November 11, 2020

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.

196 comments:

gilbar said...

Fact check: Indications of election fraud does not prove election fraud
fify

rhhardin said...

You have to do the statistics right, is all he's saying, not that doing them right can't uncover fraud.

rhhardin said...

It's better than 9 guilty men go free than that one innocent man is convicted. That's the legal threshold.

So you want a statistical test that, in a fair election, would let you wrongly call it fixed only one time in ten.

Kevin said...

Demanding “proof” before the investigation takes place is not how the law works.

Nor does a lack of “widespread” cheating invalidate that any cheating occurred.

Kevin said...

It used to be the media reported facts, such that rumors could be corrected.

Now the media report opinions, such that memes can be maintained.

Curious George said...

"She asserts...She added...she didn't...She only...she's responding...

Maybe she shouldn't worry her pretty little head over it.

Jamie said...

Ok, so (as always) the smaller the numbers, the less able we are to apply statistical analysis in a meaningful way. But can you apply Benford's Law when you aggregate the results from many small precincts, and therefore have larger numbers? Say for instance that you aggregate results from all the precincts that expected about 70% Biden support (when I say "about," I mean "statistically similar numbers"). What happens then?

If nothing else comes of this period, I hope that at least election fraud in machine cities will be held to the light and good actors will find and implement ways to spot and prevent it. Of course, the other possible result is that bad actors will learn all the "red flag" stuff and work to avoid those red flags.

Kevin said...

“So Benford's law reasoning, applied to the real data, shows no reason to suspect fraud here.”

Actually you need to go one step further. You can’t just say “I have a theory about Milwaukee, and look, it’s true.”

That’s as likely to fit theory to facts as facts to theory.

Now you have to test it. In all US precincts like Milwaukee we should see the same pattern, whether they be blue or red.

exhelodrvr1 said...

It's one piece of evidence that points towards an increased likelihood of fraud. It isn't evidence of fraud, but clearly indicates that there should be further investigation.

rehajm said...

That is refreshingly sober analysis of the application and pretty much what I said days ago- it is a tool to use when you suspect fraud but you still have to go find the fraud...

WI prolly isn't the best state to be looking for cooked votes. Recanvasing and checking the paperwork on same day registrations and machine shenanigans are where to look in WI. Benford's exposes the truck full of foxed ballots kind of fraud...

...and I'm done with parsing the way the media shills for one side- there's no way we're turning back to traditional journalism and parsing won't help. Leftie propaganda has already won...

Jamie said...

I read somewhere yesterday that one of the defenses (yes, that's the appropriate word) being thrown up against charges of voter fraud is that Republicans are cherry-picking the data from only certain cities. I mean...

In the (sort of) immortal formulation of Heinlein, how do you conduct a revolution? When you're building an engine, do you bolt on a bathtub just because you have one handy? Why on earth would fraudsters include San Francisco in their efforts? Or Boston?

Bill Harshaw said...

One of your better recent posts, providing some information.

Unknown said...

They need to apply the Climate Change Science Standard

Poll some paid "experts"

Declare consensus

then call anyone who questions them "deniers"

Family Feud Method

Mr. Majestyk said...

I would like to see a second digit analysis.

tim maguire said...

The arguments from the left remind me of the movie Twelve Angry Men, where a mountain of evidence clearly proving guilt beyond a reasonable doubt was examined, one piece at a time, with each piece considered in isolation from the other pieces. Using this method, Henry Fonda managed to convince the other jurors that, because no individual piece proved guilt beyond doubt, they could not find the defendant guilty beyond doubt. And so they let a guilty person go free.

That is what we are looking at here. Biden's defenders are insisting that we look at each individual piece of evidence to determine if it was sufficient on its own to change the outcome. If the answer is no, that piece of evidence is thrown aside and we move on to the next piece of evidence, which will also be examined in isolation.

Matt Sablan said...

It's interesting the different standards of proof used by the media depending on which ox is getting gored.

Jamie said...

And just a general comment: damn, math is cool. I really shouldn't have listened to Barbie back in the '80s. I foolishly only took what I needed to get my degrees instead of digging in more. Off to Khan Academy...

Jaq said...

Benford’s Law anomalies shift the burden of proof somewhat. If the cheating is organic, as the guy who just pled guilty to election fraud in Philadelphia says, then even massive fraud could still conform to it. This kind of analysis from real experts is how an honest democracy responds, Twitter and Facebook just ban discussions of it outright, which of course only raises suspicions.

"Ok, so (as always) the smaller the numbers, the less able we are to apply statistical analysis in a meaningful way.”

That’s not the point he was making. The point he was making was that the first digits should be expected to fall more heavily in one range of the distribution because of the numbers of voters in the precincts, and the percentage of those votes that Biden got. Steve McIntyre made this same point when the Benford’s Law thing came up in the first place.

I think that the real fraud comes in refusing to disallow ballots by the canvassers from heavily partisan districts according to the rules established by the legislatures prior to the election, which has likely been going on for decades and won’t produce any Benford’s Law anomolies. Literally trillions of dollars are at stake in a presidential election, its foolish to think that it can be run on the “honor system.”

The risk for Republicans making such a big deal out of this is that Democrats will then point out that more sophisticated analysis shows no violation, therefor the election was honest. Which is complete bullshit. Benford’s law would show if the vote counters were entering fabricated totals, which is not what anybody is accusing them of.

John henry said...

OT but mea culpa. I apologize.

I've been fairly vocal here for some time and especially over the past couple weeks about how we vote here. I've been even more vocal about how we never have election fraud.

One of the reasons for not having election, specifically ballot, fraud has been because basically everyone must vote in person on election day. Almost no early/absentee voting. (Basically just military and college students)

We did electoral reform. While everyone was spun up about the potential for electronic voting machines and the problem they cause, our legislature slipped in a great relaxing of absentee ballots and nobody noticed.

Until now. Here we are a week after the election and every day they are finding more boxes of uncounted ballots. Just like those of you in more enlightened states.

Instead of having our elections called Tuesday night with great degree of finality, we still don't know who won.

If this does not get straightened out by changing our electoral law back to the way it was, I'm done with voting. I won't participate in a fraud.

So apologies for telling you how Puerto Rico voting is so honest. It was honest. I was proud of it, if not the politicians it got us.

No more. I am ashamed.

John Henry

mezzrow said...

The people who will ultimately decide this matter will ask themselves one question - "Do we want the truth?" Many of us here "know" that the answer to this is no. At this point, irrespective of any evidence, the clean path will be to accept Biden and move on for the good of the Republic. The downside is that over 40% of the public will likely view Biden as "Your Fraudulency". What will that mean to the party that made this happen? What will that mean to the nation? What will that mean to the world? How will they keep all that inconvenient evidence in the memory hole?

That puts a lot of pressure on a 78 year old man in the world's hottest seat. How are they going to keep Trump out of the media?

It's a tough period of time to be a decider. Nobody wants that tail pinned to them. 2021 looks like such an interesting year.

Mike (MJB Wolf) said...

Did Reuters offer any explanation why FB and Twitter were censoring people from sharing information about “Benford’s Law” on social media? That bothers me more than “experts” giving their skewed interpretation for journ-o-listers to bat about. Statistical aberrations are useful for analyzing voting data. This only a toe into the deep waters of fraud to explore in this election. The more they try and rush Joe into the Waiting Room of the Presidentelect the more the ground is crumbling beneath their feet. Trump fights. You ain’t dealing with Jeb here.

D.D. Driver said...

"WI prolly isn't the best state to be looking for cooked votes."

Agreed. I feel like a broken record, here, but Wisconsin's result can be largely traced to the Dems playing dirty tricks to keep the Greens off the ballot. Jill Stein got ~30k votes in 2016. I'm sure some of those voters stayed home this year, but I would bet many of them voted for Biden. Biden won by ~20k. All everyone wants to talk about is fraud, but the election was stolen (if you want to call it that) in plain site.

Laslo Spatula said...

It should be easy then to show such a distribution that favored Trump somewhere.

You would think someone would show that, being the quickest way to cast doubt on the tool.

Everyone wants the sausage, no one wants to see it being made in Occam's Sausage Grinder.

I am Laslo.

Russell said...

The Benford's law post I saw indicated that it raised red flags in Pennsyvania more than Wisconsin. And conversely it indicated that Georgia, Michigan and Nevada's results were on the up and up (thus meaning that while PA remains a sh*T show, it still probably won't swing the overall election towards Trump).

wendybar said...

Reuters and the AP have proven to be on the HATE Trump...get him at any cost Newsfeeds. They suck, and can't be trusted either.

MikeR said...

Kind of fun reading an argument about something that none of the pundits can even understand.
That said, Steve McIntyre agreed with the last argument. https://twitter.com/ClimateAudit/status/1325638411252854785
That carries a lot of weight with me; McIntyre is the statistician who literally disproved quite a number of studies done by global warming believers using bad statistics. The one who fought Michael Mann over the Hockey Stick and won. If he thinks there's nothing here - and he has a number of twitter posts on a lot of the other election fraud issues - he's probably right.

Shouting Thomas said...

Public opinion and media spin are irrelevant here. The media is still trying to con us. The new con is that the fraud issue will be decided by media consensus.

This issue will be decided in courts. Trump’s got his lawyers in court challenging each ballot.

Those decisions are the only ones that count.

Matt Sablan said...
This comment has been removed by the author.
Mike (MJB Wolf) said...

And what about the time-traveling ballots that were recorded as received votes two days before being postmarked. Surely breaking the Laws of Physics should offend the literate if not the lawyers!

wendybar said...

https://twitchy.com/dougp-3137/2019/07/25/fake-news-in-real-time-reuters-tweet-showing-guatemalan-mother-begging-soldier-to-let-her-enter-u-s-is-missing-some-important-context/?

wendybar said...

https://twitchy.com/sarahd-313035/2019/11/20/cold-day-in-hell-how-fake-is-the-aps-fake-news-about-trump-sondland-even-anti-trump-cnn-reporter-daniel-dale-is-calling-them-out-over-it/?

wendybar said...

Why anybody even thinks the Propaganda media ISN'T above lying is beyond me. They have agendas. Wake up.

Matt Sablan said...

"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."

-- Deleted to be more clear.

Well, there's one way to test two different theories on how something happened in science. But, let me attack the fundamental problem here. It's one of logic. The person making this argument is saying, "Biden's margin is 70%, per the data we have on hand. Biden's % should therefore show this curve. And look, the data we have matches the curve."

The point here is that the person saying "This deviates from Benford's Law," is fundamentally saying "you can't trust the data."

