Title : To say "deviation from Benford’s Law does not prove election fraud took place" is not to say that it isn't relevant evidence.
link : To say "deviation from Benford’s Law does not prove election fraud took place" is not to say that it isn't relevant evidence.
To say "deviation from Benford’s Law does not prove election fraud took place" is not to say that it isn't relevant evidence.
Reuters does a fact check that begins by stating the proposition in an ultra-strong way:Social media users have been sharing posts that say a mathematical rule called Benford’s Law provides clear proof of fraud in the U.S. presidential election.
Here's how the proposition to be fact-checked could have been stated: Benford's Law is of some use in determining whether or not there there was fraud or error in the U.S. presidential election. Lawyers will recognize the test for whether evidence is relevant.
Reuter's is asking whether this evidence, standing alone, will meet a burden of proof, which is a tricky shortcut through factchecking. In real life, we don't depend on one piece of evidence. We look at whatever might be useful as we make decisions about how much more to investigate. Does Benford's Law raise suspicions that would make a fair-minded person want to look more closely and to gather more evidence?
But we don't really have fair-minded people! We have highly partisan people on one side who are eager to cast doubt on the election and on the other side who want to say Stop right now! Reuter's strikes me — the closest thing you're going to get to a fair-minded person — as falling in the second group. Why? Because of the way they stated the fact to be checked!
Now, let's look at the experts consulted (and go to the article for a statement about what Benford's Law is):
Theodore P. Hill, Professor Emeritus of Mathematics at Georgia Tech, Atlanta, cautioned that regardless of the distribution uncovered, the application of Benford’s Law would not provide definitive evidence that fraud took place. “First, I’d like to stress that Benford’s Law can NOT be used to “prove fraud”,” he told Reuters by email. “It is only a Red Flag test, that can raise doubts. E.g., the IRS has been using it for decades to ferret out fraudsters, but only by identifying suspicious entries, at which time they put the auditors to work on the hard evidence....
Yes, that's essentially what I said, above.
Dr Jen Golbeck, Professor of the College of Information Studies at the University of Maryland... told Reuters, “There is just not solid evidence that Benford works in elections at all. The results are profoundly mixed. Which means it’s not evidence of anything.”
This addresses my question. She asserts that it's not even relevant evidence. Why?
Golbeck points out that the numbers on some graphs being cited by social media users are not even labelled, whilst the law “works on very specific types of numbers”. She added that none of the research that analyzes the Benford Law is as simplistic as the analysis people are posting: instead, research uses “quite advanced statistical techniques”, often looking at the second digits which have their own expected distribution.
That's different from saying it doesn't work in elections at all, but she didn't say that. She only said there's no "solid evidence" that it works in elections. Obviously, she's responding to claims made in social media that overstate the usefulness and meaning of applying Benford’s Law in this case. But the point is that you'd need to do much more to make even a modest claim about the usefulness of Benford’s Law, and I'm not surprised that the experts aren't eager to do this work for Trump supporters who've they've gone too far making their claims.
The specific case of the Milwaukee results was also examined by Professor Boud Roukema of Poland’s Nicolaus Copernicus University. Roukema considered the application of Benford’s Law to the 2009 Iranian elections (arxiv.org/abs/0906.2789) . He told Reuters by email: "A major flaw in applying Benford's law to the Milwaukee results is that the logarithmic distribution - how many "powers of tens" there are - in the numbers of votes per ward in Milwaukee is very narrow.
In other words, half of all the wards have total votes from about 570 to 1200, and the logarithmic average (mean) is about 800. “Biden overall got about 70% of the votes in Milwaukee. So the most likely vote for Biden (in the simplest model, assuming no falsification) in a typical Milwaukee ward is something like 0.7 times 800, which is 560 votes. We expect about half the Biden votes to lie between about 400 and 850 in typical Milwaukee wards.
“So the most popular first digit of the votes for Biden should be 5 - the first digit of 560 - and 4s and 6s and 7s should also be reasonably frequent. “This is just what we see in the blue vertical bars in top left figure in the diagram at (here).
