Guest Host: Mikaela Lefrak

What do math, conspiracy theories and the 2020 presidential election have in common?

What do math, conspiracy theories and the 2020 presidential election have in common?

Many conservatives across the country still haven’t accepted the results of the presidential election — including President Trump. The president and his administration are still falsely claiming victory on social media. He and other prominent conservatives are citing massive voter fraud and other conspiracies without any evidence.

One of the conspiracy theories around the election’s outcome deals with a mathematical principle, known as Benford’s Law. However, statisticians, data journalists and mathematicians alike have all dispelled this theory as misinformation. What is Benford’s Law, and how did a little-known mathematical principle become the center of voter fraud claims?

Produced by Ingalisa Schrobsdorff and Richard Cunningham


  • Jennifer Golbeck Professor, College of Information Studies at the University of Maryland

Additional Content

You can read Jen’s Medium post about Benford’s law here:

Benford’s Law Does Not Prove Fraud in the 2020 US Presidential Election

The Netflix movie mentioned is linked below:

Connected: The Hidden Science of Everything


  • 12:00:03

    MIKAELA LEFRAKYou're tuned in to The Kojo Nnamdi Show. I'm Mikaela Lefrak sitting in for Kojo. Coming up later in the broadcast, we'll look at how local comedy clubs and comedians are trying to keep us laughing during these difficult times. We sure need it. But first, there's an obscure mathematical principle known as Benford's Law and it's being cited on some election fraud claims. A University of Maryland expert on the principle recently found herself in the middle of a social media firestorm after she explained why using Benford's Law in the case of the 2020 elections doesn't add up. She joins us to discuss. We're joined today by Jenn Golbeck, a Professor in the College of Information Studies at the University of Maryland. Jenn, welcome back to the program.

  • 12:00:47

    JENNIFER GOLBECKThanks, I'm glad to be here.

  • 12:00:49

    LEFRAKNow, first I want to say that a lot of listeners probably recognize your name and your voice, because you've been a regular guest and guest host on this show yourself. So welcome back.

  • 12:00:59

    GOLBECKThank you. I've missed being with my Kojo family. So it's great to be back even if it's virtual.

  • 12:01:04

    LEFRAKWell, this is my first time guest hosting. So if I do anything terribly wrong you'll have to give me some tips. So as we said you're a professor and you teach computer science among other things. And you're an expert of Benford's Law. So tell me what is that and what does it mean in terms that the mathematically disinclined like myself can understand?

  • 12:01:25

    GOLBECKSure. So, you know, if you think about all the numbers that you come into contact with, if I were to ask you what percentage of them start with a one versus a two versus a three and so on, I think for most of us our intuition is that like just in the world numbers are just as likely to start with a one as seven, as a nine, whatever. But it turns out that in a lot of naturally occurring systems that's not the case. So say we look at the length of all of the rivers on Earth. No matter what unit you measure that in miles, kilometers, feet, the numbers that start with one are much more common than any other. About 30 percent of all the rivers will have a distance that starts with a one, and that goes down until you get to distances that start with a nine.

  • 12:02:16

    GOLBECKThey only end up being about five percent. So it's actually a really nice formula that tells you the frequency of what we call the first significant digit, basically the first digit in that number. And this applies all over the place in kind of mind-blowing unexpected ways. The length of rivers like I said, atomic weights have it. It's used quite widely in accounting fraud. So if you take your tax returns and you just write down every number on your tax return, it doesn't matter what it is. Just write all the numbers down. You'll find that about 30 percent of them start with a one and it goes down through nine. It's so reliable that in U.S. courts you can actually use the fact that tax returns deviate from this principle as part of your evidence of fraud.

  • 12:03:03

    GOLBECKSo it shows up all over the place. And if anyone wants to just try it, a really easy way to do it is to like grab a magazine that's sitting around. Write down all the numbers. Count how many of them start with a one, a two and so on. And if you look up a chart of what Benford's Law looks like online, you're going to find out that all the numbers in the magazine match that too. So it's this really interesting thing that shows up all over the place that's a kind of reliable way of knowing what's going to be the kind of fraction of first digits from each number.