So, yes. The argument is correct. If the data is correct, the curve is correct. The point of the curve is that *the data may not be correct.* You can't argue *the data we have gives us the curve we have, so the data is correct.* By simply taking the *the data is correct* as fact, you've skipped the whole point of the exercise, which is to determine, "How likely is the data to be correct?"

Lurker21 said...

Math in the morning? Really?

Bob Boyd said...

Fact Check: Here are some eggheads who say, some people on the internet don't understand the Benford's Law.
Conclusion: There was no election fraud.

Shouting Thomas said...

So, given that the courts will decide, not the media, here are the real questions:

1. Do courts allow Benford analysis as sufficient evidence to go the next step in evaluating ballots for fraud?
2. What are the standards for determining if a ballot is fraudulent?
3. What are the remedies if ballots are found to be fraudulent?

Howard said...

If there was something like a SOP for applying Benfords "Law" to election data, then using it as one of several indications to trigger a criminal investigation is probably a smart thing to do.

The color me skeptical. Until Steve McIntyre of Climate Audit approves the analysis I ain't buying it.

MayBee said...

Literally trillions of dollars are at stake in a presidential election, its foolish to think that it can be run on the “honor system.”

This this 100% this!!!!

MayBee said...

Barack Obama won his Senate seat in part by getting all of his Dem competitors kicked off the ballot by challenging signatures. If someone would cheat just to run, why would there not be cheating to win?

Ingachuck'stoothlessARM said...

"maidengate"
https://gab.com/SomeBitchIKnow

Woman Who Voted For Trump In Texas Shocked To Find She Also 'Voted' Via Mail-In-Ballot In California

Supermajority echoes the BLM co-founder's words, asserting that women "can be the most powerful force in America

listing the states, first by switched votes, then by lost votes.
https://thedonald.win/p/11Q8O2wesk/happening-calling-every-pede-to-/

possibly a good resource for the coming days:
https://everylegalvote.com/country

Shouting Thomas said...

Tucker Carlson didn’t even mention the election in the first half of his show last night.

Combined with his statement the previous night that there was fraud, but probably not enough to change results, I’m assuming Biden has won. Carlson is a Republican insider.

I have some very smart lawyer friends on FB, all Trump guys. They all say courts are extremely reluctant to intervene in elections.

rehajm said...

The morning of the election the Wall Street Journal told me equities were rallying because the market was expecting a sweep by Democrats. Now those gains have been all but erased in the last few days. Hit hard have been major Chinese concerns, BABA and TCEHY et al, yet WSJ doesn't explain to me that this means markets are anticipating trouble for Joe Biden's candidacy or that the Democrats are in trouble...

Quelle Suprise!

Jaq said...

"Now those gains have been all but erased in the last few days.”

Manchin, who comes from a state that went something like 70% for Trump says no court packing and no change to filibuster rules, so even if the Dems win both seats in Georgia, Dems are stuck at 50-50 + Harris and can’t do anything controversial. Biden is already been crippled.

Jamie said...

its foolish to think that it can be run on the “honor system.”

Which is why the Hobbesian, conservative world view is the only appropriate one for the body politic. We don't put our faith in our supposed "better angels" (to borrow from yesterday's post). We support the establishment of cold, uniform, dispassionate processes to guard against the excesses and depredations of our worse angels.

And for this, we're labeled "inhumane" - or, lately, "inhuman." The progressive side wants to be the side of, "People are essentially good, so we can trust one another to act in society's interests," but because that never holds true at any scale larger than the individual (some individuals, some of the time), they have to hem their own philosophy about with "... once we make sure everyone has the same stuff/starting point/ease of life/whatever. Once everyone is on an equal footing, then true human nature can finally take over and immanentize the glorious eschaton!"

Jaq said...

"Lurker21 said...
Math in the morning? Really?”

Aren’t you the same poster who claimed to like women’s poetry?

sterlingblue said...

"the closest thing you're going to get to a fair-minded person"

This should be Althouse's new masthead!

rehajm said...

Here's the thing- though the courts still can change the results by invalidating ballots the GOP doesn't NEED to find enough votes via the judiciary. If via the legal process the GOP can produce convincing evidence of widespread malfeasance in PA, for example, it will raise enough questions about the integrity of the election results there AND perhaps in other states as well. Also, though the courts are involved, overturning the election still has a strong political component. The results by state can and will be thrown to the legislative bodies where it will be fought out thorough a combination of the legislative and the judiciary.

Just because this is uncharted territory it doesn't mean it's impossible to go there. The founders made contingencies for disputed elections- just. like. this...

Matt Sablan said...

Has a legislature EVER rejected their election and chosen new electors in recent history? I think people hoping for that are like people who thought Hunter Biden or Hillary Clinton would face consequences: Deluded.

Browndog said...

Shouting Thomas said...

Tucker Carlson didn’t even mention the election in the first half of his show last night.

Combined with his statement the previous night that there was fraud, but probably not enough to change results, I’m assuming Biden has won. Carlson is a Republican insider.


I read it more like Tucker is being careful, and letting the hard evidence develop. He knows if he airs even one false allegation of voter fraud it blows up the entire narrative and will put immense pressure on Trump to concede.

Marcus Bressler said...

The Hostess believes that Reuters is fair: "Reuter's strikes me — the closest thing you're going to get to a fair-minded person". I am not surprised.
Reuters is the international version of the AP IMO and just as biased. To label them as she did just makes me SMH.

THEOLDMAN

Leland said...

Don't get dragged into the litigation debate. There's nothing good to come of it. Outside the courtroom, both sides of the debate will posture, but what matters is in the courtroom. Statistics based on science is compelling evidence.

Clyde said...

Mike (MJB Wolf) said...
Did Reuters offer any explanation why FB and Twitter were censoring people from sharing information about “Benford’s Law” on social media?


I read Glenn Reynolds' post about not being able to post the linked article on Facebook, which was from a site called Gnews.com, and that other people who tried to post the link on Twitter were suspended for posting "content of an intimate nature." I also tried to post the Gnews.com article and it would not post. However, in the comments at Instapundit on that post, I read that Gnews is owned by some Chinese guy named Guo, and that other stuff on the same server or domain is apparently that "content of an intimate nature," so apparently Facebook and Twitter just ban the entire server or domain (Not sure which, I'm not an IT guy). If they were doing that and not just banning that specific article because of its content, then what they were doing may be less nefarious than we thought.

roesch/voltaire said...

Odd that so far all the Trump law suits have been thrown out due to lack of evidence, and the postman in Pennsylvania recanted his claim and signed an affidavit saying so—-this was the one piece the right wing crow about has now that laid an egg. The margins of victory for Biden are greater than the few flawed ballots that can be found. It is time to accept we live in a democracy governed by popular vote and not by the tin dictator called Trump.

Ann Althouse said...

"It's better than 9 guilty men go free than that one innocent man is convicted. That's the legal threshold. So you want a statistical test that, in a fair election, would let you wrongly call it fixed only one time in ten."

In evidence law, there is the question what is the burden of proof. You're using the criminal standard of beyond a reasonable doubt, but in a civil case, that would not be the standard.

Also, the question here is whether the evidence is admissible, which only requires that it have some effect on making a fact in issue more or less likely. You put all the evidence together before deciding whether the burden of proof is met — if and when you go to trial.

But for political argument, there are no standards. People can believe whatever they want to believe. They can consult the voices they hear in their head. They can choose the opinion that makes them seem like a nicer person.

Brian said...

1. Do courts allow Benford analysis as sufficient evidence to go the next step in evaluating ballots for fraud?
2. What are the standards for determining if a ballot is fraudulent?
3. What are the remedies if ballots are found to be fraudulent?


1. It's possible or it may be some sort of other analysis (affidavits, blocking of poll watchers, etc) as a way to go to the next step if fraud happened.

2. The good news here is that there is codified law covering the operation of elections in each and every state. It's the legislatures job to write those laws. Those laws set standards for balloting. Anything not conforming to the standard is by definition invalid.

3. As to remedies, this is the real root of the problem. There are no remedies. Those are likely not spelled out in law (I haven't done the research). They are probably spelled out in individual cases as regards to the people committing fraud, but not to the election itself. That will be left to judges (and ultimately to the Supreme Court).

Judges are going to be very reluctant to throw out an election. Even if there is fraud to be found. Just like judges are reluctant to side against jurors. The jury box represents the will of the people, the ballot box the same. Our entire judicial system is grounded in that principle.

The issue for the justices that will ultimately decide this is that if there is no penalty for attempting to defraud elections outside of individual penalties, then we will get more fraud in future elections, not less. The risk to the party cheating is very low, and the reward is very very high.

My guess is that if there are any fraudulent ballots they are likely already mixed into "valid" ballots. You already see that by the PA election officials saying that only a "small" number of ballots were received after election day, so it won't make a difference, disregarding claims that they backdated ballot received dates.

This scenario would leave the only possible remedy to throw out the results of an individual states election. The so called "nuclear" option. I suspect that is a bridge to far for judges though.

In the event that happens though the election is likely to go to the House in accordance with the Constitution. It appears we've already been down this road however as a country, in 1876 with the election of Rutherford B Hayes.

All the media talk about how fraud isn't possible though is very disingenuous. Of course it's possible.

One further comment, if and when it gets to the point in the judicial system that a judge (or set of judges) is set to rule on something I expect to see some sort of media analysis of how judges shouldn't be allowed to decide these cases, that there should be a jury involved. "Will of the people" and all.

Mike (MJB Wolf) said...

Fox still refuses to address their “Nancy picks up five seats!” call that came long before the polls were closed west of PA and they were spectacularly wrong. But we should believe their other “calls”? LOLGF as Ace used to say before iPhone decided his site is just to unstable to load on my phone. Uh huh. Big Tech has a big reckoning coming once we sort out the Granpa Votefraud issue.

rehajm said...

Has a legislature EVER rejected their election and chosen new electors in recent history? I think people hoping for that are like people who thought Hunter Biden or Hillary Clinton would face consequences: Deluded.

I'm not counting on it but don't dismiss the idea because of recent precedent of Clintons and Obamas. We could get there. It would take some stomach-turning evidence of fraud but we could get there. There's a reason Democrats are going full tilt on the results instead of basking in the glory of their victory...

mockturtle said...

Sidney Powell, former Federal Prosecutor, is currently on Maria Bartiromo's morning show. She asserted that some of the results are 'statistically impossible' due to the 'injection' of exactly the same number of ballots into several counties at the same time. This will be interesting and I'll make some popcorn.

Ann Althouse said...

So the trick is to make people want to think what you want them to think.

And saying I've got complicated math here might be a good way to make people want to agree with you -- rather than understand the math. Or it may make people want to get the hell away from you.