So Benford's law reasoning, applied to the real data, shows no reason to suspect fraud here.”
Aha! That's the most useful analysis. Roukema is asking whether there is some evidence, whether a red flag is raised, justifying looking more deeply. He's saying no. Let's talk about it from there.
Social media users have been sharing posts that say a mathematical rule called Benford’s Law provides clear proof of fraud in the U.S. presidential election.
Here's how the proposition to be fact-checked could have been stated: Benford's Law is of some use in determining whether or not there there was fraud or error in the U.S. presidential election. Lawyers will recognize the test for whether evidence is relevant.
Reuter's is asking whether this evidence, standing alone, will meet a burden of proof, which is a tricky shortcut through factchecking. In real life, we don't depend on one piece of evidence. We look at whatever might be useful as we make decisions about how much more to investigate. Does Benford's Law raise suspicions that would make a fair-minded person want to look more closely and to gather more evidence?
But we don't really have fair-minded people! We have highly partisan people on one side who are eager to cast doubt on the election and on the other side who want to say Stop right now! Reuter's strikes me — the closest thing you're going to get to a fair-minded person — as falling in the second group. Why? Because of the way they stated the fact to be checked!
Now, let's look at the experts consulted (and go to the article for a statement about what Benford's Law is):
Theodore P. Hill, Professor Emeritus of Mathematics at Georgia Tech, Atlanta, cautioned that regardless of the distribution uncovered, the application of Benford’s Law would not provide definitive evidence that fraud took place. “First, I’d like to stress that Benford’s Law can NOT be used to “prove fraud”,” he told Reuters by email. “It is only a Red Flag test, that can raise doubts. E.g., the IRS has been using it for decades to ferret out fraudsters, but only by identifying suspicious entries, at which time they put the auditors to work on the hard evidence....
Yes, that's essentially what I said, above.
Dr Jen Golbeck, Professor of the College of Information Studies at the University of Maryland... told Reuters, “There is just not solid evidence that Benford works in elections at all. The results are profoundly mixed. Which means it’s not evidence of anything.”
This addresses my question. She asserts that it's not even relevant evidence. Why?
Golbeck points out that the numbers
That's different from saying it doesn't work in elections at all, but she didn't say that. She only said there's no "solid evidence" that it works in elections. Obviously, she's responding to claims made in social media that overstate the usefulness and meaning of applying Benford’s Law in this case. But the point is that you'd need to do much more to make even a modest claim about the usefulness of Benford’s Law, and I'm not surprised that the experts aren't eager to do this work for Trump supporters who've they've gone too far making their claims.
The specific case of the Milwaukee results was also examined by Professor Boud Roukema of Poland’s Nicolaus Copernicus University. Roukema considered the application of Benford’s Law to the 2009 Iranian elections (arxiv.org/abs/0906.2789) . He told Reuters by email: "A major flaw in applying Benford's law to the Milwaukee results is that the logarithmic distribution - how many "powers of tens" there are - in the numbers of votes per ward in Milwaukee is very narrow.
In other words, half of all the wards have total votes from about 570 to 1200, and the logarithmic average (mean) is about 800. “Biden overall got about 70% of the votes in Milwaukee. So the most likely vote for Biden (in the simplest model, assuming no falsification) in a typical Milwaukee ward is something like 0.7 times 800, which is 560 votes. We expect about half the Biden votes to lie between about 400 and 850 in typical Milwaukee wards.
“So the most popular first digit of the votes for Biden should be 5 - the first digit of 560 - and 4s and 6s and 7s should also be reasonably frequent. “This is just what we see in the blue vertical bars in top left figure in the diagram at (here).
So Benford's law reasoning, applied to the real data, shows no reason to suspect fraud here.”
Aha! That's the most useful analysis. Roukema is asking whether there is some evidence, whether a red flag is raised, justifying looking more deeply. He's saying no. Let's talk about it from there.
Thus articles To say "deviation from Benford’s Law does not prove election fraud took place" is not to say that it isn't relevant evidence.
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