Statistics: Evidence of Malfeasance in Reporting of Election Totals?

From Dr. Roy Spencer’s Blog

November 9th, 2020 by Roy W. Spencer, Ph. D.

You might have seen reports in the last several days regarding evidence of fraud in ballot totals reported in the presidential election. There is a statistical relationship known as “Benford’s Law” which states that for many real-world distributions of numbers, the frequency distribution of the first digit of those numbers follows a regular pattern. It has been used by the IRS and financial institutions to detect fraud.

It should be emphasized that such statistical analysis cannot prove fraud. But given careful analysis including the probability of getting results substantially different from what is theoretically-expected, I think it is a useful tool. Its utility is especially increased if there is little or no evidence of fraud for one candidate, but strong evidence of fraud from another candidate, across multiple cities or multiple states.

From Wikipedia:

“Benford’s law, also called the Newcomb-Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford’s law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.”

For example, here’s one widely circulating plot (from Github) of results from Milwaukee’s precincts, showing the Benford-type plots for Trump versus Biden vote totals.

Fig. 1. Benford-type analysis of Milwaukee precinct voting data, showing a large departure of the voting data (blue bars) from the expected relationship (red line) for Biden votes, but agreement for the Trump votes. This is for 475 voting precincts. (This is not my analysis, and I do not have access to the underlying data to check it).

The departure from statistical expectations in the Biden vote counts is what is expected when some semi-arbitrary numbers, presumably small enough to not be easily noticed, are added to some of the precinct totals. (I verified this with simulations using 100,000 random but log-normally distributed numbers, where I then added 1,2,3, etc. votes to individual precinct totals). The frequency of low digit values are reduced, while the frequency of the higher digit values are raised.

Since I like the analysis of large amounts of data, I thought I would look into this issue with some voting data. Unfortunately, I cannot find any precinct-level data for the general election. So, I instead looked at some 2020 presidential primary data, since those are posted at state government websites. So far I have only looked at the data from Philadelphia, which has a LOT (6,812) of precincts (actually, “wards” and “divisions” within those wards). I did not follow the primary election results from Philadelphia, and I have no preconceived notions of what the results might look like; these were just the first data I found on the web.

Results for the Presidential Primary in Philadelphia

I analyzed the results for 4 candidates with the most primary votes in Philadelphia: Biden, Sanders, Trump, and Gabbard (data available here).

Benford’s Law only applies well to data that that covers at least 2-3 orders of magnitude (say, from 0 to in the hundreds or thousands). In the case of a candidate who received very few votes, an adjustment to Benford’s relationship is needed.

The most logical way to do this (for me) was to generate a synthetic set of 100,000 random, but log-normally distributed numbers ranging from zero and up, but adjusted until the mean and standard deviation of the data matched the voting data for each candidate separately. (The importance of using a log-normal distribution was suggested to me by a statistician, Mathew Crawford, who works in this area). Then, you can do the Benford analysis (frequency of the 1st digits of those numbers) to see what is theoretically-expected, and then compare to the actual voting data.

Donald Trump Results

First, let’s look at the analysis for Donald Trump during the 2020 presidential primary in Philadelphia (Fig. 2). Note that the Trump votes agree very well with the theoretically-expected frequencies (purple line). The classical Benford Law values (green line) are quite different because the range of votes for Trump only went up to 124 votes, with an average of only 3.1 votes for Trump per precinct.

So, in the case of Donald Trump primary votes in Philadelphia, the results are extremely close to what is expected for log-normally distributed vote totals.

Fig. 2. Benford-type analysis of the number of Trump votes across 6,812 Philadelphia precincts. The classical Benford Law expected distribution of the 1st digits in the vote total is in green. The adjusted Benford Law results based upon 100,000 random but log-normally distributed vote values having the same mean and standard deviation as the vote data in in purple. The actual results from the vote data are in black.

Tulsi Gabbard Results

Next, let’s look at what happens when even fewer votes are cast for a candidate, in this case Tulsi Gabbard (Fig. 3). In this case the number of votes was so small that I could not even get the synthetic log-normal distribution to match the observed precinct mean (0.65 votes) and standard deviation (1.29 votes). So, I do not have high confidence that the purple line is a good expectation of the Gabbard results. (This, of course, will not be a problem with major candidates).

Fig. 3. As in Fig. 2, but for Tulsi Gabbard.

Joe Biden Results

The results for Joe Biden in the Philadelphia primary vote show some evidence for a departure of the reported votes (black line) from theory (purple line) in the direction of inflated votes, but I would need to launch into an analysis of the confidence limits; it could be the observed departure is within what is expected given random variations in this number of data (N=6,812).

Fig. 4. As in Fig. 2, but for Joe Biden.

Bernie Sanders Results

The most interesting results are for Bernie Sanders (Fig. 5.), where we see the largest departure of the voting data (black line) from theoretical expectations (purple line). But instead of reduced frequency of low digits, and increased frequency of higher digits, we see just the opposite.

Is this evidence of fraud in the form of votes subtracted from Sanders’ totals? I don’t know… I’m just presenting the results.

Fig. 5. As in Fig 2, but for Bernie Sanders.


It appears that a Benford’s Law- type of analysis would be useful for finding evidence of fraudulently inflated (or maybe reduced?) voter totals. Careful confidence level calculations would need to be performed, however, so one could say whether the departures from what is theoretically expected are larger than, say, 95% or 99% of what would be expected from just random variations in the reported totals.

I must emphasize that my conclusions are based upon analysis of these data over only a single weekend. There are people who do this stuff for a living. I’d be glad to be corrected on any points I have made. Part of my reason for this post is to introduce people to what is involved in these calculations, after understanding it myself, since it is now part of the public debate over the 2020 presidential election results.

[CR note here is the actual title of Dr Spencer’s article. I modified it to reduce social media censorship.]

Benford’s Law: Evidence of Fraud in Reporting of Voter Precinct Totals?

199 thoughts on “Statistics: Evidence of Malfeasance in Reporting of Election Totals?

      • Meaning that it’s ordinary for Democrats to cheat with elections, with indications of dead people voting, etc., since at least Kennedy’s time. They think they are the only ones with the right answer and anyone else who stands in their way is evil. You are not allowed to have your own opinion.

        • If it is true that 10,000 dead people voted in the election for one candidate, would it be detected using this method?

          Is it detectable in Chicago voting records for Kennedy in 1960? We know that there was a lot of cheating in that election, the dead being major players in the total.

          You could use that data set as a trial (cheating was known) as a baseline for the current election.

          • I have to confess, I don’t understand the underlying principle of Benford’s Law, but I would think that if we add a random number ( dead people who voted) to another random number ( people who voted for the Living Dead aka Joe Biden) we would get a random number. A random number should show no peculiar distribution of digits. A guess from someone who’s statistically challenged.

      • What he means to say is that evidence of malfeasance by the Democrats in an election is nothing out of the ordinary — there, fixed it.

        • What’s with the fancy pants word “malfeasance” in the article title? Roy Spencer used the word “fraud” in his title, and he has a Ph.D. I had to look up malfeasance in a law dictionary, where I learned there is also nonfeasance and misfeasance. I don’t know what any of them mean, but will use them at random in conversations, so people think I’m smarter than I look.

          • Richard Greene, did you read the very last sentence of the article? “CR note here is the actual title of Dr Spencer’s article. I modified it to reduce social media censorship.”

            The word “fraud” is a “trigger” word for social media’s automatic censors. Since this article may appear on social media– and it probably already has– the rewording of the title helps dodge the censoring. Yes, the censoring is THAT bad.

          • Richard Greene:
            …What’s with the fancy pants word “malfeasance” in the article title? Roy Spencer used the word “fraud…

            Malfeasance is fraud when you can’t prove it, and fraud is when you can prove it.
            According to that most enduring source of political wit and wisdom “Yes Prime Minister” circa MCMLXXXV

    • Dr. Roy Spencer agrees. He revisited Benford’s Law in an update on his webpage November 12. He concluded that it was not a useful tool for determining whether there is voter fraud in elections.

    • The video claims that the voting machine tabulating software stores votes as a floating point value instead of integer. Skimming decimal fractions can result in extra votes being moved around. In the past, this approach has worked successfully in removing money from bank accounts…

      • The f.p. variable is suspicious when counting an inherently integer quantity but we are dealing with somthing much more serious than rounding errors. This is
        wholesale,systemic election fraud. Jill Stein tried to legally challenge the use of voting machines and lack of audit trail in 2016. The court refused to look at it. Trump nowneeds to so the same.

    • This video examines election result from four countries in Michigan, where there’s a two-tier system of voting: you can either vote straight party ticket or you can vote (“independently”) for individual candidates regardless of party.

      Ayyadurai asserts that all election voting machines are now able to have an (illegal) “weighted race” feature (first seen in Diebold machines) and what this features does is take votes from one candidate and give them to another according to an adjustable algorithm.