Math is an interesting public opinion weapon, but it cuts both ways. It will make people defer to you or make people run away from you. It's probably a wash. Or as we say in math: same difference.

Brian said...

Odd that so far all the Trump law suits have been thrown out due to lack of evidence, and the postman in Pennsylvania recanted his claim and signed an affidavit saying so—-this was the one piece the right wing crow about has now that laid an egg.

I think you might be misinformed. Have you seen the affidavit? Because the Washington Post hasn't. From their article: But on Monday, Hopkins, 32, told investigators from the U.S. Postal Service’s Office of Inspector General that the allegations were not true, and he signed an affidavit recanting his claims, according to officials who spoke on the condition of anonymity to describe an ongoing investigation.

Hopkins has said he didn't recant. "But in a YouTube video he posted Tuesday night, he denied recanting. “I’m here to say I did not recant my statements. That did not happen,” he said."

If there is an affidavit, produce it. Hopkins has produced the tape he made of his interrogation, I know you won't see that in the Washington Post however.

Jaq said...

"and the postman in Pennsylvania recanted his claim and signed an affidavit saying so—“

Why is he saying he didn’t then?

Clyde said...

roesch/voltaire said...
Odd that so far all the Trump law suits have been thrown out due to lack of evidence, and the postman in Pennsylvania recanted his claim


False. The postal worker in PA did NOT recant his claim. The media is reporting that he did, but I saw video of him doubling down and saying he did not recant.

rehajm said...

The election situation calls to mind how convincing probability analysis was used to catch online poker cheats. Using poker probability and expected win rates it was easy to spot outliers that could see hole cards of their opponents...

How they caught online poker cheats

Jaq said...

"So the trick is to make people want to think what you want them to think.”

Reminds me of this poem from Smollet’s translation of Don Quixote

O Book! thou make thy steady aim,
No empty chatterer will dare
⁠To question or dispute thy claim.
But if perchance thou hast a mind
⁠To win of idiots approbation.
Lost labor will be thy reward,
⁠Though they'll pretend appreciation.

steve uhr said...

Trump won’t concede for one reason. He wants money from his supporters. Suckers all.

Howard said...

Well, with all the bad news at least you people have Tucker Carlson standing up for Diaper Don.

tim maguire said...

Howard said...If there was something like a SOP for applying Benfords "Law" to election data, then using it as one of several indications to trigger a criminal investigation is probably a smart thing to do.

There are two arguments against Benford's Law in this instance--(1) You can't use Benford's Law to examine election outcomes because data sets are too small (Dr Jen Golbeck...told Reuters, “There is just not solid evidence that Benford works in elections at all.), and (2) you can use Benford's Law, but proper application doesn't show anything suspicious (Professor Boud Roukema...told Reuters by email...: "Benford's law reasoning, applied to the real data, shows no reason to suspect fraud here.”).

As to (1), Benford's Law has been used to identify election fraud and there is a standard for applying it. As to (2), I have no idea, but experts for both sides will hash it out either outside or inside the courtroom.

Leland said...

Has a legislature EVER rejected their election and chosen new electors in recent history? I think people hoping for that

That's a lot of arguments and qualifiers.

1) "Has a legislature ever rejected their election" Without doing a lot of studying of the 1876 and 1888 elections; I can't be sure, but both elections show an electoral situation equivalent to what we have today.

2) "and" Why must both events happen to be meaningful. Either event could and in some cases have happened.

3) "chosen new electors" This seemed to happen in 1876, but I'm not sure it was done by the legislature of the state without more research.

4) "recent history" Perhaps you mean to ignore 1876 and 1888 as not being recent? Does "recent" only mean the last 2 years and not 200 years? Why have a qualifier? Can't any precedent in the US general election suggest there is nothing extraordinary about today's events?

In 1876, Rutherford B. Hayes won the Presidency despite losing both the popular vote and the electoral vote. Indeed, much of Hayes Presidency mirrors Trumps today, including an impeachment attempt.

Jaq said...

"that other stuff on the same server or domain is apparently that "content of an intimate nature,"

There is stuff their of Hunter and a very young girl given to him by the ChiComs. Don’t worry though, Joe is not compromised!

Gusty Winds said...

People are signing affidavits. Whistle-blowers coming forward. Yesterday the Wash Post, a favorite source for this blog, tried claiming that Ralph Nicholson that USPS Pennsylvania whistle blower recanted his claim after being intimidated by agents. Within like an hour, Nicholson but up a video denying his recantation, and calling out the Post. GoFundMe took down the page started for him in anticipation of him losing his job.

Fernandinande said...

ProTip: falsify your tax return in binary so all the numbers can start with 1.

Jaq said...

"Trump won’t concede for one reason.”

Because you believe it, that proves it.

Mike (MJB Wolf) said...

We cannot allow this same lax “honor system” to be the standard going forward. There’s a reason France outlawed mail ballots 45 years ago and THIS is the reason. This election is exactly the clusterfuck predicted. Exactly. People said “Whoa don’t send out ballots en masse” but no, rogue election officials put into office through the Soros Project (the guy is brilliant as rogue DA and rogue SOS officials proved INTEGRAL to so much we’ve witnessed this year) and egged on by D governors did the wrong thing with impunity right in front of us using COVID as the excuse. We are NOT going to forget what we witnessed this year. It’s so clear the riots and the lockdowns were theatre designed to enable the illegal ballots, illegal “curing” of votes and as a predicate to use outdated lists to send every D voter and their dog extra votes. There was no science behind locking up healthy people. We said so here at the time. WHO has since admitted lockdowns do nothing. Viruses gotta virus, after all. But it is so on III us that one was used to allow the other. That’s why the “emergency rules” just happened to suppress normal activity while allowing horribly violent (though mostly peaceful gag) riots. Riots that scared people in select cities to stay home. The same cities still counting. You progressives can harrumph all you want about the proof being elusive but you have really pissed off your fellow Americans. When people truly lose faith in a system they turn on the tyrants first.

Jaq said...

Imagine if the "pee pee tapes” actually existed and were publicly available from some Russian domain. I bet the standards would be different.

Howard said...

Back to Hunter Biden nice pivot there Tim

steve uhr said...

All legal votes must be counted. It necessarily follows that a vote can be disqualified only upon a showing that that particular vote is unlawful. Statistics alone won’t get you there.

Bob Boyd said...

the postman in Pennsylvania recanted his claim

Fake news.

Howard said...

Do you have guys have a link to the recant recant that does not only quote project veritas

rhhardin said...

"It's better than 9 guilty men go free than that one innocent man is convicted. That's the legal threshold. So you want a statistical test that, in a fair election, would let you wrongly call it fixed only one time in ten."

In evidence law, there is the question what is the burden of proof. You're using the criminal standard of beyond a reasonable doubt, but in a civil case, that would not be the standard.


No, it's the standard that the public is happy with. It's a similar big deal to invalidate votes. Let it happen wrongly only one time in ten when it's suspected but (as it happens) present. Like a criminal trial.

The not present part is the useful feature: you can calculate the probabilities of everything when it's not fixed, so you can know the false alarm rate you're hitting in that case. That test you then use on the election that you have, that may or may not be fixed.

Darrell said...

@JamesOKeefeIII 1m
We have recordings of the federal agents, who COERCED this man through a 4 hour interrogation Without representation, who stands by his original affidavit re: backdating ballots.

Standby for recordings doubling down on backdating ballots.

This is soviet style truth suppression

Jaq said...

"ProTip: falsify your tax return in binary so all the numbers can start with 1.”

During WWII, after the Brits had broken the German codes, they had to pick and choose which ships they would save, carefully avoiding the appearance of doing very much better than chance, to avoid tipping off the Germans. Gravity’s Rainbow, by Pynchon is a WWII novel about a guy who could describe the pattern of how V2s would fall using statistics, but people kept demanding that he tell them *where* the next one was going to fall, which of course he couldn’t. He could only say that the next one would fit into his statistical model, most likely.

rhhardin said...

.. but not (as it happens) present...

rhhardin said...

You can read binary as octal or hexadecimal and do the same test. As you can read decimal as base 100 instead of base 10.

Gusty Winds said...

The fraud doesn’t have to be “massive” or “widespread”. The media loves to claim incidents are isolated as a lack of proof. You don’t need a fraud operation in Idaho. In Wisconsin, Milwaukee knew how many votes they had to deliver. I’m sure Madison was in on it too. The ballot harvesting in the park was in-your-face. Philly delivered the same, just took a little longer to cheat a 400K margin. Detroit the same. Atlanta as well. You need Democrat controlled population centers, and a staff full of those willing to subvert and oppress. Plenty in the Wisconsin Democrat Party.

Mike (MJB Wolf) said...

https://saraacarter.com/usps-whistleblower-demands-washington-post-retract-story-saying-he-recanted-allegations-of-voter-fraud/

Ah the false confession #FakeNews story that RV is already trying to spread. You guys never stop. Affidavit NOT withdrawn, duder.

Jaq said...

“My name is Richard Hopkins, I am the postal employee who came out and whistle blew on the Erie PA postal service,” he said in the video. “I am right at this very moment looking at a article written by Washington Post, says that I fabricated the allegations of ballot tampering – I’m here to say that I did not ‘recant’ my statement, that did not happen, that is not what happened and you will find out tomorrow.”

https://saraacarter.com/usps-whistleblower-demands-washington-post-retract-story-saying-he-recanted-allegations-of-voter-fraud/

Wince said...

"So get off your 'ath' and let's do some math. Math, math, math, math, math."

Gusty Winds said...

I’m starting to wonder if a commitment to “cruel neutrality” is really a false claim regarding commitment to the truth. Questions, Questions, Questions…but never a conclusion. In regards to the fraud in Wisconsin, we know there are plenty of citizens that thirst for Madison and Milwaukee control. They know the fraud is real. There are more than just a few people involved. They just don’t care. They are hoping they can “count” on it. They did the same thing to Walker in 2018. It’s how we got our Beta-Cuck Governor Evers.

narciso said...


The data is corrupted at the source


https://mobile.twitter.com/CodeMonkeyZ/status/1326522109674229761

Readering said...

All this math expensive to establish in court. As Trump supporters you must be getting the same dozens of daily $$ requests as me. Contribute! And get Trump rewards points in the bargain. Plus 1000 percent match. (I wonder if there is a statistical law with a name to check those matching promises?)

Spiros said...

Things went haywire after the count "stopped" at 1 AM. Shouldn't statistical analysis focus on the period afterwards?

Howard said...

So the bottom line is we'll find out tomorrow from the recanting recanter what the deal is. It sounds awful with those investigators did to him. I mean who do they think he was some black teenager?

D.D. Driver said...

