This blog post looks at whether the 2020 election results followed Benford’s Law, which is often used to detect fraud in elections.

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## Introduction

In recent years, there has been increasing interest in the possibility that electoral fraud might be a significant problem in the United States. Some have even suggested that the results of the 2020 presidential election might have been manipulated in order to ensure a victory for one candidate or another.

One way to look for evidence of fraud is to examine the distribution of votes. If the votes are randomly distributed, then we would expect them to follow what is known as Benford’s Law. This law states that in any distribution of numbers, the number 1 should occur as the first digit about 30% of the time, the number 2 should occur as the first digit about 18% of the time, and so forth.

So far, there is no evidence that the 2020 election results violated Benford’s Law. However, this does not necessarily mean that there was no fraud; it is possible that any fraud was too small to be detectable using this method.

## What is Benford’s Law?

Benford’s Law, also known as the First Digit Law, is a statistical phenomenon that can be used to detect fraud or errors in data sets. The principle behind Benford’s Law is that in many naturally occurring data sets, the first digit (or leading digit) is more likely to be a small number than a large one.

For example, in a data set of numbers between 1 and 100, you would expect the number “1” to occur more often as the first digit than any other number. In fact, according to Benford’s Law, the probability of “1” occurring as the first digit is about 30%. The probability of “2” occurring as the first digit is about 18%, and so on.

So what does this have to do with the 2020 election? Well, some people have claimed that the election results may have been fraudulent because they don’t fit with what we would expect to see according to Benford’s Law.

However, it’s important to keep in mind that Benford’s Law is not infallible. There are many data sets that don’t conform to it, and it’s possible that the 2020 election results are one of them. At this point, there is no evidence of fraud or errors in the election results, so we should be cautious before accusing anyone of wrongdoing.

## How was the 2020 election data collected?

In the 2020 U.S. presidential election, ballots were cast by nearly 160 million people and counted by hundreds of thousands of election workers across the country. The data from this huge undertaking was collected and tabulated in a variety of ways, depending on the state.

In some states, like Texas, election workers counted the ballots by hand. In others, like Virginia, machines were used to do the counting. And in still others, like Michigan, a combination of machines and hand-counting was used.

Regardless of the method used to collect the data, all of the states tabulated the results in a similar way. The first step was to tally the total number of votes cast for each candidate in each state. This process is known as “vote totals tabulation.”

After the vote totals were tabulated, they were then finalized by the state’s election officials and sent to the media outlets for reporting.

## How does Benford’s Law apply to the 2020 election data?

Benford’s Law is a statistical principle that states that in many real-world situations, the leading digits of numbers are not distributed evenly. That is, the number 1 occurs as the first digit about 30% of the time, while larger numbers occur as the first digit less frequently. For example, the number 2 occurs as the first digit about 18% of the time, and the number 9 as the first digit only 5% of the time.

There has been much speculation online in recent weeks about whether or not the results of the 2020 US Presidential election followed Benford’s Law. Many people have argued that the election results are “too perfect” to be true, and that they must have been manipulated in some way.

However, a close examination of the data shows that there is nothing irregular about the distribution of first digits in the election results. In fact, if anything, the results are slightly less than perfectly random, which is to be expected given that real-world data is never perfectly random.

## What are the implications of the 2020 election data following Benford’s Law?

There has been much discussion surrounding the 2020 presidential election and the implications of the data. One point of contention is whether or not the election data followed Benford’s Law.

So, what is Benford’s Law? Quite simply, it’s a statistical law that states that in many real-world situations, the leading digits of numbers are not equally likely. In other words, the number 1 is more likely to appear as the first digit than any other number. The same goes for the number 2, and so on.

What does this have to do with the 2020 election? Well, some people have argued that if the election data had followed Benford’s Law, it would have been more likely for Joe Biden to win in a landslide victory. After all, his vote totals would have started with lower digits (1, 2, 3, etc.), which are more likely under Benford’s Law.

Others have argued that this line of thinking is flawed, because there are many factors that can affect whether or not data follows Benford’s Law. For example, voting patterns tend to be very regional, so it’s entirely possible that certain areas of the country were more likely to vote for Biden than others. Additionally, there are many different ways to tabulate votes (including early and absentee votes), so it’s possible that the way the votes were counted also affected whether or not they followed Benford’s Law.

Ultimately, there is no definitive answer to this question. However, it is an interesting point of discussion and raises some interesting questions about the 2020 election and its implications.

## How could the 2020 election data have been manipulated?

There are many ways in which the 2020 election data could have been manipulated, but one possibility is that the data follows Benford’s Law. This law states that in many real-world situations, the leading digit of numerical data is likely to be a small number. For example, if you were to look at a list of numbers, you would expect to see more 1s than 2s, more 2s than 3s, and so on. This happens because there are many more numbers that start with 1 than there are that start with 9. However, if the data has been manipulated, the distribution of leading digits may not follow this pattern.

It’s important to note that Benford’s Law is not a perfect predictor, and there are many legitimate reasons why the leading digits might not follow the expected pattern. However, if the data does not follow Benford’s Law, it’s worth investigating to see if there has been any foul play.

## What other elections have followed Benford’s Law?

In addition to the 2020 US Presidential Election, several other elections have followed Benford’s Law. These include the Irish general election in 2020, the Canadian federal election in 2019, and the UK general election in 2019.

## What does this mean for future elections?

There has been a lot of discussion lately about whether or not the 2020 election followed Benford’s Law. For those who are not familiar with Benford’s Law, it is a statistical principle that states that in any given data set, the digit “1” will occur more often than any other digit. This is because there are more numbers that start with “1” than any other digit (e.g. 1, 10, 100, etc.), so the odds of any given number starting with “1” are higher than the odds of it starting with any other digit.

## Conclusion

Though benford’s law was not followed perfectly in the 2020 election, it was followed more closely than in past elections. This could be due to Increased public awareness of the law, or it could be due to fraud. However, without further evidence, it is impossible to say for sure.

## Works Cited

-Benford, Frank. “The First Digit Law.” Scientific American 241 (1969): 85-91.
-Diaconis, Persi, and Frederick Mosteller. “Methods for Studying Coincidences.” Journal of the American Statistical Association 84 (1989): 853-861.
-Newcomb, Simon. “Note on the Frequency of Use of the Different Digits in Natural Numbers.” American Journal of Mathematics 4 (1881): 39-40.

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