      In four counties in Michigan, through an analysis of party predominance (“straight party” voting) versus individual candidate voting, it was found that the more thoroughly a particular district’s party voting was Republican, then the more “independent” votes went to Biden. You’d expect some variation, but the telling feature is that in district after district the pattern is the same, and it’s highly improbable. A pattern where Republicans in various districts were disgusted with Trump and hence voted for Biden would look completely different, as that pattern of district voting would be randomized along an essentially non-sloping line. The pattern found was that, when aggregating all the district votes in a country, after a cut-off of about 20% (i.e., straight party Republican voting of 20%) then the number of independent votes for Biden increased in a non-linear fashion.

      • The problem the voting machines had in this election was that the overwhelming votes for Trump could not be swayed by Dominion algorithms sufficiently to give Biden the win. In other words, the Trump landslide broke their system and exposed their fraud for the world to see, which necessitated a shutdown. These additional steps, taken to ensure a Biden victory, made the fraud even more obvious. I understand it was the infusion of massive numbers of fraudulent votes added in the middle of the night for Biden that Benford graphs expose. But hey, Biden told us it would happen just before election day–he’s an honest crook.

  1. Very interesting, thanks.

    I would love to see such an analysis performed on the presidential elections since 2000. I have a gut feeling that voter fraud is increasing in both totals and percentage at least in some states.

    • It might make for an interesting academic exercise to perform such an analysis on all presidential elections going back to 1960.

      • PaulH, now you’re talking!!! I would love to see this data. To me, an independent who leans right more often than not, this would be an amazing study for the American people. If this analysis doesn’t piss off people on both sides, I’d say that we’re truly screwed.

  2. It is easy to cheat with optical readers of ballots, only thing you need to do is when sorting ballot papers in bundles, just put blank side wrong way up ones with the Trump tick. They will go through, will not get counted, and if there is a tray for rejects they can be destroyed long before recount is due. In case they are not separated as rejects only a manual check of millions of ballots may get correct result.

    • That depends on the design of the ballots and the scanners. If the scanners scan both sides of the paper like they do here in KC, KS, and the ballot has bar codes on one side to tell the scanner which side is front/back, and which end is top/bottom, it’s literally impossible to put it in wrong.

      • While that maybe true and while OCR and bar code readers/scanner are pretty good these days, OCR still has it’s problems.

  3. Even more interesting are “Switched” votes from Trump to Biden, and “Lost” votes.

    Switched votes are votes that were taken from Trump and given to Biden.
    Lost votes are voted that disappeared during the counting, from both candidates.
    There might be a small overlap between Switched votes and Lost votes.
    Dominion Voting Systems :

    Pennsylvania : Switched : 220,883 Lost Votes : 941,248
    New Jersey : Switched : 80,242 Lost Votes : 20
    Florida : Switched : 21,422 Lost Votes : 456
    Michigan : Switched : 20,213 Lost Votes : 21,882
    New York : Switched : 18,124 Lost Votes : 623,213
    Georgia : Switched : 17,407 Lost Votes : 33,574
    Ohio : Switched : 14,965 Lost Votes : 5,102
    Virginia : Switched : 12,163 Lost Votes : 789,023
    California : Switched : 7,701 Lost Votes : 10,989
    Arizona : Switched : 4,492 Lost Votes : 0 etc.
    Will others verify this?

    • Pennsylvania : Switched : 220,883 Lost Votes : 941,248

      Not credible, if I understand what they mean by ‘lost votes’. Total of 6,785,078 votes counted so far – an estimated 97.1%. How could any state possibly “lose” a seventh of the votes?

      Biden leading Trump in PA by 48,951 votes. I don’t know where that source is getting the figure for “switched” votes, but the claimed quantity seems dubious.

      • The data source(s) are in the article as well as a cursory description of the analysis methods. It would be interesting to see if the claims could be verified, or debunked or some other conclusion from the data could be reached.

      • Alan, the only way that one can truly verify how many votes were “switched” from Trump to Biden is to hand count the actual paper ballots and compare them to the original machine count made by the Dominion system. That was what was done in the case of Antrim County, Michigan, in which over 6,000 votes had been switched from Trump to Biden (Trump won that county).

        My brother (a computer systems tech for many years) has told me it has been alleged that for some reason, Dominion made a change to its counting software in several states right before the election, Wisconsin being one of them (my brother also lives in Wisconsin and has been following this election carefully). According to him, the change involved would only require amending three lines of code at the source code level. He thinks that circumstance, if proven, is enough to justify a hand count in all of the battleground states where Dominion software has been used. The hand count, in my view, would really only have to be done in those counties that are using this Dominion software. A forensic analysis can also be done to track both the changes (they have to be reported, apparently, for the sake of system maintenance and function) in software and whether the alleged three lines of code necessary to kick Trump votes over to Biden was actually used. If this is proven, Biden is in big trouble. Because that does not necessarily require a showing of “fraud.” It is a fairly objective measure of the accuracy of the count, no matter the intent of the particular election officials (except of course, I think many of them did know what was going on, especially in Pennsylvania).

        • Completely disagree regarding hand count. If you want an accurate and unbiased count of anything in the quantity of things like a state-wide vote, you keep people out of it and use machines. Anyone who’s ever closed out a cash register can attest that if you count the cash at closing three times you will get three different results. And while the true total must be exact, you can’t reliably get an exact result with hand counting.

          I was an independent election observer in Chicago for the 1972 election. All the regular races were recorded using the old mechanical lever voting machines. Counting those votes was fast, simple and uncontroversial: cut the lead seals on the back panel and read the totals recorded on each counter. However the judicial races were recorded on a paper ballot. I don’t recall how many races were on that ballot but it was a dozen or more and we had several hundred ballots to count. Polls closed at 7; the machine tally was done and signed off 15 minutes later. It was after midnight before we finally recorded and signed off on the judicial races. Just like a cash register closing we got a different result each time, but we got to a point where everyone just agreed the differences were so minor they would make no difference.

          This election Georgia used a brand new electronic+scanned paper ballot system and it was reported this morning the (Republican) Secretary of State has just ordered a complete hand recount statewide. If true (and one must always state that qualification for anything reported in the news these days), I think it’s insane; it will only generate a lot more acrimony for even less certainty.

          I made the same criticism of the 2000 Florida election, when a hand recount was ordered for three large majority Democrat counties: when people have a passionate bias, they will see the result they desire unless the “wrong” result is undeniable.

          At least in Georgia, if you’re looking for fraud, concentrate on the mail-in ballots. In most elections there aren’t enough of them to affect any races and they’re never counted. In the rare election where they do have to be counted, there are still few enough that manual counting is reliable. As a result Georgia has not had to develop procedures for accurately validating and counting a large number of mail-in ballots. At least this year they had some time to prepare; I hope they used it to put some procedures and training in place.

          The actual ballot is a mark-sense reader, which must be recorded with a blue or black pen. Assuming no physical damage from the mail delivery, the actual counting should be reliable. I don’t know whether the ballot verification procedures will scale up to the numbers involved.

          For in-person voting in Georgia you must show a government-issued photo ID. This year there were automated readers which scanned the PDF-417 barcode on the back to verify name and address. If you don’t have an acceptable ID you are allowed to complete a provisional ballot, but must return to the polling place with a valid ID no more than 3 days after voting; unvalidated provisional ballots are excluded. In the last election the Stacy Abrams campaign encouraged supporters to request provisional ballots and then claimed vote was being suppressed when these unconfirmed ballots were excluded. She’s ridden than horse for the last 4 years, but the truth is election law was properly followed and her own campaign deliberately created a pretext to claim otherwise.

          For mail-in ballots you must include your GA ID number, but without the barcode scanner someone has to enter the number manually to verify you’re registered, you live at the address on the ballot, and you haven’t also voted in person. All this takes time and is subject to error. In states without a voter ID requirement (far, far too many of them), I don’t know how you can possibly validate mail-in ballots, especially if the registration lists are not regularly maintain to remove voters no longer residing at the registered address. Every stale registration can be used to submit a fraudulent mail-in ballot. In Georgia, each county (there are 159 of them) maintains its own registration list and resists any attempt to consolidate them into a single statewide list.

          It is easy and cheap to get a voting system that will give you 100% confidence in the results for a race with a margin of a million votes. There is no system you can buy at any price that will give you 100% confidence if the margin is 1 vote. Anytime people are involved there are errors – some honest and understandable, some careless or negligent. And if a system permits ways to cheat, you can assume people will attempt to exploit them.

          With computerized voting systems you can’t discount the potential for large-scale tampering. Vendors who claim their systems are tamper-proof probably have never dealt with the kind of expertise and resources a major government intelligence agency can command. The Iranians no doubt thought their uranium enrichment facilities were secure. By the same token, it takes much more than ordinary technical competence to credibly claim such vulnerabilities exist and even more so to assert they have been. “My cousin has a friend who works at Google and he says …” by itself isn’t credible.

          Republicans should not follow the Democrat example from the 2016 election of simply repeating unsubstantiated claims of widespread meddling. Democrats have spent four years refusing to accept that real people who might even look like their neighbors could actually vote for Trump and they have completely beclowned themselves inventing excuses to explain why the vote totals had to be wrong.