They just don’t care. They are hoping they can “count” on it. They did the same thing to Walker in 2018.

Walker was definitely the victim of a fraud, and it cost him the election. But here is an instance where I will blame the victim because he should have known better. The fraud was not perpetrated by the Democrats, the fraud was perpetrated by Foxconn.

Qwinn said...

So this thread matches every other thread since the election: conservatives posting links to mountains of evidence of fraud, and lefties post nothing but snark and insults and imputation of venal motives. No concern at all for addressing conservatives' concerns... if 72 million people come out of this convinced the election was stolen, there isn't a hint that this would trouble lefties here in the slightest. In fact, they are taking absolute delight in the prospect.

The SINGLE attempt to address a concern, by claiming Hopkins recanted, is not only an outright lie, it serves to cover up the recording of 4 hours of intimidation by leftist officials, and his suspension from his job, and GoFundMe blocking any donations.

We need mass arrests of leftist fascists before this can end well.

Ray said...

One of the big strategies of the Trump lawyers is do state courts have the ability to change voting law. The Constitution gives only state legislatures that power. Even a veto by the executive is not mentioned. This issue will be determined by the Supreme Court. It really depends how brave they are. If the Court rules in Trumps favor, then all votes received in Pennsylvania after 8 pm on the 3rd will be invalid. If Pennsylvania didn't adhere to the Courts directive given twice, then the Pennsylvania vote should be declared invalid and the Pennsylvania Legislature will have to determine the next move.
I think if Trump fails on this issue, he probably will have little chance on winning on disputed ballots. Even if there was massive fraud.

Spiros said...

So it's a dead heat across the country. One vote for Biden, one for Trump: its like flipping a coin. But after 1 AM, in four cities, Biden starts getting all the votes. Isn't this like flipping a coin and getting ten thousand heads in a row?

Jaq said...

"So the bottom line is we'll find out tomorrow from the recanting recanter “

He never recanted anything, he called bullshit on people who say he recanted. Produce the affidavit he purportedly signed. You only have the widely discredited WaPo as a source here. Produce that and we can talk about any recanting.

Mike said...

So I have to listen to baseless election fraud accusations from the right after years of baseless Russia election conspiracies from the left? Cruel neutrality has never sounded better.

DINKY DAU 45 said...

trump ,a fluke 1 term president,only 3rd incumbent to lose popular vote 2x and I believe 4th incumbent to lose so big(will be over 5 million popular vote)...trump is whining,lying and claiming false conspiracies with no evidence or proof right until the end.The courts are throwing out his bogus claims left and right. He is now an irrelevant 1 term lame duck individual who will be gone January 20th one way or another.He will reek as much havoc as he can before he goes or gets dragged out.No health plan,no infrastructure,biggest national debt in American History, divided the country as much as he could,detested by our allies and world leaders,allowed Kim and Iran to pursue their nuclear ambitions to the max,INDIVIDUAL#1 in the courts of Cy Vance and Letitia James who are coming for his criminality in a few short months..The country has been rid of the authoritarian ,wanna be dictator rule of this Russian asset in the nick of time...ORANGE JUMPSUIT NEXT..No more insane TWEETs We now have a leader ,not a tweeter..The R's wjhine and complain with no evidence or proof and the courts agree....trumps plan to elect a right wing judge to help him steal aint working..ACA will be upheld,,as trump team also bogus claims in that court..Of all the top shelf lawyers representing he sends RUDY to the parking lot of the FOUR SEASONS next to a porn shop and a crematorium to spout conspiracies,it is a fitting end for the worst criminal organization in American history.This will go down in history books overtaking the Bendict Arnold sage,,,BET

DINKY DAU 45 said...

trump ,a fluke 1 term president,only 3rd incumbent to lose popular vote 2x and I believe 4th incumbent to lose so big(will be over 5 million popular vote)...trump is whining,lying and claiming false conspiracies with no evidence or proof right until the end.The courts are throwing out his bogus claims left and right. He is now an irrelevant 1 term lame duck individual who will be gone January 20th one way or another.He will reek as much havoc as he can before he goes or gets dragged out.No health plan,no infrastructure,biggest national debt in American History, divided the country as much as he could,detested by our allies and world leaders,allowed Kim and Iran to pursue their nuclear ambitions to the max,INDIVIDUAL#1 in the courts of Cy Vance and Letitia James who are coming for his criminality in a few short months..The country has been rid of the authoritarian ,wanna be dictator rule of this Russian asset in the nick of time...ORANGE JUMPSUIT NEXT..No more insane TWEETs We now have a leader ,not a tweeter..The R's wjhine and complain with no evidence or proof and the courts agree....trumps plan to elect a right wing judge to help him steal aint working..ACA will be upheld,,as trump team also bogus claims in that court..Of all the top shelf lawyers representing he sends RUDY to the parking lot of the FOUR SEASONS next to a porn shop and a crematorium to spout conspiracies,it is a fitting end for the worst criminal organization in American history.This will go down in history books overtaking the Bendict Arnold sage,,,BET

Paul Snively said...

Jamie: And just a general comment: damn, math is cool. I really shouldn't have listened to Barbie back in the '80s. I foolishly only took what I needed to get my degrees instead of digging in more. Off to Khan Academy...

You have a computer and an internet connection, so run, don't walk, to buy Statistical Rethinking: A Bayesian Course with Examples in R and STAN (Chapman & Hall/CRC Texts in Statistical Science) 2nd Edition. I also recommend working through the text using these Jupyter notebooks. This will give you an excellent foundation upon which to evaluate claims around incomplete and/or uncertain data.

D.D. Driver said...

In Wisconsin, Milwaukee knew how many votes they had to deliver. I’m sure Madison was in on it too.

If you are going to keep spouting nonsense about Milwaukee, I will keep correcting it.  Trump did well in Milwaukee.  Also, by and large, African Americans greeted Biden with a shrug.  Turnout and enthusiasm was low among African Americans (particularly in Milwaukee). Why would you suspect that predominately African American areas are the one perpetrating fraud in favor of Joe? I think its time to let go of some of the old stereotypes.

I do not think there was fraud. The results are explainable without resorting to far fetched conspiracy theories. That said, if there was fraud--I would look the city where state senators are being assaulted on the street and lawless thugs are tearing down statues. Leave Milwaukee out of this.

Leland said...

We need mass arrests of leftist fascists before this can end well.

I don't know about the arrests, but at least recognition that it is the leftist that are behaving in a fascist manner. And as I write this, have you considered listening to Althouse's podcast? I think she has something to say about this. I suspect maybe you have.

DINKY DAU 45 said...

TRUMP WILL BE SELLING CLASSIFIED INFORMATION TO HIGHEST BIDDER TO PAY OFF HIS DEBTS,,what he can remember anyway..This guy has the loosest lips of any president ever ,has already shared info with our enemies,GOOGLE it...He'll always be a clear and present danger..Thank the Lord,the American people rejected this guy in a very big electoral and popular win...Check the numbers,,JOE WON BIGLY! and still pumping out the jams..trump is deemed irrelevant ,a lame duck ,crying and acting like a impetious child,because he now has no one to save him,he will die knowing with the monicker of LOSER ,the thing a narcissist cant stand..Thank you America for not letting APATHY recreate 2016...lesson learned...

Qwinn said...

DD Driver: Are you serious? Why would we suspect it occurs in AA districts? Because that's where Dems ALWAYS focus their voter fraud. High number of voters historically disposed towards them, and if anyone calls out the fraud, all you have to do is scream "Racism!" and it goes away. That has always, always, always worked. Why would they bother anywhere else?

Qwinn said...

Leland, no, I havent had a chance to listen to the podcast yet. Not sure I'll find an hour to do so for now. Can you give me the gist please?

Spiros said...

Something very strange happened. In the big cities that counted early, Biden took about 65 to 75% of the vote. In cities like Philadelphia that counted late or halted counting, Biden took 90% of mail in votes.

I don't think a "Deep State" conspiracy get Biden elected. But I do think that voter fraud happened. And I think the fraud is closer to sabotage. In war, saboteurs are often mentally disturbed individuals, terrorists or local sympathizers. What if thousands of vote counters believed that the presidential race was a war and sabotaged the count when it became apparent that the election was not a blow out? The woke believed that their lives depended on Biden winning, that a vote for Biden was the single most important thing they could do with their lives...

RMc said...

Judges are going to be very reluctant to throw out an election.

If this thing goes to the Supreme Court, no matter which way they rule, every member of that Court (and their families) will require Secret Service-like protection for the rest of their lives.

wendybar said...

https://youtu.be/ibU5KVFCg4Y Here you go Howard...right from the Whistle blowers own mouth. Now are you going to call him a liar??

Qwinn said...

Of course lefties will call Hopkins a liar. They have been brazenly dismissing thousands of sworn affidavits as "no evidence". Conservative affidavits don't count. It's exactly the same ethos Twitter is employing, in that every conservative post is slapped with "disputed" while leftist posts on the very same subject are not disputed. Only leftist assertions can cou t as truth. Welcome to the gulag.

D.D. Driver said...

DD Driver: Are you serious? Why would we suspect it occurs in AA districts? Because that's where Dems ALWAYS focus their voter fraud.

[citation missing]

Lee Moore said...

Clever Math Prof : 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.

Presumably Benford's Law works in the same way - albeit with different pobabilities - whatever base you are using. So if the problem is having too few "powers of tens" then presumably one can have another go, redoing the numbers into, say, base 5.

John henry said...

Blogger tim in vermont said...

During WWII, after the Brits had broken the German codes, they had to pick and choose which ships they would save, carefully avoiding the appearance of doing very much better than chance, to avoid tipping off the Germans.

Neal Stephenson's excellent novel "Cryptonomicon" uses this as a major subplot in an overarching plot about cryptography and digital money (Like Bitcoin)

Great book, I've read it 15-20 times. I always find some new easter egg that I've missed on previous readings.

One of the particularly cool things is how it is a sequel to the Quicksilver trilogy published 5-6 years later.

John Henry

Ken B said...

The last argument, which Althouse likes, has a bit of circularity. The question at issue is, did he really get 70%? Imagine he got 100%. The professor's argument carries through, and you get the digit distribution you expect from a 100% vote.

Michael K said...

Boy, the lefties are swarming this thread.

Must have something to do with the topic.

OldManRick said...
This comment has been removed by the author.
Dear corrupt left, go F yourselves said...

WaPo(D) is not a truth worthy source for news.

OldManRick said...

How about a simple test. An easy to do test, that will provide mathematical certainty not maybe it's because of some this or that.

Do the Benford's Law analysis on the past five presidential elections in those areas that the show major discrepancies in current election. If the same discrepancies at the same level show up previous elections then it doesn't apply here. If this election is a one of a kind, then you know something is different.