  • 12:03:35

    LEFRAKOkay. So as you explained it this seems pretty logical and pretty straight forward. So how exactly did you find yourself in the midst of a Twitter battle over this seemingly pretty benign principle?

  • 12:03:48

    GOLBECKYeah. So, you know, the fact that it's used to detect accounting fraud I think is part of the basis of this because a lot of us who research this use it to try to find when people are making up numbers. And the intuition there is like if you're going to cheat on your taxes and you're putting in some numbers that aren't legit, you might go like "Oh, gosh, I don't have any that start with a seven. Let me put some more numbers with a seven in here." Because you feel like there should be more sevens and you're going to do it in an unnatural way. That's how we kind of detect fraud with this.

  • 12:04:20

    GOLBECKPeople do things that are not natural behaviors. And so it kind of common sense, I think, if you know about this principle to say, "Well, can we do this with elections?" Can we get a bunch of numbers from an election and see if they follow Benford's Law. And you can download a lot of election data online. So people were getting precinct data from states that Biden won mostly the swing states looking at how many votes Biden got in each precinct and how many votes Trump got.

  • 12:04:50

    GOLBECKAnd then mapping those first digits. So basically saying, "What percentage of Biden's vote total started with a one and a two and so on?" It turns out that doesn't work for some interesting statistical reasons. And I'm sure we'll get into that, but it violates all sorts of things that we need to be true for Benford's Law to be applicable. And so I started explaining that to people who were pushing this conspiracy theory that the election was rigged and Benford's Law pushed it. And to say the least, they weren't very happy with me about that.

  • 12:05:21

    LEFRAKNow, Jenn, okay, so dive into the arguments about where these folks are going wrong. What are the reasons that the vote distribution in this election may not follow Benford's Law?

  • 12:05:33

    GOLBECKYeah. So I like said, when we're looking at Benford's Law we look at the first digit. So if Biden got 853 votes, that's an eight. The eight is the first digit. So for Benford's Law to be applicable to look for fraud there's a few things that we need to be true. And the main one that matters here is that the numbers are independent. So what that means is Biden's vote count in a precinct shouldn't depend on anything else, like if he gets one vote he gets one vote. If he gets 10,000 votes, he gets 10,000. It doesn't depend on anything. But that's not true. First the number of votes that Biden or Trump can get is dependent on how many people are in that precinct, right? If there's 2,000 people in a precinct, he can't get 3,000 votes.

  • 12:06:18

    GOLBECKSo because it depends on how many people are there, this is a situation where we wouldn't use Benford's Law. And even more important when we're thinking about this, the number of votes that Biden gets depends on the number of votes that Trump gets. Right, if there's 1,000 people in a precinct, if Trump gets 600 votes Biden is going to get 400. They depend on each other. And that violates one of the core principles that's necessary for Benford's Law to work. Also, we tend to see Benford's Law -- we would say over many orders of magnitude basically lots of different numbers of zeroes at the end. So you've got a bunch of things in the tens, in the 100s, in the 1000s, in the 10,000s, and with precinct data, that's not really true.

  • 12:07:01

    GOLBECKWe want the precincts to be small enough that we can count them, but not tiny. And so they tend to be in the like thousand range mostly. And because they don't spend -- span lots of orders of magnitude, they don't get super big and they don't get really small. That's also missing something that's really necessary for Benford's Law to work. On top of that, we've spent like 25 years researching this. And everybody who does work on Benford's Law knows that it doesn't work on election data like this, and so while it's not like a stupid idea just to jump in and try it. If you do any researcher or you really have an understanding of how Benford's Law works, you would know that that's not a right approach here.

  • 12:07:42

    LEFRAKNow let's go to the phones. John in Fairfax, Virginia. John, you're on the air. Go ahead, please.