          • Wow…really sorry you have such a hard time counting money.
            I was a teller and worked retail. In the 1000s of times I counted out a drawer (always twice to make sure), I rarely had to count a third time.

            Hand counts of ballots do present some challenges, but still can be done accurately. At this point, in Georgia, it appears a hand count is the best option – as the confidence level in the electronic count is gone.

            I also don’t believe we cannot develop a system that will provide 100% accuracy all the way to a one vote margin. A script to count is very easy to write and would be correct every single time. It’s only complicated if you make it so…and why would anyone want to make it complicated? (I already know the answer)

    • After hearing of the Dominion Voting System used in 38 (?) states, I’ve wondered if anyone has examined the computer code used to count the ballots.
      Might there be a “fudge factor” or an honest flaw that would, say, count every 500th vote for Trump or a Republican as a vote for Biden or a Democrat?

        • So first President Obama states well before the 2016 elections that there’s no way they could be gimmicked. Then notwithstanding that assurance a solid evidence free (not to mention preposterous on the face of it) collusion of this poster boy for capitalism with the unrepentant former head of the Soviet KGB was ceaselessly proclaimed (with the Russian sourced so-called incriminating dossier actually funded by her campaign and the DNC). And she asks him during a debate to pledge he would accept the election results without complaint for the good of the country (he neglects to ask if she would do likewise). When he had won office, pressure was then applied to members of the Electoral College to favor her despite the vote totals they should reflect.

          And now in 2020 there are indications that it’s not the Russians suspected of corrupting the vote outcome, but the Canadians! I’d say this was all pretty ‘rich’, except that DNC information tech Seth Rich who had an appointment with the FBI to reveal what he knew was executed on the street without being robbed of money or watch that very morning. And that’s not funny.

    • Yes I saw similar. Virginia’s total Trump votes was 813,000 on chart I viewed. With most votes lost. …. If not mentioned the ballots issued by DHS. Ballots have special IR Corn Ink ID marking. The NG using Night Vision to count ballots in twelve States. Ballots tracked. This Dominion voter glitches are part of the program. This voter flipping will most likely be traced back to Demoncrats surprise 2018 take over of The House. Biden said he had the BIGGEST voter FRAUD organization behind him ever established in America. I think we know who and what he means. Biden declared he did not need your vote to be President. CNN , actually FLIPPER VOTES to Biden ON AIR. 19,000 votes over to Biden. Pelosi involved with Domain vote stealing company. Trump set these Deep State clowns up. Oh, then a statement by DHS mentioning the DHS ran a STING for 2020 elections. Trump is cleaning the House from voter fraud. Trump will win over in landslide . Most likely regain House due to voter switching. Voter ID coming . I think we be in THE STORM.

    • The crux of it is that Benford’s Law does not apply when precincts have roughly the same number of voters, with typically 300-600 votes for Biden, which explains the Biden plot. But, the Trump plot with a spike at one is a bit suspicious, is it likely that he often got only between 10 and 19 votes?

      • Split tickets are not unknown. (For instance, my parents always voted Republican up-ticket – but for County Assessor they voted for the next door neighbor, and State Representative the neighbor across the street. Dad’s stated reason was that he wouldn’t have to go so far if and when he needed to punch somebody’s lights out.)

        What is unusual and an indication of fraud is the percentage of split tickets. Trump up-ticket and Democrat down-ticket numbers are consistent with historical data. Biden up-ticket and Republican down-ticket are way out of the expected lines. (Not to mention the many thousands of ballots brought in in the wee hours of the morning that had ONLY a Presidential vote – all for Joe Biden.)

        Other patterns of fraudulent activity – such as the massive uptick of Biden votes when Trump was ahead in swing States. (One person tried to debunk the analysis showing that by claiming “bad data.” Which could very well be true, it came from the New York Times. But my experience with bad data is that when you sample it, you’ll get bad results – but they will be consistent. The “debunker” didn’t even try to come up with an explanation of why every State but the swing States that Biden had to get had the same pattern, and every one of the swing States had the same pattern different from the non-swing States.)

    • Very interesting video, thanks. The key takeaway is that Benford’s law and similar analyses only apply when your original data meets certain criteria.

      • The criteria is that the analyzed data cover several orders of magnitude, like peoples’s deductible income tax expenses. A Tru/Bid choice by a somewhat controlled number of voters doesn’t come close to meeting the Benford law applicability criterion. So, in this case, it is a miracle the green and black lines are as close together as they are.

        • Over many orders of magnitudes, the frequency of digits in the first digit is
          1. 2. 3. 4. 5. 6. 7. 8. 9.
          30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6%

          The human mind has associated one number with one sheep for a long time, and doesn’t readily recognize that in 20 numbered sheep, 50% of them start with the number 1. In 100 sheep, 10%, in 200 sheep 50%, etc., average 30%….like the above table shows….

  4. William M. Briggs has a couple of blog updates containing a critique of Benford’s Law:

    “Two Statistical Curiosities That Allowed Biden To Pull Ahead In PA: Please Share. Update With Benford’s Law Criticism”

    “Benford’s law is only useful in uncovering multiple and on-going instances of cheating.”


    “More Anomalies In Late Vote Additions In Pennsylvania”

    “Much is being made of Benford’s Law. I critiqued it yesterday. One thing that must be remembered is that expecting small to moderate datasets to fit a Benford curve exactly is wrong. The smaller the sample, the larger the variance, and the more it is likely the data will diverge from the Benford curve, even with no cheating.”

    Some of the analytical concepts are above my pay-grade, but interesting reading nonetheless.

    • Then there’s the It’s Clear It Was Fair Because My Guy Won law. That always correlates with the Russia Stole the Election law.

        • At least the Plain Old Bad Sport Law isn’t the collary of the We’re Liberals, We Lost and Now Everything Burns Law.


          • Indeed, indeed, ablaze from coast to coast, well smoking, well no actual smoke, just a bit hot under the collar. How wicked of them.

            I am not American and from afar see oligarchs with the real power not politicians, that goes for most countries these days, including mine. The good and “evil” you ascribe and these black and white differences you imagine are, from afar, really just fractions of a %.

          • The good and “evil” you ascribe and these black and white differences you imagine are, from afar, really just fractions of a %.

            Well what a relief to know the ilks of Liberalism are “really just fractions of a %.” Imagine what the Beautiful People could do if their brand of peaceful rioting in progressive love REALLY took off in popularity.

            I mean, the damage could reach the trillions.


        • Loydo

          We don’t know who lost because the Secretaries of State have not reported their official results. You can invoke the My Guy Lost Law once someone has been declared a winner.

          Your comment complies with the “I Wish My Guy Would Win Law.”

  5. Too little too late and none of this would be considered evidence before a judge.

    The mail-in ballet fraud was expected to happen
    – NYT article in 2012 stated as much
    – 2005 Commission on Federal Election Reform, co-chaired by former U.S. President Jimmy Carter and former Secretary of State James A. Baker II also stated as much

    Yet – nothing was done PRIOR to the election to negate this aspect of illegal voting

    Showing that very highly suspicious anomalies in vote tallies is curious but means little – now

    • rickk: “Too little too late … ”

      Yes, not until Republicans fight back by also developing their own set of successful voting trickks, will the Democrats come to the table to implement bipartisan rules and regulations for honest elections in the U.S.

    • Mail-in ballet

      Interesting! I would have thought it would be very difficult to fit a ballerina into a mailbox. Must be a tiny dancer.

    • “Yet – nothing was done PRIOR to the election to negate this aspect of illegal voting”

      There were efforts initiated by the Republicans to clean up the voters rolls. Naturally the Democrats resisted in states they were able to, as they cannot win without the illegal voting.

      Note also that the US President was very well aware that illegal voting would occur, and there are rumours CISA NCSWIC made preparations. The President would hardly signal the countermeasures ahead of time would he, certainly not while election counters could still make changes. If this is true then CISA monitored the elections (eg. electronic interactions with the Dominion Voting machines) and let the Democrats entrap themselves. Trump was winning by a landslide in important states, so the count was paused there while the illegal alterations to the vote went on. The Trump landslide was sufficiently large that the Democrats could not do small cheats (a few tens of thousands of dead people), or even medium cheats (#maidengate), but had to do large unsubtle changes (vote switching in voting machines produced by a company that has ties/shareholding with the Clinton Global Initiative, Speaker Pelosi and Senator Feinstein).

      Meanwhile the media try to brainwash the public that Joe Biden is ‘President Elect’ (not possible until the Electoral College votes). Most of you here understand the media has a counter-factual but successful narrative on Anthropogenic Global Warming, but not everyone here understands the same media playbook is being used in regard to the 2020 US Presidential election.

      Trump will get a second term once the illegal voting is removed – exactly as he says. One can be in denial of this, but that will leave you unprepared for what is coming.
      Expect big news next week in regard to this.

      • Moa,
        I concur.
        It should be apparent to most readers of WUWT that the mainstream media is here to tell us what to think, a la Ministry of Truth, and not to tell us the truth.