Until the Benford's Law skeptics show proof like this that it shouldn't apply, then it should apply.

This still doesn't expand the discrepancy in down ballot percentage discrepancy, which can also be tested against previous election.

John henry said...



Blogger DINKY DAU 45 said...

Welcome back, Squeamish.

John Henry

Mattman26 said...

Spiros: "Something very strange happened. In the big cities that counted early, Biden took about 65 to 75% of the vote. In cities like Philadelphia that counted late or halted counting, Biden took 90% of mail in votes."

I'm not doubting that, but would love to see the evidence of it. (But would love even more for someone else to go find it!) That strikes me as highly relevant, in both the legal and everyday use of the term.

On Benford's (Confession: pretty sure I'd never heard of it til last week): It seems clear it is of value only where wide orders of magnitude are involved, and if it's true that most wards in Milwaukee have between 570 and 1200 votes, then I don't think Benford's is helpful on a ward-by-ward basis.

bbear said...

A few days ago I posted a comment here linking to a skeptical 2011 academic study out of CalTech and the U of Oregon. Evidently nobody saw it, perhaps because it was late and came at the end of a very long thread...

Benford's Law and the Detection of Election Fraud
https://www.cambridge.org/core/journals/political-analysis/article/benfords-law-and-the-detection-of-election-fraud/3B1D64E822371C461AF3C61CE91AAF6D

Recommended, and freely downloadable as a pdf. As I said there, I don't doubt the election was compromised, but I think Benford's Law is unlikely to be dispositive in this case.

John henry said...

Still in print after 65 years, a book that helped me a lot in grad school and available via the portal:

"How to Lie with Statistics" by Darrell Huff

https://amzn.to/2JZJGjB

Link is to the book via the portal.

Re statistics, I am in the process of republishing John McConnell's excellent series of books on statistical quality control.

Hopefully we'll make a few bucks but it is basically a labor of love. Especially since it turned out he did not have electronic copies and I had to scan and clean 3 of the 4 books. "Analysis and Control of Variation" is VERY heavy on the statistical math. Having to redo all of it by hand reminded me of why I have never enjoyed statistics.

Nearly done, hoping to publish by Christmas for those Deming/SPC/Quality fans.


John Henry

John henry said...

"How to Lie with Statistics" by Darrell Huff

https://amzn.to/2JZJGjB

Actually, Ann, I have a question for you. I went to Amazon via the portal and found the book. The URL when I pasted it was about 5-6 lines long. In that link is a code that credits you.

I used bit.ly to shorten it.

If I shorten the link, do you still get credit? If not, apologies. I will not do so in the future.

John Henry

BJK said...

“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.”

...but the absentee ballots were not tabulated at the ward level in Milwaukee (and most of the other cities who "shut down" vote counting on election night). If the fraudulent totals were processed in a central location, with the results distributed between the various wards where the absentee ballots came from....wouldn't that undermine the methodology? Genuine question, since I had never heard of Benford's law before this morning.

Greg The Class Traitor said...

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.

Is this an honest quote? Because there's nothing very "advanced" about running the test on the 2nd number, as well as the 1st

Whiskeybum said...

Sorry to be joining this discussion so late...

I had started a general conversation about the applicability of Benford's Law to the election on Monday nights open cafe. Mandrewa had provided the link below to a forensic experts (Mark Nigrini) to the Marcopia County data. He does a very complete analysis, including the second digit analysis mentioned in the current article, and also assesses the level of nonconfirmity, i.e. how strongly do we believe the analysis shows/doesn't show fraud. I suggest that if you are truly interested in this subject, you watch this video:

https://www.youtube.com/watch?v=FrJui5d7BrI

Back on Monday, I had raised many of the same questions being addressed here in this current article. In particular, do the data sets span a large enough range for the "Law" to be applicable? I suspect that the answer is 'yes' in some cases, an 'no' in others. For Milwaukee (which Nigrini is going to analyze today or tomorrow), I suspect that the answer might be 'no'. THAT DOESN'T MEAN THAT SOME KIND OF FRAUD WAS NOT PERPETRATED IN MILWAUKEE! I'm not saying it was or wasn't - what I'm saying is that Benford's Law applies to a certain type of fraud - data manipulation. It does not detect voter suppression, late mail-in ballot fraud, etc. So, Milwaukee could have had other types of fraud going on that Benford's Law would never have any application to.

Ann Althouse said...

"If I shorten the link, do you still get credit? If not, apologies. I will not do so in the future."

I really don't know. I'm going to guess that Amazon takes the first opportunity to channel the money toward itself. Why wouldn't they be vigilant?

Greg The Class Traitor said...

The specific case of the Milwaukee results was also examined by Professor Boud Roukema of Poland’s Nicolaus Copernicus University

Roukema gives a reasonable argument. The correction for that is to use that same analysis to determine how many precincts you would have to add together to get the required logarithmic distribution. Then join up the Milwaukee wards into groups of that size. To prevent cherry picking, group wards 1 - X, X + 1 - 2X, etc, then chart that. There's at least 324 wards, so you should be able to get useful charts with X up to 6 or so.

You would think that honest reporters would ask someone to do that test (heck, I may end up doing it)

gilbar said...

so, it turns out? That mailing absentee ballots to EVERY SINGLE REGISTERED VOTER IN THE US,
turns out to Drastically Increase numbers of people voting; including dead or imaginary people?
WHO would have thought? Oh, that's right; the democrats would have thought

Ice Nine said...

I'd like to rely on these expert opinions. However, in the age of Trump Derangement Syndrome you cannot count on unbiased analysis even from the experts in math and statistics. A pity but that's where we are.

gilbar said...

serious question(s)

does ANYONE think that the 2020 election was valid?
I'm NOT asking, if you're happy with the results
I'm NOT asking, if your happiness MAKES it valid
I'm asking; does ANYONE think that the 2020 election was valid?

More seriouser question
Does ANYONE (ANYONE AT ALL) Think that Jo Biden will be President in October 2024?

Whiskeybum said...

Lee Moore @ 9:19

The 'trick' you mentioned for narrow data sets of changing the logarithmic base was brought up very briefly by Nigrini in an earlier YouTube video of his which was focused on just explaining Benford's Law in general. It would be interesting to hear how applicable that technique would be on, say, Milwaukee's election data.

Old Man Rick @ 9:25

Not only would it be illustrative to apply the Law to past election results where fraud was suspected, but as I said in Monday night's post, it would be very instructive to apply the Law to past data where NO FRAUD was suspected to see that Benford's law is truly applicable to election results.

bbear @ 9:38

Sorry I missed your comment about the Cal Tech article on Benford's law applicability to elections in general. I'll for sure check it out now.

Guildofcannonballs said...

Fair minded people know abortion is wrong 99% of the time Althouse. You've gaslit yourself.

OldManRick said...

Two other thoughts on Benford's Law.

The size of the wards proposed solution does not explain why Trump's and the other candidates distributions follow Benson's Law. If the wards are stacked in an unequal distribution, it should show up in all the results and not just Biden's. The fact that Biden's are seriously out of alignment with the other candidates should be enough alone to indicate fraud. If wards are stacked in unequal distributions, then show us the distribution of ward size.

It would be interesting to know where all the Biden with no down ballot votes appeared. Spreading them over these wards in clumps would explain the problems with Benford's law and re-enforce the proposition that these were massive fraudulent ballot dumps.

I'm sorry, I'm just a math major (with an emphasis on statistics) from MIT and I expect people to understand the astronomical level of improbability that this implies. I defer to other peoples specialties, I expect the same from them.

mandrewa said...

Jen Golbeck said, "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."

Of course there are going to be people out there, and lots of them, not doing it correctly. That is completely and 100% predictable. If by some miracle every Trump supporter was doing it correctly, you would still have deceptive people deliberately doing it wrong to cloud the situation.

So the right thing is obviously to focus on the people that are doing it correctly. And for that matter since Jen Golbeck is claiming to be an expert, why doesn't she do it herself?

As for the business about the second digit, well guess what? There are people looking at the second digit, Mark Nigrini does, and he fact he normally plots against the combination of the first and second digit.

It still looks just like Benford's Law. It still works, and if anything it's even more impressive when you see a hundred numbers all lining up perfectly to make that counterintuitive curve.

And then here we have a possible confusion. (But we always get that with math!) But it does touch upon whether Jen Golbeck is being sincere. Is she talking about just looking at the 2nd digit in isolation? Well she could be, but that's not normally meaningful.

Or is she talking about sorting the numbers into a hundred bins based on the first two digits? That is very useful, and it is the same kind of curve as we get from looking at just the first digit.

Paul Snively said...

Spiros: So it's a dead heat across the country. One vote for Biden, one for Trump: its like flipping a coin. But after 1 AM, in four cities, Biden starts getting all the votes.

To be fair, that's because whether a voter believed it was safe to vote in person vs. mailing in a ballot also divided almost exactly along party lines, and mail-in ballots are counted after in-person ballots—in some cases, due to state legal requirements. So the safe bet was that Trump would do well on election day, and that advantage would dwindle as mail-in votes were counted. And that much is true whether you believe there was fraud or not. What's in question is exactly how much fraud there was, with "What!? There's never voter fraud in US presidential elections!" and "every mail-in ballot in the 2020 election is invalid" as the delusional ends of the spectrum.

Isn't this like flipping a coin and getting ten thousand heads in a row?

Fun probability fact: you can reliably tell when a human being has tried to "simulate," say, 100 coin tosses ("HTHHTHTTHT...") due to the lack of runs in practice, you get surprising (to humans) runs. This is, of course, assuming a naïve tosser. A knowledgeable tosser can produce any distribution they want. I'm an amateur sleight-of-hand magician; you should never trust me with a coin toss under any circumstances.

Bruce Hayden said...

“ The Bedford's law post I saw indicated that it raised red flags in Pennsyvania more than Wisconsin. And conversely it indicated that Georgia, Michigan and Nevada's results were on the up and up (thus meaning that while PA remains a sh*T show, it still probably won't swing the overall election towards Trump).”

That is not accurate. Bedford raises red flags for specific types of fraud - notably the creation of fake ballots and insertion into the system, etc. it says much less about fraud that doesn’t lose its random or probabilistic characteristics. Thus, it might not detect destroying every other Republican ballot.

Something else (and you know that the “experts” there are misleading because they ignore it) is that lower order digits are probably more important in identifying fraud than higher order digits (which is why the “expert” concentrated on the high order digit). Low order digits should be somewhat randomly distributed - much more than high order digits. And that what apparently was found - too many low order zeros. Way too many.