  • 12:07:49

    JOHNHello. I've been using Benford's Law for quite a few years as a sort of audit check informally at best on the numbers that I get in my reports from my employees. Nurses report all kinds -- you know, just most of their reports are lots of numbers. And I figure that my sampling has brought enough to be valid at least for a rough estimate and to catch egregious examples of what we call pencil whipping when you just, oh, I forgot what I did then, and just make up numbers. And I have occasionally at least asked people to double check their numbers and let them know that we're looking at the numbers when they make stuff up.

  • 12:08:35

    LEFRAKThank you, John. Now, Jenn, how do you think -- what do you think of how John is using Benford's Law?

  • 12:08:42

    GOLBECKYeah. I mean, that's the classic way that you would apply this. And I love this example, oh, I didn't really write down that stuff I was supposed to write down. So I'm just going to make some numbers up. And we tend as humans not to make up numbers in a very convincing way. And he actually brought up a great point at the end there where he'll sometimes ask people to go back and check their numbers. It doesn't mean that they outright have lied. There are times where you'll see Benford's Law violated when you might expect it to be.

  • 12:09:11

    GOLBECKAnd like the classic example of that if we're talking about say like taxes or financial stuff is that you'll have a company and like their most popular product by far sells for $7.50. And so there's this big spikes in sevens. Those seven show up all over the place. But there's a reason for it. So not following Benford's Law even when, you know, when it's applied correctly, it doesn't necessarily mean that there's fraud. But it means there's something going on that's a little unusual. And so that process John described is exactly the right one that you use it to kind of do a spot check in the right circumstances. And then if you see something that looks weird it means you can go do a little more investigation.

  • 12:09:51

    LEFRAKNow as we said, you responded on Twitter to people who are erroneously citing Benford's Law in relation to the 2020 election. You've also written a post on Medium. And as Twitter tends to do, it's gotten a little ugly at times. So tell me how your Twitter feed is looking these days?

  • 12:10:09

    GOLBECKI would love to read some of it to you, but it is definitely not radio appropriate. I was trying to go through some of them and see if there's any that I can read you. I think this one has no curse words in it or I'll leave those out. So I've been doing like the very professor response. Like I understand what you're doing here, but this is not how Benford's Law works, and here's all the reasons for it. And here's what you can do and here's what it shows." And then people just yell at me. This is what my week has been like.

  • 12:10:37

    GOLBECKSo this guy responds in all caps, "Bootlicker alert. No one is reading your BS thought vomit. You're dumb followers can't read let alone comprehend math. Why are all liberal women so fugly? It's because you have no soul. Are you a ginger? Gross." And then it goes on to say some more things that I can't read.

  • 12:10:54


  • 12:10:55

    GOLBECKSo that's sort of -- it's just a bunch of that. Including some of it -- interestingly I got in a back and forth with the U.S. House candidate from Missouri's 1st District, which is St. Louis that was won by the Democrat and the GOP member running there he was pushing this conspiracy theory. And said a lot of ugly things, which were in line with what I expected in general from Twitter, but surprising from a candidate for the U.S. House.

  • 12:11:24

    LEFRAKNow we just have a couple -- about a minute left. But I want to hear a bit about your classroom. And we all know data and stats are often manipulated these days. So briefly, what do you teach students about the right way to use stats?

  • 12:11:36

    GOLBECKYou know, I think that the core thing is that like statistics can be used in all kinds of ways. But once you get passed the basics it's actually quite complicated. There are ways, for example, to use Benford's Law to analyze election data. But it requires using different digits. It's not as conclusive. You use it with a bunch of other methods. And so what I want my students to come away with is an understanding of, okay, this principle is cool, but also you need to go deeper to understand all these other statistical concepts so that when you apply it, you're doing it in the right way. Otherwise you end up kind of pushing a lie that's hard for people without a mathematical background to detect or see through.

  • 12:12:14

    LEFRAKJenn Golbeck, Professor in the College of Information Studies at the University of Maryland. Thank you so much for joining us today.

  • 12:12:20

    GOLBECKMy pleasure.

  • 12:12:21

    LEFRAKNow we're going to take a short break and when we come back we'll be talking about the region's comedy scene and how it is keeping us laughing. Stay tuned.

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