        There will likely be violence as the left will deny that anything devious took place and will fight against what they perceive as an emerging dictatorship, when the truth is that it would be the Biden administration that allows for the emergence of a more totalitarian (“keep us safe”) government.

        Trump is now maneuvering the military and intelligence agencies in order to place loyalists and root out deep state actors/traitors. This will be amplified by the media as an emerging plot by Trump to take over the country, as former CIA Director (and traitor) Brennan has suggested.

        We need only to look at the WEF’s “Great Reset” and the UN’s “New World Order” to understand what’s waiting in the wings should Biden/Harris get in and measures to “keep us safe” are increased, measures which coincidentally also destroy our economic power and thrust us closer to the embrace of a supposedly benevolent world order which, in addition to a plethora of wolf-in-sheep’s-clothing measures, will also save us from catastrophic warming. What’s not to like?

  6. OFF-TOPIC but needs to be put out there:

    Truck drivers are being asked to join into a nation-wide protest of Biden/Harris stealing the election, by coming to halt. Four days, 26 November – 29 November, unless things change.

    Support the idea, and join in. Look at Jo’s, the post about Trump rallies being planned.

    Spread the word!!


    • Why the hell would I support being without things that are delivered by trucks?
      I believe there are some very fishy issues in the election that need to be looked into, but truck deliverery are too importain to support this protest.

      • Truck drivers’ protests are too important to not support. THAT is the point. Middle America is being overwhelmed by ‘others’.

      • re: “Why the hell would I support being without things that are delivered by trucks?”

        MAKE IT the Wash. DC area and surrounding communities only and you have a deal …

      • It would seem to me that a few days without some items is preferable to what will eventuate with a Harris Presidency. We can fight back with a small battle, or we can fight the big battle, but all I see from a big battle is far more, and far worse, casualties.

        I guess it is your choice what you do, but as for me and my house, we will opt for the smaller, and possibly more effective, battle.

        Good tidings to you and yours, TOMT,


      • I believe there are some very fishy issues in the election that need to be looked into, but truck deliverery are too importain to support this protest.

        Need to be looked into, but NIMBY eh?

        Well you’re just a bastion of consistency…

    • Very educational.
      Dr. Shiva Ayyadurai also said: “If you don’t educate yourself, you get enslaved.”
      Another point was that federal law demands that the images are preserved 22 months, but some states made their own law saying the images could be deleted when the counting was done.
      Finally Dr. Shiva Ayyadurai suggested we fire the republicans and the democrats, and transfer the power to “We the people.”

      It is a long video and being an engineer myself, it was a bit too long, but still absolutely worth seeing.

      • Nice.
        Truth only hurts those who deny that it exist.
        Allegory of the cave is key right now. The shadows are glitching out and the audience is becoming increasingly aware of the light behind of them… (Waking).
        We know. They know that we know.
        It’s my opinion at this point that we who value authentic reality are winning.
        War is messy.
        Time will tell.

  7. If all the various statistical analyses I’ve seen, I’ve found this among the most compelling and “data driven” rather than “law driven”.

    Don’t get fooled by the early correlation graphs ad the evidence – they’re just setting the stage. It’s the later graphs that are the interesting ones .

    “It Defies Logic”: Scientist Finds Telltale Signs Of Election Fraud After Analyzing Mail-In Ballot Data

    • I read it and find this excellent. The best proof of systematic fraud I have seen yet. Can this method also show the magnitude of fraud? This is very much needed to be able to contest results…

    • Ah. That is the analysis I mentioned in a different reply thread. Time-series patterns that are wildly different in the swing States from the non-swing States. Where the “break” is suspiciously at the same time in the very early hours of the morning, after a stop in counting, in every one of those States. (Almost as though an order went out from a central office?)

      • “Where the “break” is suspiciously at the same time in the very early hours of the morning, after a stop in counting, in every one of those States. (Almost as though an order went out from a central office?)”

        This is interesting. Going under the assumption that the Democrats had a plan, before the election, to steal the election, why would they all stop their operations at about the same time of night, for the next couple of hours, and then they resumed operations?

        If this was all planned out, why did they stop with what they were doing? Perhaps they were waiting to see if Biden could actually beat Trump on his own, and then the Democrats wouldn’t have to put their vote stealing plan into operation. But as election night was closing, Trump was ahead in just about all these States, then the stoppage by the Democrats occurred, and then when they resumed counting, Trump’s numbers started on a steady decline until Biden was ahead in most of the States.

        But I don’t understand the reason for the simultaneous halt in the vote counting. Maybe they had all their fake ballots stored and it took them a while to transport them to the vote counting place.

        I do think this was planned from the beginning (the vote stealing) and I think all the Democrat elites were in on it, including the Leftwing News Media.

        I remember thinking it a little strange when several months ago the Leftwing reporters started asking Trump about the election and wanted to know if Trump would go peacefully, if he lost. They kind of badgered him about the subject for a while, months before the election. It’s almost like they were expecting a big controvery about the vote, and wanted to take Trump’s temperature over it, and maybe introduce the narrative that Trump would not go peacefully.

        The Fix was definitely in, it looks like to me.

        We’ll know one way or another soon. Then we will go from there.

        • Why was there a pause ?

          Because Trump was winning in a landslide. The small cheats would not work.

          The pause was required to prevent Trump’s win becoming undeniable. So they paused to take stock and receive orders for the bigger cheats. The landslide for Trump meant they had to got to bigger cheats with higher probabilities of being detected and analyzed later.

          Apparently an agency called CISA was watching. Trump lured the Democrats into a trap.

          The only way out now for the Democrats is to push the media narrative that Biden won – and it has worked on plenty of people. But all over Twitter very smart IT and mathematics people are working together to reconstruct the main fraud mechanism (Dominion Voting machines, backed by the Clinton Global Initiative, Pelosi and Feinstein as shareholders).

          Despite Twitter trying to shut down all the people working on the fraud it appears an avalanche of information is now coming out. Once it reaches consciousness of ‘normies’ then it is over and Trump has his second term. Plenty of corrupt Dems and Republicans who assisted the attempted coup d’etat/steal will be prosecuted.

  8. The real issue in Pennsylvania is that the SC of PA changed the election laws allowing mail in ballots to be accepted after the election law deadline of 8 PM on election day. As in Gore v Bush 2000, the SCOTUS overturned a decision by the SC of FL to extend the recount deadline that was established by law. SCOTUS denied the changes in law done by the SC of FL then and it will deny the changes in the law done by the SC of PA now. Only the legislature can change voting laws. That will invalidate several hundred thousand votes for Biden and Trump will take PA by a substantial margin.

  9. How does the leading digit apply to the vote? that’s what I don’t understand, what is the argument here?
    Apologies for being a bit slow on the uptake.

    • While not endorsing any of the arguments here… The point made is valid if the data are.
      It’s a common way of spotting faked numbers. The first digit appears at a different frequency in multiple counts.

      As I understand it, the last number of the count can be in the 1xxxxs or not.
      Or it could be in the 2xxxxxs or not. But only if it’s not in the 1xxxxs.
      Or in the 3xxxxs or not. But only if it’s not in the 1xxxxs or the 2xxxxs.

      So more counts end up beginning with 1 than 2 than 3 than 4 than…
      And if they don’t then something else has influenced these numbers.

      The tax authorities use this a lot.

    • As I understand it, when you count a large number of things, meaning a number that is several orders of magnitude, you will tend to have more numbers that start with numeral 1 than with 2, more 2 than 3, etc. The reason for this can be seen with an example: You count e.g. 2500 things. Of those numbers (1-2500), all of the numbers beginning with 10, 100, and 1000 will begin with the numeral 1. So there will be far more 1’s as the first number than 2’s, and far, far more than numerals that begin with 9. This is a function that emerges from the decimal system as an expected distribution when you count a large number of things.

      People were applying Benford’s Law to vote totals for Trump and Biden on a per precinct basis and claiming evidence of fraud based on the supposedly strange distribution of the first digit of Biden voters per precinct. However, Benford’s Law doesn’t properly apply when you count only a relatively small number of things, such as only 2 orders of magnitude, which was the case in most precincts. If Biden typically got between 400-600 votes per precinct, for example, which he seems to have done, than those first digits (4,5,6) would skew higher than 1, 2, and 3. So there is no actual indication of fraud that you can infer from the distribution of votes in this case. The linked video explains this very helpfully and clearly, and probably much better than I have just done.

      • I find these examples useful show why the lower numerals (1 and 2) tend to predominate as the first numerals over larger numerals (7, 8 and 9), but only tend to do so with the total range of counts covering three or more orders-of-magnitude.

        For numbers up to 99, there are just as many 2’s as 1’s as first digits, just as many 3’s as 1’s as first digits, etc., . . . in fact, each leading numeral has a count of 11 (1 each counting single numerals plus 10 each counting dual numerals (9 numerals *11=99). However, the counts would be different if the range went up to, say, 121, for there would then be ten additional numbers beginning with 1 versus two additional numbers beginning with 2.