Think of it this way: You have a problem - your side has too few ballots. Because you are (intentionally) counting late, you have an idea of how many ballots you need to push the total over the top, your way. There is too much work for one person, so you divide up the work, for example assigning 100 people to create 1,000 votes each, for a needed 100k votes. And they may similarly divide up the work, at 200 ballots each for five people. No surprise then that the low order digits of the new votes violate Bedford’s law - they help disclose the underlying plan for and organization of the fraud. (I noted a couple days ago here that this can be compensated for by assigning the units of fraud using a random number generator - but that is the last thing that the fraudsters are usually thinking about). I would suggest that the statistically highly significant number of low order zeros in the late figures strongly suggests just what I have proposed - a division of labor in order to create a very large number of bogus or otherwise illegal ballots.

Bedford’s law probably won’t disclose discarding every other Republican vote - but it very well might disclose creating a duplicate Dem vote for every real one (because the low order digits would be predominantly even). The difference between halving and doubling is just that - that halving doesn’t affect the frequency of low order digits (unless you apply some rounding rules that eventuates even/odd). What you need to do to determine whether Bedford’s rule might disclose fraud is look at whether and how that fraud might affect counts. An auditor would probably tell you that they have other tools for detecting other types of fraud (I enjoyed Auditing in college, but never pursued the field professionally, after learning that I would have to do (highly boring) accounting first, for 5-10 years, before I could start doing the fun stuff).

bbear said...

Tim in Vermont, 8:16am

"...describe the pattern of how V2s would fall using statistics..."


Quite right.

"Consider the statistics of flying-bomb hits in the south of London during World War II . . . The fit of the Poisson distribution is surprisingly good as judged by the chi-square criterion . . . [M]ost people believed in a tendency of the points of impact to cluster . . . [but data] indicates perfect randomness and homogeneity of the area; we have here an instructive illustration of the fact that to the untrained eye randomness appears as regularity or tendency to cluster."

An Introduction to Probability Theory and Its Applications, (vol 1)
by William Feller, Eugene Higgins Professor of Mathematics, Princeton University

chuck said...

As I have said before, Benford's Law is not the strong play, it is not the basket in which to carry your eggs, the criticism in the article is a valid. There is much stronger evidence of fraud out there.

Bilwick said...

Benford's Law? Nothing to see here, people. Move along.

Bruce Hayden said...

Let me summarize my last post. Concentrating on high order digits to show that there wasn’t fraud was extremely deceptive, because what was significant here was the statistically almost prohibitively high number of low order zeros.

Mattman26 said...

Bruce Hayden, that was very interesting (both the long and short version). Thanks.

Howard said...

Blogger Bruce Hayden said...

Let me summarize my last post.


You should do that for every post, more people might actually bother to read you.

Pretend you are briefing Trump and he's just doubled down on Adderall.

Lawrence Person said...

I did a post on this.

John henry said...

Blogger bbear said...

Tim in Vermont, 8:16am

"...describe the pattern of how V2s would fall using statistics..."

They also did some fake news, with cooperation of the British press.

They would report a V2 as flying right over london when it actually hit the city. This caused the germans to change the trajectory of the V2s so they would fall short.

But they couldn't make them all fall short or the Germans would realize the fakery. So they had to lie about as many as they could while still staying in the distribution of expected randomness.

They would falsely also claim that some of them fell short so the National Socialists would increase the trajectory causing them to overfly London.

This whole question about what to do with intelligence when you do have it is fascinating. Several books have been written about it.

John Henry

Jaq said...

"'m sorry, I'm just a math major (with an emphasis on statistics) from MIT and I expect people to understand the astronomical level of improbability that this implies. I defer to other peoples specialties, I expect the same from them.”

I would be a lot more likely to defer to your judgment if you whipped up a decent counterargument to the one presented based on the data and premises that he presented instead of just saying “trust me, I’m right.”

I was no math major, but Probablity and Statistics was probably the most useful course I took in college.

Jupiter said...

"In real life, we don't depend on one piece of evidence."

The critical question is, what level of proof is required, before one takes action? For example; when a person is being tried for a capital crime, we want a very high level of proof, because, while we are perfectly willing to have a national system of highways that kills tens of thousands of innocent people every year, as long as it raises the standard of living for the survivors, we are unwilling to take the same approach to the national system of laws.

But in this case, it is hard to see any strong argument against accepting the evidence of fraud. What innocent reason could there possibly be for election officials to illegally exclude poll-watchers, and cover the windows of the counting-rooms?

When you think the cat may have taken a shit in the cookie-dough, you don't hold a solemn inquest, with the verdict "Not Proven". You toss the cookies, and make another batch.

Jupiter said...

And I'd a lot rather eat cat-shit cookies than let the Democrats steal an election!

Professional lady said...

There are some commentators I always skip because they are not worth my time. Bruce Hayden is not one of them.

Brian said...

Do you have guys have a link to the recant recant that does not only quote project veritas

The Washington Post mentions it in their article. Quote: "But in a YouTube video he posted Tuesday night, he denied recanting. “I’m here to say I did not recant my statements. That did not happen,” he said."

The Washington Post is quoting him, not Veritas. That's your source.

They have 2 competing narratives, one with anonymous sources, the other on video record. But I get it, the anonymous sources, are being quoted all across the media so they must be right.

This is the same playbook as the Russia stories.

Greg The Class Traitor said...

The problem with the CalTech article is taht it exclusively focuses on the 2nd digit.

If they'd done 1st & 2nd, I would have found it much stronger

D.D. Driver said...

But in this case, it is hard to see any strong argument against accepting the evidence of fraud. What innocent reason could there possibly be for election officials to illegally exclude poll-watchers, and cover the windows of the counting-rooms?

There were already poll watchers inside. You can see them because the video was taken from inside the count room. Am I supposed to believe conspiracy theories or my own lying eyes?

OldManRick said...

For Tim in Vermont:

If the returns for Biden violate the law and none of the returns for other candidates up and down the ballot don't, then the distribution of wards argument fails. The basic hypothesis is that any distribution without a name attached to it should follow Benford's law. From what I've seen only Biden's votes fail the law, only in democratically controlled precincts, and only in swing states that Biden needed to win.

The Biden statisticians are addressing only the Biden distribution with what may be a plausible explanation to some. They are not addressing the difference between other candidates, the location of these discrepancies, the ancillary evidence of ousted poll watchers, down ballot votes, higher than average turn out, better performance by Biden than Obama in these areas.

This can be cleared up by a complete all wide Benford's Law analysis and compared to ward distributions. Checking the historical record for these precinct in the last five elections where the need to oust Trump was not the number one priority would also give insights.

As for me, I've seen enough coincidences in this to assume fraud. My logical explanation is fraud in the form of large numbers of Biden only ballots dropped into these wards. I have given the criteria to prove me wrong. If indeed, this curve is the case in all elections show me. If not, don't try to pick apart only one aspect of the problem.

Bruce Hayden said...

“ I did a post on this.”

Giving credit where credit is due - I had read your article before debarking on my diatribe (and, no, it isn’t Adderil induced, but maybe caffeine with a bit of Aspartame kicker, plus maybe a bit of OC (but not nearly as bad as my partner)). Not sure where I linked from for your article. Could have been here. Maybe Instapundit. First saw Benford’s law used by Larry Corella (Monster Hunters, Inc) in regards to this election, an accountant in a previous life.

rcocean said...

I'm finding this analysis, like much of what's i'm reading, very FRUSTRATING. You have to STOP looking at numbers in ISOLATION and look at them in context.

1) For example, if Biden's number don't obey Bedford's law because they are "too small". then why do trump votes obey the law? They're even SMALLER. And we have the numbers from 2016. What happened then?

2) Steve Cortes says Wisconsin turnout was an absurd 90% of registered voters. Frank Luntz says its 72% of voting age, which is believable. Luntz also says that 12% of voters in 2016 registered on election day. OK, so how many registered on election day in 2020? Neither man says. Or, what was the registered to voters ratio - PRE ELECTION DAY - in 2016? IOW, you can ADJUST the numbers to get an apples to apples comparison, but neither man does. This isn't rocket science.

Or just guessing, if 3.3 million voted out of 3.6 million registered, and an additional 400,000 registered on election day, that's still a turnout of 82% of registered voters in 2020, which is 20% HIGHER Than 2016. So, Luntz if full of shit, but Cortes never provides the REAL Numbers and refutes him. Why not?

3) Did Hillary's numbers in 2016 obey Bedford's law? NO one says. Did Biden's number in OTHER STATES obey Bedford's law? No one says.

4) Cleveland had 51% turnout. Milwaukee had 80%. Trump won 12% of the African American vote nationwide but in the contested areas his vote share drops to 5%. Why?

5) Bottom line is there are all kinds of statistical anomalies in Biden's vote count but that doesn't PROVE just by itself. And if you just take the stats ONE BY ONE without looking at them in context it proves even less. If Biden voting stats in swing states violate Bedfords Law AND are out of line with History AND out of line with votes elsewhere, you have a much stronger case.

Bruce Hayden said...

“ The critical question is, what level of proof is required, before one takes action?”

What Corella talked about were red flags which were very where with this election. They are suggestive, but typically not determinative. One or two red flags get flagged for a little more scrutiny. In his experience as an auditor, a lot of red flags as here, almost guarantees some sort of mischief.

rcocean said...

One thing i've been looking for in the results is this:

How many of the Big city voters weren't registered? And how many who were registered and voted, were (1) Dead (2) Illegal Aliens (3) not of age (4) not residents. I hope Trump and his team are looking into this. To state the obvious Biden victory could be based on:

1) Votes made by dead and imaginary people
2) Votes cast by unregistered people
3) Votes cast by people who should NOT have been registered or voted
4) Votes that were invalid (lacked the necessary signatures, witnesses, etc).
5) votes that were cast AFTER the allowed deadline.

mandrewa said...

Thanks bbear for the link to the paper:

Benford's Law and the detection of election fraud

I haven't read the full thing yet, but it seems to me that the heart of this
argument is whether Benford's Law applies to election returns. Now I can
see all sorts of reasons why in the real world you can't rely on it, and in particular
because in the real world people and political parties know about Benford's Law and it is easy
to fake an election in all sorts of ways and still obey Benford's Law.

And even in the ideal case where the people committing the fraud didn't know about
Benford's Law, there are still lots of frauds that Benford's Law would never detect.

So skipping many things in the paper that my intuition tells me are probably right,
I'm left with what I think is the heart of the remaining argument, or at least one heart
of the argument, that is the question should of whether Benford's Law, in the ideal
case, would apply to election results.

And they try to answer this by constructing simulations of an election, see section 3
of the paper.