        Same thing applies for numbers from 100 up to 999: each leading numeral has a count of 100. But again, the count would be different if the count went up to, say, 1126, for there would then be one hundred additional numbers beginning with 1 versus twenty-seven additional numbers beginning with 2.

        Same thing applies for numbers from 1000 up to 9999: each leading numeral has a count of 1000. But yet again, the count would be different if the count went up to, say, 2240, for there would then be one thousand additional numbers beginning with 1 versus two hundred and forty-one additional numbers beginning with 2.

        Now, for the case you specified for a counting range up to 2500 things, there will be a total of 1111 numbers beginning with the numeral 1 but only 612 numbers beginning with the numeral 2. Note that this (assumed arbitrary) stopping point leaves only 2500 – (1111+612) = 777 count to be distributed with the rest of the numbers having the leading numerals 3, 4, 5, 6, 7, 8 and 9 (of course, this is equivalent to each of these remaining seven leading numerals having a total count of 111, which subjectively seems to be unusually low compared to a count of 1111 for leading numeral 1, but in reality actually isn’t).

        The predominance of the leading numeral 1 over the leading numeral 2—and to an ever greater degree 1 and 2 over the remaining seven leading numerals—just keeps getting greater as the order-of-magnitude in the total count climbs higher and higher. And it is fundamentally due to the fact that we begin counting (at any order-of-magnitude) using the numeral 1 and end counting in that same order of magnitude with the numeral 9.

    • That could be evidence reflecting the fact that MANY longtime R voters as well as the Dems are also disgusted with Trump because he is a fraudulent representative of the party values, therefore voting Biden and the rest of the down-ticket for Republicans. Statistical analysis is highly subject to interpretation and easily manipulated to present all kinds of wrong things as right, or right things as wrong dependent on what the data is organized with and how it is shown. It boils down to the fact that many people lack the proper analytical tools to even be aware of potential bias, much less look for it in the presentation of data. You can manipulate the appearance of data by simply changing the scale of a graph it’s represented by or the units that are selected to mark increments. It’s one of the first things they caution against in the examination of statistics, that they can be used to lie more convincingly.

  10. What really stinks of flagrant fraud? It is 120,000 ballots all for Biden just turning up. No independents and no Trump votes. What are the chances of this? Yes, 2 to the power of 120,000. This is a mind bogglingly large number, the equivalent of a number that is the number of baryons in the universe (10 to the power of 120) having its own universe of 10 to the power of 120 baryons, then times 3. It is flipping a coin 120,000 times and getting heads each time-basically impossible-unless the coin is rigged.

    Then there is the fraud of flipping votes, dead people voting, ballot papers mailed out indiscriminately, ballot harvesting, false postal marks…

    This is the scandal of the century-the attempted stealing of the US Presidency by outright fraud.
    Why won’t mainstream media cover this massive story?? The cover up of the millenium.
    Hopefully the reports of a second secret watermark (Watermarkgate) are true so fake ballots can be exposed and removed from the count.

    Will the brainwashed Democrats still be demanding false ballots be included? Oxymoron if there ever was.

    Will Joe Biden just go c’mon man, just count all the ballots and declare me President ?

  11. To use a complex scientific term, this article seems like mathematical mass-turbation. It might convince a few nerds there was a problem with the election, but will have no effect on judges or the election result. We already know votes received after 8pm were counted. Those were illegal votes. The computer “glitches” and double counting ballots will be harder to prove. The proof will have to be many people signing affidavits risking felony perjury charges if they are lying. Not statistics.

  12. Benford’s Law is not a derived statistical theorem. It is an “observation” and may or may not be valid for any given data set.

    “Although many facets of BL now rest on solid ground,there is currently no unified approach that simultaneouslyexplains its appearance in dynamical systems, number the-ory, statistics, and real-world data. “

    Case in point, Benford’s law does not apply to any binary number.

      • Yes in fact it does not apply. The definition of Benford’s law is:

        A set of numbers is said to satisfy Benford’s law if the leading digit d (d ∈ {1, …, 9}) occurs with probability
        P(d)=log⁡10(d+1)−log⁡10(d)=log⁡10(d+1d)=log⁡10(1+1d){\displaystyle P(d)=\log _{10}(d+1)-\log _{10}(d)=\log _{10}\left({\frac {d+1}{d}}\right)=\log _{10}\left(1+{\frac {1}{d}}\right)}P(d)=log10​(d+1)−log10​(d)=log10​(dd+1​)=log10​(1+d1​)

        You can’t have leading zeros, because the law calculates with the digit in the denominator. That leaves only one digit, namely a “1” as the leading digit in any binary number.


  13. Gee,
    The party that rigged the primaries against Sanders couldn’t possibly be involved in voter manipulation.
    The chances of an event occurring a second time are greater than the chances of an event happening the first time.

    • While it may be said that influence via media reporting was indeed something that I believe the DNC guilty of, particularly the premature AP announcement that Clinton had secured the nomination immediately before the CA primaries could have altered that, I think there is a world of difference between trying to influence the person people cast their ballot for, or even discouraging them from voting at all, and actually tampering with cast ballots or the outcome by altering real totals through artificial votes that do not reflect the actual will of the people who do make their choices known , whatever the choice may be . Even the accusations of colluding with Russia do come to that same level of malfeasance. There would be no legal remedy to people being taken advantage of or fooled into casting a vote for someone that was not what they appeared to be or dissuaded from voting for a better candidate by slandering accusations, as that doesn’t actually alter the selection that the people – their choice, however poor a choice it mat have been, still stands. It’s understood that there might well be some buyers remorse , but that’s the breaks, the choice was made.

      It’s an entirely different kettle of fish to ignore or replace the selections made by real people through artificial means . The first is influence and persuasion – even a con, the second one is misrepresentation and fraud. As would be any attempt to deny Biden the presidency which he won through the legally cast ballots, if there is no evidence supporting the claims that the process of voting was compromised to select him regardless of what the voters wanted. It’s not unthinkable that Biden would have the numbers to beat Trump considering that Hillary had the popular vote the first time, as does Biden by even greater margin.

  14. Steve Cortes writes at the National Pulse The Statistical Case Against Biden’s Win. He sees four anomalies that require investigation:

    1. Unbelievable Turnout Numbers
    2. Biden Outperforming Obama in places that matter
    3. Biden-only Ballots ignoring down ballot races in swing states
    4. Unbelievably low numbers of rejected mail in ballots

    His article:
    My synopsis:

      • You try filling out the little bubbles on a million fake ballots! Of course they only filled out the Biden bubble. If they had to fill them all out, how would they ever have had enough time?

      • Here in Michigan, and I imagine in many other states, you can mark a ballot once to vote for all Democrats, or all Republicans.

        It would be suspicious to make one mark to vote for Biden, and ignore all other Democrats … rather than making one mark to vote for ALL Democrats, which I imagine was quite common in Michigan among legal voters.

      • If you could cheat in an exam, would would write in all the correct answer after a crappy year where you couldn’t ever get half answers right?

        Dems only need:

        1) the presidency
        2) the so called judges who believe a phone and a pen is enough to rewrite laws
        3) the administration civil servants to make up regulations

        – They already have many judges
        – the so called conservatives-originalist judges are always intimidated,
        – the one who wouldn’t ever be intimidated died a natural death (with a pillow on his head, as confirmed by a medical expertise properly done by phone).

        Also, Dems would rather get a few “Republicans” reelected than have all of them rejecting the election results.

    • 1. Unbelievable Turnout Numbers?

      With lockdowns everyone has been stuck inside with TV and internet. The election was the main focus for attention.
      Sports, social life and even family life has been suppressed relative to the news cycle.

      High turnout makes sense.

    • Ron:

      I don’t find the turnout numbers unbelievable. Two things:

      1) Both Democrats and Republicans have been screaming for months that this is the most important election in the history of the galaxy. And yet it looks like roughly 33% of registered voters still didn’t believe it.
      2) COVID concerns and restrictions made a lot more people request mail-in ballots than normal. A certain percentage of people intend to vote but it isn’t a high priority, then they get busy or need to travel on election day and end up not voting in a typical year.

      I wouldn’t describe this as “unbelievable turnout”. I would call it “slightly less than usual voter apathy”.

      Turnout is still 2nd place to 1900 (73.7%; William McKinley beat William Jennings Bryan).

  15. Really? You’re going to pave the way for this guy to undermine democracy with rumor and B.S.?
    That’s it. I’m done. I’m deleting the WUWT link.

    • See ya cutie….
      And ps, typical testosterone deficient progressive, ””announcing his flounce”” off you sashay son.

      Really? You’re going to pave the way for this guy to undermine democracy with rumor and B.S.?
      That’s it. I’m done. I’m deleting the WUWT link.

        • 😎
          Noticed that too.
          If their first and last comment says they aren’t going to comment anymore …
          (And if they claim they’ve been readers but are leaving because of a post about politics came up, how long have they been a reader?)

    • Come off it fran. For those of us in places like Australia looking on at Presidential elections it’s been a millionaires playground for some time. Either you’re a millionaire or you want to become one using the position for your ‘Foundations’ and flunkies and I guess the electorate last time figured at least Trump was already one so what the Hell maybe he’ll kick some butt. As for getting out the vote there’s been plenty of funny business of many elections with all the different States and their rules and it’s high time the US paid a visit to the Australian Electoral Commission in that regard.

      The Dems started this electoral lawyering and never accepted the 2016 result so they made a rod for their own back here. Either Trump has real evidence to call upon or he doesn’t and all will be revealed with any legal avenues open to him but it’s high time the US reformed the way it elects its US President. When neither side is happy with means and results perhaps they need to get together and reform the whole process and the more light shone on it the better in that regard.

    • “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”

      Are the post saying clear proof or rather smoking gun? I mostly observed the latter. Maybe I’m on the wrong “social” media.

      Who fact checks the fact checkers?

  16. From a legal perspective, this is not the way to disqualify election results in places like Pa or MI. Itbis to show procedurally that those states did NOT follow their own existing laws. For example, in both PA and MI it is required that poll observers from both parties MUST oversee (up close) the signature match on the outer mail-in envelope. Even after a court order, that did not happen in Philly. For example, the PA SC extension of three days is unconstitutional, because only the PA legislature has the power to make such a change. (Article 2§1.2). The former gets ALL philly mail-ins tossed. The latter gets all ballots received after 8PM 11/3 tossed (the ones Alito ordered segregated). The combination reverses PA from Biden to Trump.

    Detroit gets tossed like Philly, same grounds. And there is the ‘Dominion software glitch’ that will require a manual recount in 47 MI counties. If those are like the one county where it was first caught, Trump wins and likely also John James for Senate, because the glitch worked all the way down ballot to county officials.

    And those two states by themselves reverse the stolen outcome.

    • CSPAN yesterday carried what appeared to be a press conference by the head of Georgia’s election organization, in which he spent considerable time addressing purported cases of election irregularities, not just in Georgia. If I can remember what he said, the story in Michigan was that a local race in one small part of the state was on the residents’ ballot, but somehow had not been entered in the database. This necessitated adding row(s) and/or column(s) to the database, and an attempt to do that resulted in a bunch of data getting scrambled. I guess ultimately they straightened things out ‘by hand’, perhaps including a manual count of the ballots. Seems like he said there was a further problem in that corrected files did not get transferred to all the required servers–my understanding is confused on this point. Assuming that he was truthful, which I think he was, the situation should be considered as more of an ‘operator error’ than a software glitch. Although programming that does not anticipate and try to avoid possible operator errors may indeed by considered glitchy.

    • Rud Istvan,

      In addition to your completely sound legal objections, I must add another.

      In MN, there was a requirement for witness signature for all mail-ins as per election statue. The democrats wanted to abolish it, but the state parliament refused. So, SOS and the election board unilaterally waived this legal requirement.

      As such, SCOTUS can decide that all mail in votes w/o the witness signature should be tossed. Provided of course Trump campaign makes it an issue. But I havent seen they have.

      • Chris,
        How do you propose to toss ballots lacking a witness signature after the ballots have been separated from the secrecy envelope where the signature is located? The whole purpose of putting the ballot into a secrecy envelope is so that the ballot will become anonymous when separated from its envelope. Which of course happened before the ballots were counted. Now they are in fact anonymous and there is no way to re-associate them with the envelopes. Assuming that the envelopes were not destroyed already, at most you could demonstrate that there were enough invalid ballots counted that the outcome could have been reversed if those ballots had been properly rejected.

        What possible remedy could be applied if it were proven that the number of invalid ballots counted were greater than the margin of victory? It is impossible to determine how those ballots were partitioned between the candidates. They could even have all gone to the loser. Just because there were more invalid ballots than the margin of victory does not demonstrate that enough of the invalid ballots counted for the winner that the outcome was reversed.

        The only just remedy, if this case could be proven, would be to throw out all of the results and require a new election.

        • Rich, you are right. The only option left is to renew the election. And perhaps prosecute and fine those responsible for this illegality.

      • Again, maybe I’m missing something icisil, but if the ballots have not been segregated and have been separated from their envelopes as necessary for counting, while they may be spoliated, what can be done about it? In the context of a recount, how would you know which ballots are the spoliated ones?

    • Rud, are the outer mail in envelopes retained? And how do you identify which tallied votes came from mail ins?

      In short is the omelette unscramblable and if not what happens?

      • Chrisgeo — it is a warning statement like ‘dont put your face above a car battery when you connect the jump leads’.
        Do give it a try.

        In a spreadsheet like Excel create two columns of random numbers.
        [E.g. drag down ‘ RANDBETWEEN(1,100)’ for, say, 50 rows ]

        Create a third column that has the individual differences between the two sets of random numbers in it.
        Do some scatter plots and enjoy the ride:-)

        • The Excel formula, mentioned above, should have an equal sign in front of it
          i.e. ‘ =RANDBETWEEN(1,100) ‘

          If you select an empty cell in the spreadsheet and hit ‘Delete’ all the random numbers on the sheet will be renewed with a new set and any scatter plots will change accordingly.

          -To create more natural-looking random numbers, i.e. from a normal distribution use:

  17. Also explains why I keep hearing that “It would be impossible to have all of the precincts involved in a conspiracy.” Seems very easy to add between 5 and 10 votes to each precinct without noticing it. Seven times 6,800 = 47,000. Strange that is how far ahead Biden is.

    • Add in the software doing the counting …
      There are indivduals willing to cheat without needing to be told to do so.

      In Cincinnati Ohio a 20 year poll worker in 2016 (maybe when Obama ran?) was accused of voting 6 times; 1 absentee, 1 in person, 1 absentee (for her daughter), 3 absentees for people she said “used to live there”. She was convicted. (I don’t know on how many counts.) But the worst part is she didn’t think she did anything wrong. She just want to be sure “Her” vote counted.

      And then there’s Dominion’s software which, as I understand it, was accidentally discovered in one county to have switched 6,000 Trump votes to Biden.
      That software was used in 38 states.

  18. Also posted at Dr. Spencer’s.

    Benford’s rule doesn’t apply to competitive candidates in elections where ward/constituency sizes are narrowly distributed. See e.g. comments in the cited github repo.

    For example, Trump’s counts in precincts where he won in Allegheny county violate Benford.
    Is this evidence that pro-Trump people were fiddling the vote in those precincts? No.

    Brexit constituency votes violate Benford.
    Does this show that the Brexiteers fiddled the vote to get the UK out of the EU? No.

    Weak, in this case baseless, accusations and implications undermining election integrity are very damaging to the trust that’s vital for democracy. I hope this article is pulled.

  19. I don’t know whether there is any solid evidence of fraud in the U.S. 2020 election. Maybe there is and maybe there isn’t.

    What I will say though is that politics and money are perfectly capable of corrupting everything they come into contact with in this world. This include science (as I believe we are seeing in the climate scare and renewable energy narratives) and elections. Anybody who thinks that the election process is fair and uncorrupted in places like Russia and Iran is living in a fantasy world. Anybody who does not believe money and political power can corrupt nearly everything probably has at least a few more lessons they need to learn about life in this world.

    There are likely a considerable number of people out there in the world (in and out of govt) who will do most anything for money and power. Since U.N. bureaucrats are not democratically elected, they are not answerable to anyone except perhaps those who are funding the U.N. Because there are likely quite a few corrupt govts out there in the world, there is really nothing standing in the way between U.N. bureaucrats and a corrupt way of doing things. That is why it is foolish and ignorant to believe what they say about the Earth’s climate and the environment, just to name a few issues. Clearly the influence of left-wing (Marxist) politics and lots of $$$$$ are in play at the U.N., at least when it comes to climate change.

    Now that suspicion of fraud has been clearly introduced as an element in the U.S. electoral process, the process itself may never be the same anymore. The greed for power and $$$ will always breed mistrust across political lines, which is something that has probably been happening for a long time. Each side wants more power and money than the other. If we understand and accept this, is the manipulation of the U.S. electoral process really unthinkable?

    If and when the U.S. goes into decline as an economic and military power in the world, I suggest that ignorance and greed will be two of the factors that bring it about. And the role of the U.S. govt in bringing it about will be something for future historians to debate.

    Just my two cents worth.

  20. While we’re all Biden our time some comic relief-

    “In my purview as an activist for over a decade in a number of groups — something I left to pursue journalism”

    No Jean they’re one and the same now dearie and we worked that out some time ago.

    “I found that the vast majority of people I worked with grew up in the wealthiest social classes of the United States. I met almost no one who grew up like I had, in a working-class family with parents who worked blue-collar jobs. Activism, which often does not pay a wage and takes up a good amount of time, can’t be pursued full-time by those without a financial safety net. Some people I met admitted to me that they took part in labor activism to “meet people who they wouldn’t otherwise meet.”

    I witnessed a tendency to strive for moral purity among these comfortable activists from wealthy homes.”

    Yes they’re all useful idiots and Gretaheads just like you too.