And then I'm puzzled by the complexity of their simulations.

I have a hunch that this implies that if you do a simple simulation you get Benford's Law.
Because otherwise why are they making all these complicated and non-universal assumptions?

I take the point that there are ways to set up your vote gathering regions that are going
to give non-Benford distributions even when one is doing the election properly.

And if true that makes everything more complicated. Or sort of, does this really change
things that much?

Because this was always about probability. A violation of Benford's Law does not mean
fraud. Instead it's about estimating the improbability of a situation.

That's the function I would like to see. The function that gives the probability
of fraud for a given set of data -- if we assume the people that might have invented
data in that election were unaware of Benford's Law.

So for a given county in the United States we might be able to say from a Benford's Law
perspective (and only from that perspective) that there is a 5% chance that it's count
is legitimate and 95% that is illegitimate.

OldManRick said...
This comment has been removed by the author.
OldManRick said...

To summarize. The theory of fraud in the form of large numbers of Biden only ballots dropped into this precinct's wards can explain all of the potential discrepancies.

1. Mass drops into specific wards would distort the Benford's Law curve for Biden but not for other candidates..

2. The large number Biden only votes speaks for itself and gives an idea of the scale of the fraud.

3. The added Biden only votes increase the turnout in these precincts, creating the much higher than average turnout percentages. This is already noted as suspicious.

4. The added Biden only votes in these precincts would show why Biden out performed Obama in these precincts by larger percentages than in other precincts. This has been also noted as suspicious.

If you can provide another theory that explains these things, I will consider it. But the current circumstantial evidence points to this simple but depressing explanation.

rcocean said...

The way stats and numbers work is:

1) one anomaly could happen
2) two anomalies could possibly happen
3) three anomalies never happen

It like the OJ Simpson case. That he cut himself just like the killer, possibly innocent. That he cut himself and had the same shoes, possible. That he cut himself, had the same shoes, had the same gloves, had his blood at the scene - impossible.

Jupiter said...

rhhardin said...
"It's better than 9 guilty men go free than that one innocent man is convicted. That's the legal threshold."

Yes, but we're not talking about whether innocent men are convicted. We're talking about whether guilty men (and women) are allowed to profit from their crimes. So the rule is reversed - better that 9 fraudulent elections be overturned than that the majority be disenfranchised by lying thieves once.

Jupiter said...

And the burden is on those managing the election to demonstrate that the election was conducted according to the rules. When they illegally hide their actions from observers, it should be assumed that they are acting in ways they could not possibly justify. Why else would they conceal their conduct?

Jupiter said...

Sorry, that should be, " better that 9 honest elections be overturned than that the majority be disenfranchised by lying thieves once."

Seriously, we spend billions on elections, because they are important. If County X couldn't -- or wouldn't -- do it right the first time, they can bloody well do it again until they get it right. It's not like there's any hurry. The country isn't going to go away.

RichAndSceptical said...

I don't see the big deal. If its use suggests where to look and someone looks there and finds fraudulent votes, it's the fraudulent votes that become evidence.

D.D. Driver said...

"If the returns for Biden violate the law and none of the returns for other candidates up and down the ballot don't, then the distribution of wards argument fail."

Here is a thought experiment. Assume every ward is 1000 voters. The incidence of 1 in the first left position would only occur when one of the candidates captures 81%-90% of the vote, leaving one of the candidates with 100-199 votes. It seems illogical to assume "fraud" if the majority of wards do not fall into this very specific pattern.

On the other hand, assume that every ward has 2000 voters. In this case, in order to land a first left position 1, you just need a candidate to score 50-99.95% of the vote--translating to 1000-1999 votes. In that scenario adherence to Benford's law is much more likely.

I don't trust any Benford's arguments that do not take ward size into account. The size of the wards clearly matters. The math doesn't lie on this.

Greg The Class Traitor said...

D.D. Driver said...
>>In Wisconsin, Milwaukee knew how many votes they had to deliver. I’m sure Madison was in on it too.

If you are going to keep spouting nonsense about Milwaukee, I will keep correcting it. Trump did well in Milwaukee.


You can keep on making up the same lies, and I'll keep shooting them down:

https://www.politico.com/2012-election/results/president/wisconsin/
Milwaukee
100.0% Reporting
B. Obama (i) Dem 66.8% 328,090
M. Romney GOP 32.3% 158,430

State:
B. Obama (i) Dem 52.8% 1,613,950
M. Romney GOP 46.1% 1,408,746

https://results.decisiondeskhq.com/2020/general/wisconsin
Milwaukee
>99% Reporting
J Biden Dem 69.4% 317,251
D Trump GOP 29.4% 134,355
State:
J Biden Dem 49.6% 1,630,579
D Trump GOP 48.9% 1,610,022

So, while underperforming Obama 3.2% in the State, Joe Biden OVERperforms Obama among the black voters of Milwaukee by 2.6%

In an election where Trump beat Romeny with black voters by, what, 2x on a percentage basis?
At least, beat them every place but the 4 cites of vote fraud?

So:
Obama's "margin" in Milwaukee 169,660
Biden's "margin" in Milwaukee 182,896

Obama had a legendary turnout machine, and a strong connection with black voters. Yet Biden beat him like a drum with black voters, in Milwaukee, Detroit, Philly, and Atlanta.

Pull another one, it plays Jingle Bells

Bilwick said...

Steve ("Kreskin") Uhr looks into his crystal ball and writes: "Trump won’t concede for one reason. He wants money from his supporters. . ."

I only became a Trump supporter when he became the alternative to the liberty-phobic Gang of State-fellators. If he did want money from me, he's out of luck: I'm in the arts, and like most of us in the arts, not rich. But unlike Steve and his fellow government humpers, I do value something priceless: liberty. So anything Trump does to stick it to The Hive gets at least my full spiritual support. (If my novel gets published and I can also sell the novie rights I will be happy to contribute, not to Trump, but to pro-freedom organizations like FEE, the NRA, etc.)

mccullough said...

The Polish professors explanation is coherent. He explains it well.

My only issue is that it would be certain wards or precincts in cities (or counties) where fraud would occur.

You could compare present data on those precincts with the past few elections.

But with so much mail in voting this year, that is an important factor making comparisons less helpful.


I’d also want to see the break down of mail in voting vs in-person voting in each precinct in a city or county.

Seems easier to commit voter fraud by mail in voting. Did these precincts have a greater percentage of mail-in voting than precincts in Milwaukee County and the suburban counties?

Tyrone Slothrop said...

I'm as receptive as anyone to evidence of election fraud, but I don't think Benford's Law is the best tool to use here. Applicability of the law increases as the range of orders of magnitude increases. If votes tabulated by precinct provide the numbers in your data set, it's unlikely Benford's Law will be accurate. Most precincts will return between 100 and 1000 votes, a span of only one order of magnitude

mandrewa said...

D. D. Driver said, "Here is a thought experiment. Assume every ward is 1000 voters. The incidence of 1 in the first left position would only occur when one of the candidates captures 81%-90% of the vote, leaving one of the candidates with 100-199 votes. It seems illogical to assume "fraud" if the majority of wards do not fall into this very specific pattern."

"On the other hand, assume that every ward has 2000 voters. In this case, in order to land a first left position 1, you just need a candidate to score 50-99.95% of the vote--translating to 1000-1999 votes. In that scenario adherence to Benford's law is much more likely."


The simulations constructed in the paper, "Benford's Law and the detection of election fraud
are so complicated that I'm not totally certain, but I think that is in essence more or less what there are doing.

That is you can construct elections where the size of the precincts will push the result towards a non-Benford distributions.

But in other cases, when the precinct sizes are not tuned to give such a non-Benford result, then you would expect a Benford distribution.

And one way to deal with that in general would be to plug in actual precinct sizes into your simulation and then run it, assuming no fraud, and see how often non-Benford results turn up.

The results of this then can be plugged into to the function that I'm imagining that would give us the odds for a given result being fraudulent (but note this is only with respect to Benford's Law, it says nothing about other kinds of fraud) or not.

Bruce Hayden said...

“Here is a thought experiment. Assume every ward is 1000 voters. The incidence of 1 in the first left position would only occur when one of the candidates captures 81%-90% of the vote, leaving one of the candidates with 100-199 votes. It seems illogical to assume "fraud" if the majority of wards do not fall into this very specific pattern.”

The big issue here with Benford’s law strongly suggesting fraud, is that it isn’t the high order digit that really matters, but the low order digits (and esp here with all of the zeros in the low order digit). You appear to be making the same distraction that one of the “experts” in the article made - there can be legitimate extenuating circumstances why the high order digits might look bad, but aren’t. BFD, as I pointed out above. Benford’s doesn’t predict the actual level of fraud, but rather whether or not it occurred, and in that situation, the low order digits are often far more telling, or useful. There are invariably far fewer justifications for legitimate correlations in low order digits than in high order digits.

NYC JournoList said...

Chess.com also uses algorithms (math+stats) to ferret out cheaters. Althouse is 20 years behind the theory and trapped in a legal mindset (words). The election stinks to high heaven. At this point half the country is going to think whoever the president is is illegitimate. The law and the courts are helpless to solve the crisis. I predict some out of the box compromise as in 1876. Both sides have to end up equally unhappy for the results to be accepted.

mandrewa said...

Tyrone Slothrup said, "Applicability of the law increases as the range of orders of magnitude increases. If votes tabulated by precinct provide the numbers in your data set, it's unlikely Benford's Law will be accurate. Most precincts will return between 100 and 1000 votes, a span of only one order of magnitude."

I haven't read the Polish professor's explanation that several people have referred to, but I think I get the point, or even if I've misconstrued the argument, my misunderstanding would still seem to be a valid argument.

If the precincts in a given county or state are so constructed that they are biased towards certain leading digits, then you can around that by combining precincts. As long you have enough precincts to play with, now you will have enough pseudo-precincts that are not biased by size, and then you can apply the Benford Law test to that.

Rabel said...

“Biden overall got about 70% of the votes in Milwaukee."

78.83% "officially"

Why should I trust an analysis that got this basic fact wrong?

City of Milwaukee Election Commission:

(WITH 327 OF 327 PRECINCTS COUNTED)
Joseph R. Biden / Kamala D. Harris (DEM) 194,661 78.83%
Donald J. Trump / Michael R. Pence (REP) 48,414 19.60%

Bruce Hayden said...

Part of the basis for Benford’s law is that humans think in decimal. Nature doesn’t. Activities like bomb damage and election results have statistical distributions that appear random in the lower level digits. Let’s try a thought experiment. Take a random number generator, and multiply by a 3 or more digit period (N) to yield a series of integers from 0 to N-1. Using modular arithmetic, divide by 10, and look at the remainders (a series of numbers from 0 to 9). The digits generated (the low order digits) will almost always appear randomly distributed with roughly the same number in each of the ten categories. Run it 100, 1,000, etc times, and the results aren’t going to change very much - close to 1/10th of the total samples in each category. But you say, the underlying distribution isn’t linear. Doesn’t matter. Run it through a function that provides a normal distribution based on the same random number generator, and the distribution of low order digits won’t change much, if at all (excluding computational anomalies in either the random number generator or the Normal function generator).

Which is why getting too high of frequencies of specific low order digits is problematic. As I noted above, we think in decimal, and a significantly skewed distribution of lower order digits suggests that the results were biased by human use of very arbitrary Base 10 arithmetic. Which suggests human intervention.

One of the things that you should have learned in K-12 mathematics is modular arithmetic. Those of us who have spent extensive time in programming typically get adept at calculating in Base 2 (8, 16), because computers have almost always utilized Base 2 arithmetic since almost the first. That is because you can build circuitry (such as adders, multipliers, dividers etc) using binary devices such as transistors. I’ve done it, and no doubt others here have too. Humans mostly picked Base 10 for their arithmetic because we have ten fingers and ten toes. There is nothing magic about Base 10 arithmetic, except that is what we, collectively, settled on.

Gator McCluskey said...

"and the postman in Pennsylvania recanted his claim and signed an affidavit saying so—-this was the one piece the right wing crow about has now that laid an egg."

https://twitchy.com/gregp-3534/2020/11/11/i-did-not-recant-alleged-usps-whistleblower-richard-hopkins-demands-a-correction-from-the-washington-post/

try again, asshole.

D.D. Driver said...

"So, while underperforming Obama 3.2% in the State, Joe Biden OVERperforms Obama among the black voters of Milwaukee by 2.6%."

Where are you getting the local numbers about "black voters"? Just curious, I have not seen any Milwaukee-specific exit polls (and your race is not recorded on your ballot.) The data I have seen show that predominately African American wards did not show up to the polls this year in Milwaukee.

https://www.politico.com/2012-election/results/president/wisconsin/
Milwaukee
100.0% Reporting
B. Obama (i) Dem 66.8% 328,090
M. Romney GOP 32.3% 158,430

State:
B. Obama (i) Dem 52.8% 1,613,950
M. Romney GOP 46.1% 1,408,746

https://results.decisiondeskhq.com/2020/general/wisconsin
Milwaukee
>99% Reporting
J Biden Dem 69.4% 317,251
D Trump GOP 29.4% 134,355
State:
J Biden Dem 49.6% 1,630,579
D Trump GOP 48.9% 1,610,022


Doesn't this show that Biden got 11,000 fewer votes than Obama in 2012? It's just that Trump under-performed Romney by ~24,000. In other words, Biden did worse than Obama, but Trump did way worse than Romney. Why is that so hard to believe--Trump is a very decisive figure?

Don't see how that suggests fraud. Your argument would be stronger if Biden actually outperformed Obama.

Birkel said...

The problem is that Milwaukee, Detroit, Philly, and Atlanta have different distributions than other pro-Biden cities.
The problem the professor has is stopping with Milwaukee and not comparing Milwaukee results to similarly situated cities.

And that is where you find Milwaukee's numbers are different.

Purpleslog said...

I’m a big fan of Golbeck’s golden retriever stuff on the Internet. That being said, she is hardcore anti-Trump and really can’t be trusted to be impartial or non-partisan on anything related to Trump,

Rabel said...

You guys are mixing up the City of Milwaukee with the County of Milwaukee.

OldManRick said...

Again, it's not just that Biden's votes profile violates Benford's Law, it the fact that every other candidate's totals follow it while his do not. Down ballot candidates follow Benford's law. This happens in Milwaukee, Detroit, Chicago, and Philadelphia - four very democratically controlled cities. Violations of Benford's Law haven't been reported favoring Trump anywhere.

Every ward size explanation I've seen says his profile might be good but doesn't address why the same factors that make his ok do not effect the other candidates. Whatever your explanation is for Biden's profile being legitimate, that same explanation has to show why the others don't reflect your magic. This is not a single event analysis; it is an analysis of an event with multiple parallel events not getting the same results.

In the end many will believe what they want to believe and are unpersuadable. Give me a comprehensive rationale that addresses Biden's profile vs other profiles, that addresses the differences in turnout in these locations from historical turnouts, that addresses overperformance of Obama in these areas among blacks while Trump got a larger share of black votes then before, and that addresses the massive increase in "no-down-ballot" votes in swing states only and I then can be persuaded. A hypothetical about ward sizes with no data, distribution, and no analysis of why all other candidates follow Benford's rule doesn't cut it.

stevew said...

The "Fair Minded Person" is a mythical creature. Our country's founders knew this to be true, which is why they designed the country and its laws the way they did. It is an adversarial system with layers of checks and balances, both process and institutional.

You can't trust anyone to be objective. You can trust the system to find and expose the truth.

Jaq said...

"If the returns for Biden violate the law and none of the returns for other candidates up and down the ballot don't, then the distribution of wards argument fails.”

Maybe, what he said was this:

“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.

I got this little factoid at Roy Spencer’s blog

"The average total vote is 660, for Biden 595 and for Trump 148. So Biden will get a lot of first digits 4-7, Trump will get a lot of 1’s.”

http://www.drroyspencer.com/2020/11/benfords-law-evidence-of-fraud-in-reporting-of-voter-precinct-totals/

What’s kind of weird is that you would think that Trump would have gotten more 9s than 3s

Anyway, the data is available for download from the Spencer blog link, if you want to look at it yourself. I think I might take a look. Unfortunately, my favorite tool TAWK is no longer available, and I will have to settle fot the Unix tools that come free with my macbook.

I think this is a dead end, but what the heck.

JackOfClubs said...

People that want to understand the issue should watch this video on YouTube. This talks about Chicago, not Milwaukee but the principle is the same. Basically Biden's numbers are normally distributed because he won about 70% of the vote in precincts with populations that were mostly three-digit numbers. So Benford's law doesn't apply because it relies on changes in order of magnitude and all of Biden's votes were order 3. Trump's votes, on the other hand, were mostly order 2 with a few order 3s sprinkled in, so Benford's law succeeds.

If anyone has access to the numbers, I predict you will find comparable but reversed distributions in counties where Trump did extremely well (i.e. had more than a 2-1 advantage). In those precincts, Trump would be getting all 3-digit numbers (and thus a normal distribution) and Biden would be getting 2 & 3 digits and wold be Benfordized.

BrentonTalcott said...


The SINGLE attempt to address a concern, by claiming Hopkins recanted, is not only an outright lie, it serves to cover up the recording of 4 hours of intimidation by...

GOVERNMENT JACKBOOT MINDTHUGS

QFT and edited slightly.

2020 is Delivering Big Time!

https://www.youtube.com/watch?v=PBAl9cchQac

Semper Fi

M Jordan said...

Reuters, fair? Seriously?

I continue to be astonished by people like Althouse and Scott Adams as they reveal their complete blindness to the bias against Trump and anyone who supports him. Actually bias is way too small a word. But here’s a tip: Every single syllable the media including Fox utters has as its true North Star this intent: Get Trump!

D.D. Driver said...

JackOfClubs-Thanks. That video is really well done.

bagoh20 said...

"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!'

First, they are not eager to cast doubt. They are eager to find the truth when there is unprecedented levels of suspicious, illegal activity in the election process.

Second, who has the more responsible position, the ones interested in finding answers and getting it right, or the ones who want to "stop right now", before we do that.

It's the same dichotomy that forces the questions of why would only Republican observers be kept out, and why was counting stopped when Trump was leading and gaining, and then suddenly restarted with the emergence of thousands of suspect Biden votes.

It's not just two differences of opinion. One side wants answers, and the other wants obfuscation. Why would a fair honest person want to avoid finding the answers to these questions?

mandrewa said...

JackOfClubs that was a pretty good video that you linked to. The author does a good job of explaining the non-Benford distribution for the Biden vote in Chicago.

But I do wonder, why not go to the next step? Combine precincts so we can actually test the Benford distribution. Because what just happened in that video wasn't actually a test. The result was inevitable because of the narrow range of vote sizes in the different precincts for Biden in Chicago and the apparently very uniform percentage of the population that voted across Chicago precincts.

But it doesn't mean everything is okay with respect to Benford's Law.

By randomly combining precincts, or alternatively doing all possible permutations of combinations of precincts, we can explore once we've repackaged the data in a form where it should show Benford's Law, whether it actually does.

mandrewa said...

Also where are the intermediate vote counts kept? Are they kept? On election night, intermediate counts are being reported throughout the evening. All of those numbers give us a much larger sample size. And the more numbers we have, the higher the odds, if there is a discrepancy, that this will mean there is a problem, or alternatively, there is a good explanation for the discrepancy.

OldManRick said...
This comment has been removed by the author.
OldManRick said...

I'll try again but this is getting pointless.

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 Trump should have had 30% of those wards or 240 votes and a matching bulge and normal distribution around the 2 digit. Biden's should show a normal distribution around five not a massive tail at one. If this ward model is right then you should be able to show me precincts, say in Texas, where Trump got 70% of the vote and had an unnatural bulge.

Again, if you want to convince me let's see the historical distributions. I would agree that if they follow the current you may be right but that doesn't explain the bulge at 1, if they don't match I have a point. Both the turnout numbers and Outperformance vs Obama comparisons to historical data already show statistical aberrations. I expect the historical models will too.

Spiros said...

"Biden received 78.8 percent of [Milwaukee] votes, and the president received 19.6 percent." It's not 70%:

https://www.tmj4.com/news/election-2020/no-joe-biden-did-not-get-100-percent-of-all-milwaukee-absentee-ballots

SAGOLDIE said...

My understanding was always that Benford's Law was useful in identifying suspicious values originating from a person. For the IRS, "How much did you pay for that computer for which you have no receipt?"

Can't see how this applies to an election when the machine prints out the results. Could a person provide made up numbers where there's not automated collection? Sure but they can be verified/audited so easily . . . .

The real risk is at the "front end" - who cast the vote: legally registered voters, dead people, or an election worker "stuffing" ballots.

Anyway, that's what I think.

DINKY DAU 45 said...

trump is hanging on under the auspice of voter fraud but we all know its just so he can solicit his minions to send in money for the fight9little do they know the fine print says it can be used to pay off his debt) Send it in R's he'll drain you right untill the end 60 solicits a day,emails to send $$$ worse than televangelists selling pieces of Jesus' real cross..Can you say gullible and clueless?