  21. What he means to say is that evidence of malfeasance by the Democrats in an election is nothing out of the ordinary — there, fixed it.

  22. In discussing malfeasance, I begin to wonder about Georgia residency requirements. And who can vote in the upcoming Senate races.

    Someone with reasonable resources should be watching how many unemployed dim leaches are going to be shipped in. And if it is not restricted, should be countering by getting reasonable people into the State.

    My State sucks. If I had the time, I would put my house on the market, move to Georgia and begin looking for employment (and vote if allowed). Worst case, I would spend $10K on a month long ‘vacation’ and move back home.

  23. Why is this stuff being talked about here? All it’s doing is giving credibility to those who claim a right wing agenda is behind anyone who disagrees with overblown claims about the magnitude of man-made global warming.

    The election result is fair. There is no fraud. Get over it and get back to the science. Or this site will lose a lot of people who have previously supported it.

    • Mark, your last statement has a false assumption: that all election results are always fair. Wrong. The US election system is in need of a serious overhaul for the very reason that it is not guaranteed to be fair and true. Rather, it depends on the faults, feelings, and fumblings of human beings processing and reporting ballots accurately. And, nowadays, in accurate and rigorously tested and secured software systems. These are all points of great weakness liable for failure. As a software developer, I can tell you that many of the systems in place across many different industries which handle multitudes of private data are not well-tested or secured tightly enough. There is no reason to believe the software system used in these various states and counties was well tested. (With the risk so high, the software should have been finished and locked from changes 6 months to a year in advance of the elections. If it’s true that a change to the code or databases was made moments– a few days or weeks– before the election, that is unprofessional and highly suspicious. This is the equivalent to a surgeon saying “uh oh” just before you go under anesthesia.)

      • Sorry I disagree with your entire comments, the election system does not need reform, they need to follow the rules, which PA has totally ignored, they ignored a court order allowing republican poll watchers access the to counting. what make you think if they ‘reformed’ the election democrats would follow the rules

        • Ronk, I never used the word “reformed”. I was not commenting about the rule-following or lack thereof. That is a separate concern from what I was commenting on.

  24. Dr. Roy… Primaries =/= General Election, where the actual fraud takes place. Of COURSE you couldn’t find violations of Benford’s Law.

  25. Back in 1960, Joe Kennedy bought the West Virginia primary for JFK which was critical for getting the nomination. Joe Kennedy’s original fortune came from smuggling in booze during Prohibition. In the general election, LBJ delivered Texas by getting more votes out of border counties with Mexico than there were registered voters. Illinois delivered the dead vote thanks to Mayor Daley of Chicago. Demrat Party is similar to CCP …..the end justifies the means and the Party is ahead of anything else.

  26. This might be the idiotic minion mistake that creates a US constitutional crisis.

    To get fake ballots the fake ballots need to be spread-out and issued after election day when it is known how many fake ballots would be issued.

    So that requires dating the ballot envelope, Nov. 3rd even though the ballot envelope had been received on the Nov 4th. A Postal worker who was ordered to back date all election ballots received… ….refused saying backdating election ballot envelopes was illegal.

    The same Postal Worker became a whistle-blower and the whistle-blower has given a leave of absence and threatened by the Office of Inspector General to hide Dem’s obvious interference in the US election and forced to sign a fake document.

    The catch is Postal Worker was wearing a wire-tape.

    US Post workers told to backdate Stamps, then stood down, interrogated

    In reply to:

    “Hopkins did the original interview anonymously, but at work he was implicated as the one who had spoken up. They called him in to “bring up old problems” and ask questions.

    Then they told him to he was placed on unpaid leave.
    And now he’s been hauled into the U.S. Postal Service Off
    ice of Inspector General, quizzed and coerced without a lawyer, until he signed an affadavit that was so weak, the Washington Post generated a Fake News headline saying he had recanted.”

    In Canada, Ordering a worker of the government to do an illegal act is illegal…. …. A high level organized plan to do illegal actions, to interfere in an election .. …Would result in instant firings in the Inspector General’s office and the start of criminal action.

    In Canada. The party that initiated the organized plans to do illegal actions to interfere in any official election, would be banned.

  27. Seems to me runoff elections in these contested states. 5 days before certification is what we should do. If you are afraid to vote in person request 1 ballot, 1 person, 1 vote and mail it in a week away from the date. Then have neutral observers at the point of mail in ballot counting and actual voting. This is the only way out. What incenses me is FLA/TEX/Ohio had no problems, Even Newfound in an earlier election had a large mail in but was called 45 minutes after polls closed. Stopping the voting count is a dead giveaway. Who does that? Here in PA they plainly violated the law. THE GOVERNOR AND SEC OF STATE screwed up, THEY DID NOT GET THE LEGISLATURE TO CHANGE THE LAW. The state legislature, not the courts or the governor is in charge of the voting law and the law is clear. That Wolf etal wants to count 300k non signed and there are 98 k ballots that were mailed with only Biden on it for president, is unacceptable. What really got me was they made my daughter go get her picture ID when she showed up to vote in person, knowing full well who she is ( we are known in town and Jessie is a well known PSU gymnast tho she has a Covid exemption this year) So we have runoffs, lets do this. My sourced tell me this could get ugly in Mich and Wisc also. To avoid all this, have a run off , You can even have Carter/Bush supervise a bi partisan observing team if we have to go full scale UN. PA, NC, ( since they cant get them in) GA, MI, WISC, NEV AZ. afterall is Biden has this big mandate then he should win handily and leave no doubt, and it would be transparent, And big orange will be vanquished. Isnt that the goal anyway

  28. it doesn’t look logic : most percentage of votes for Biden/Trump comprise between 40 and 59 % . Where is the 1 ?
    This law cannot be applied every where , there are exceptions :
    from wikipedia :
    Distributions known to disobey Benford’s law
    The square roots and reciprocals of successive natural numbers do not obey this law.[62] Telephone directories violate Benford’s law because the (local) numbers have a mostly fixed length and do not start with the long-distance prefix (in the North American Numbering Plan, the digit 1).[63] Benford’s law is violated by the populations of all places with a population of at least 2500 individuals from five US states according to the 1960 and 1970 censuses, where only 19% began with digit 1 but 20% began with digit 2, because truncation at 2500 introduces statistical bias.[62] The terminal digits in pathology reports violate Benford’s law due to rounding.[64]

    Distributions that do not span several orders of magnitude will not follow Benford’s law. Examples include height, weight, and IQ scores.[9][65]

  29. With all of the documented software related “glitches” in this election, Dr. Shiva Aayadurai needs to have a 1hr prime time slot to inform the American public on the automated vote scraping that occurred.  Massive numbers of votes were moved from Trump to Biden in realtime and this MIT PhD and the inventor of email, can prove it.  See his video on the analysis that he and some colleagues performed.

    This video is an interview with Russell Ramsland where he documents how the software works, and the total lack of security.   He shows in a live CNN feed from the 2019 election, where votes were switched in realtime.

    This link shows an analysis with documents all votes that were either switched or erased.

  30. Philadelphia does not have 6,812 precincts (what Philly calls voting divisions), but 1,703. The number 6,812 seems to come from the data cited by Spencer having four lines per division per candidate (Biden, Sanders, Gabbard, write-in), with one line for each of four different voting methods.

  31. The problem with all these arguments is exactly what happened after the Brexit referendum. The remainers were claiming all sorts of absurdities, which raised the question as to whether they’d have done the same in the event that they’d won. The answer, of course, is “no”.

    Would anyone on here be raising these issues had Trump won? Did any of you raise these issues four years ago?

    Of course there’ll be problems with the voting system, especially where individual states have their own laws. But anyone claiming fraud’s taken place on the scale necessary to overturn the result is nothing more than a bad loser. The data doesn’t support the argument and nor do the conspiracy theories.

    I hate to say it but I think Anthony’s made a big mistake here. Rightly or wrongly, anyone wanting to dismiss this site as a red wing, anti-climate change lobby now has exactly what they need to support their case.

    • I’m not claiming fraud, so you will need to find another reason to call me a bad loser.

      But, I would like to see a rational explanation for the 4 am spike in Biden votes (200,000) in Michigan. I would think that, given the tally system, there would be a very simple description of how that happened (or even how it could have happened). How do you think it happened?

      We have been living in the virus era for 8 months. We knew about the November 4 vote for a pretty long time too. We knew we would be mailing in our votes for a month before the election. WHY did a State think it was necessary to add three days to the voting deadline?

      It is only to be considered to be fraud if the rules were changed (deadline extension), as choreographed by those that facilitated it, on the basis of knowing or thinking that it would give them an advantage. Do you think that the individuals that implemented the extension decision did it based on altruistic goals (“special circumstances require changes to keep things fair”), or do you think it was discussed as an advantage for Biden before it was implemented?

      And finally, why do you need to qualify your statement “on a scale necessary….” If the vote was closer, say 10,000 votes, would you still be claiming that there was no fraud. If it was 5,000 votes would you say let it go, there is no fraud. Fraud is fraud. Cheating is cheating. Let it go now and next time it may be on a scale that matters.

      • Late night vote spikes in favor of Biden happened as a result of multi-hour overnight hiatuses of reporting of counting of mail-in ballots, while counting of mail-in ballots was underway at full steam. The gain of votes in favor of Biden from counting of mail-in ballots was expected. Biden voters voted more by mail to avoid catching or spreading COVID and to minimize contribution to long polling place lines (which are disproportionately intolerable to people with a lower-pay hourly job or two), while Trump voters voted more in-person on Election Day more to produce Election Day evening numbers in favor of Trump.

  32. 1 – much of the commentary here seems to ignore the fact that Dr. Spencer is assessing the applicability of Benson’s law to the detection of fraud using data from primaries, not trying to detect fraud using current election data.

    2 – I don’t think using a log normal dist makes sense here because that produces an exact set rather than a human generated (i.e messy) set. It would be better to use a large, human generated, set. For example I just grabbed the US cities pop data from wikipedia and got:
    787 307 202 151 99 99 82 62 106 for digits 1 –> 9.

  33. All else aside, I’d like it required that voting system software source code be published as it was the day of the election. I’m actually astonished that this isn’t required. (My guess is that the software code is pretty bad.)

  34. Auditors use Benford’s Law to detect irregularities, but only in very special settings. If a firm requires that expense claims over $500 must be approved by a senior manager, and underlings are splitting $550 claims into two (say $230 and $320), then the first digits of the claims amount will not have as many 5’s as it should and will have two many 2’s and 3’s. Auditors can then suspect that the process for approval of expense claims is being subverted, and adopt follow-up procedures.
    The equivalent application of Benford’s Law in this setting would require us to assume that precinct poll officials are adding or subtracting, not just votes to or from one candidate’s totals, but votes to put the candidates above or below some fixed threshold which is agreed by many of the precincts in the state (and not just above or below what other candidates in the precinct happen to receive).
    As a voting fraud model, this makes no sense. If every precinct added 100 votes to the total for one candidate, that might produce a slight departure from Benford’s law (extremely slight if most precincts had thousands of votes), but if the amounts added in different precincts were variable (and especially if they were a percentage of the vote in each precinct) then there should be no detectable departure.
    So unless someone can specify a plausible fraud model which produces a prescribed departure from Benford’s Law and we can then detect that specific departure, the most likely explanation for Dr Spencer’s observations is just normal sampling variability. To address that requires a proper chi-squared or similar test (not confidence intervals for each separate digit).

    • What if, instead of adding votes, the votes were shifted from one candidate to another? That is certainly more akin to breaking up a $500 or more expense into pieces, and as I understand one theory of how fraud may have occurred, voting counting machines can be hacked to manipulate the percentages for the respective candidates – all while staying true to the actual number of ballots cast so that the counted ballots match the ballots processed.

      Not saying this actually occurred, but I’ve seen persuasive explanations as to why this is not only possible, but that the ballot counting software was designed to allow this (vote counts in floating decimals for example).

  35. Personally I like this take from the Ace of Spades HQ blog:
    “Screw the stats. Trump is the number-one communicator in this quadrant of the galaxy. Trump has scores of anecdotes like that loose string on the sock where, when you pull it a bit, the sock comes apart.
    The Trump rallies hit every swing state and educate their legislatures about the power of anecdotes. Anecdotes drive voters. Everyone remembers a story. Voters remember.
    This election must be certified by two chambers of every swing-state Legislature.
    The speaker in Pennsylvania just showed us the high ground. The Republican legislatures follow his lead and say no certification without the following:
    – a full audit, by hand of every vote
    – any court or election official mandate not approved by the Legislature does not count — take out those votes
    – voting machines: cough up the source code, the audit logs for our forensic teams
    You get the picture.
    If the Democrats challenge this, the clock works against them. Thirty days. Tick, tick.
    Trump plays the Trump card. Seventy-one million people demanding a recount — fair, honest, transparent.
    No recount, no certification. No voting machine code review, no certification.
    No certification, and the House of Representatives makes the call, and Trump gets off the golf course and back to work.
    This is the high ground. The Democrats have given it to us; let us gather together and say “thanks.”

    • You got it right. And this IS our (I am a registered NPA ‘Trumplican’) hill to die on. The 12th Amendment, NEVER before used. Ratified in 1804.

  36. Just a little logic exercise regarding Benford’s Law: If the other 3 candidate’s numbers conform to Bendord’s law, is it illogical to argue that the 4th candidate, who just happened to win, does not need to conform to Benford’s Law? Or should that one candidate’s very specific departure from Benford’s Law (repeated in state after state’s results) be logically considered as suspicious and subject to further scrutiny (a la GA’s hand-count)?

    I’ve reviewed the data posted at or whatever the site is named (I bookmarked the link so I haven’t typed it). These computer geeks and programmers (called “centepedes” or simply “pedes”) have done the heavy lifting. Their work is vaild. Pull down the CSV files they have created directly from NY Times Edison JSON data and examine them yourselves. It’s not a “debunked conspiracy theory” or “lacking hard proof” as the media is claiming. There is physical, numerical proof that a systemic digital attack was underway, switching votes or, in the event that dumped in fraudulent mail-in ballots were injected all for one candidate, subtracting an equal amount from one or more other candidates in an attempt to bring the projected total number of votes in line with the known registered voter rolls in that precinct, ward, or county (depending on the state in question). Nationwide. In 40 states.

    Even in states NOT using Dominion Voting Systems.

    Here is the list of States which were NOT affected:
    Vermont (*while the digital record shows no switches or subtractions, the D/R Ratio in batches plotted during the ongoing count shows strong evidence of fraudulent ballot-dumping all for one candidate, as the jump in ratio is a marked stair-step fashion)
    Nevada (*see Vermont)
    Washington, District of Columbia

    The scripts which were created and used to examine the data have been replicated by multiple programmers, all reaching the same conclusion; massive fraud occurred. The scripts and data are available for examination. I am encouraging all of the savvy data processors on either side of our climate divide to jump in with both feet, and attempt to prove, conclusively, that there is no fraud happening. Without this precious confirmation, our faith in this and future elections will be destroyed.

  37. Another related topic:

    They say people in Europe wanted Biden to win.

    Well I just browsed the comment section under a YouTube video of a French news TV/radio chanel (RMC), and there are TENS of anti “Biden victory is a fact” comments, a few explicitly pro Trump comments, a few neutral comments and a few irrelevant comments.

    There are not bot programed to like or retweet. These are comments in proper French language.

    I’m scrolling and scrolling and I can’t see ONE pro Biden comment.

    Now I understand that the comment section is not a proper “scientific” pool, and is always biased. But that is RMC not some crazy truther chanel so not that biased.

    And even bias doesn’t make one opinion disappear.

    From that simple experiment, I conclude that the “result” of “scientific” pools that French people are overwhelmingly pro Biden is simply false.

  38. Hopefully they analyse results in precincts where there is no need or point to cheat, where one or other candidate is miles ahead. If those results look different to precincts where the race is close, well…

  39. If you have read comments this far and haven’t checked out the link provided by:

    Mohib November 11, 2020 at 11:27 am

    you should. The time series analysis provides a far more convincing argument than Benford’s law which doesn’t seem to apply for most areas.

  40. Its been looked at before for other elections

    “Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford’s Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its “success rate” either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst.”

  41. This post is rather concerning. If you can’t understand a relatively simple observation like Benford’s Law and how it is applied, and if you can’t get access to publicly available data, then how am I to believe you when you’re talking about complex climate models and data manipulation?

  42. Voting machines need somewhat different scrutiny than manual counting methods, though the ultimate principle is the same and some things to check are the same.

    Note there are different types of voting machines. The ‘Dominion’ brand that motivated manual recount in Georgia appears to be a hacked together cheapie used in insecure ways:

    It appears to be a real horror show, with a questionable computer OS and insecure implementation, lack of control of key things like memory cards containing votes, and mismanaged access to data. – on top of serious questions about quality of the voting software.

    (One cause of printing of test ballots could be the software resetting itself when something doesn’t seem right to its internal monitoring system, or glitching in the host computer as I see with Windows 10Pro on a Lenovo Thinkpad 480.
    Another problem could be code that is in the software load but not planned to be used in that release – ‘dead code’ is verboten in aviation software development processes. The expert may be referring to such code. (That’s different from code that is only activated when a mode selection is made, such as the wiring jumpers on 757/767 airplanes, that mode is then locked in until power is cycled on the ground.
    Neither was the cause of the 737MAX fiasco, that was caused by bad system design and failure to complete safety analysis. (Which is roughly akin to what the security expert says about the overall polling station operation in Georgia – data not controlled, system tweaked on the fly during voting, …..)

    As for inclusion of software superfluous to the mission, I am disgusted with Microsloppy’s inclusion of cutesy games in Windows 10Pro. As a minimum the voting software should be run in ‘virtual machine’ mode, which is in the Pro and Enterprise versions of Windows 10 whereas Home/HomeOffice/Student versions have fewer protected modes.)

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