Joe Biden’s votes violate Benford’s Law (Mathematics)

Source: GNews.

You can’t say there is no evidence of election fraud in the 2020 presidential race. There is, in fact, statistical evidence to suggest that something unnatural occurred in various states and counties.

I think of it this way: Statistical anomalies are like probable cause. They are enough to warrant investigation, but not enough to establish guilt or innocence of a crime.

34 thoughts on “Joe Biden’s votes violate Benford’s Law (Mathematics)

  1. With all due respect this is one of the dumbest “analysis” that you have ever managed to root out of the dark web. If you do not understand why – and obviously you don’t – I am here to help. Statistical patterns fall apart the more you drill down. In this case, the authors acknowledge that overall all three candidates returns follow the expected pattern but lo and behold, if you drill down into smaller data sets you can find some that don’t. Well, duh.

    If you flip a coin 100,000 times you expect heads to be seen 50% of the time. If you flip a coin 100 times it is very unlikely that it will yield exactly 50 heads.

    Liked by 1 person

    1. Statistics is not my area of expertise, OBVIOUSLY. Smile.

      However, after reading through a couple explanations of JTR’s post, I googled “what kind of anomaly regarding elections deem benford’s law unhelpful?”

      There are some out there it seems. But, one thought stood out to me and I quit the search. It was that BL is often used by Qanon as they try to find fraud.

      Enough said, I say.

      Liked by 3 people

    2. RE “In this case, the authors acknowledge that overall all three candidates returns follow the expected pattern…”

      No, they don’t. The authors show that in some counties all candidate counts followed the expected pattern, but in other counties the Biden counts uniquely deviated.


      1. Read it again.

        This is the link from the article showing that the big picture is that all three candidates follow the “law” overall.

        Then they go on to find individual places where the pattern is not followed. That sort of cherry-picking is absolutely meaningless. Plus, no effort of any kind is made to find other sources of such a result – notably, the sizes of the precincts in the cherry-picked sample. The assumption is that they are a random size in those counties but that is generally not the case.

        Bottom line, your claim that there is statistical evidence for voter fraud is 99 and 44/100th desperation speaking.

        Liked by 2 people

        1. RE: “This is the link from the article showing that the big picture is that all three candidates follow the ‘law’ overall.”

          Nope. The data source for the graphic isn’t identified. You are making unwarranted assumptions.


          1. The authors provided the graphic but also a link to the source. If you follow the link you will find these words above the graphic . . .

            “Votes numbers for Trump, Biden, and West follow Benford’s Law.”

            THAT is precisely the statement I made and you are stupidly quibbling about. Are you being obtuse deliberately or can you just not help it? I did you the courtesy of reading and understanding what you linked to. You owe me the courtesy of doing the same before casting your usual brickbats.

            BTW, I do not know if that source is authoritative or not. That is a separate question.

            Liked by 1 person

    1. Interesting article. I notice that it doesn’t dispute the validity of Benford’s Law, only many of the attempts to derive (or prove) it. As the last sentence says, “most experts seem to agree with [Few] that the ubiquity of BL, especially in real-life data, remains mysterious.”

      But proving the validity of BL is not the issue. Noting that Biden vote counts violate BL in some instances is the issue.


        1. What kind of indication of failure do you require? Benford’s Law is thought to be a feature of the natural world, like the Law of Gravity. Just because it cannot be explained doesn’t mean it doesn’t exist.


  2. These games are all well and good over a beer or coffee.

    But here is what irks me. Trump is working hard to sow permanent distrust for our democracy and its electoral system. A scorched earth policy that will have a lasting impact on a country that is already seriously divided.

    If he really cared about America, which has treated him and his family very well for close to a century, he would find a way to gather his supporters and tell them that supporting our country no matter who is in office is of prime importance.

    If the Democrats actually had a vast network of people working secretly to steal an election spread over 50 states with 50 Secretaries of State and 10’s of thousands of people sorting, counting, verifying and supervising the ballots then they would have swept all the down ballot races too. But the actually lost seats in the House and probably won’t take control of the Senate. A lot of Republicans voted for GOP Congressmen but did not vote for Trump. Is that a hoax? Of course not.

    So my point is simple: saying that the election was a fraud, that it was crooked, that the results are tainted is damaging to our national interests. Trump is leading this Mephistophelian chorus because he is so self centered he couldn’t care less about what is good for our nation. People who believe him are unfortunately undermining our Democracy but without awareness.

    Liked by 1 person

    1. Totally agree with the entirety of your 4th paragraph that begins with: “If the democrats actually . .

      And, I absolutely must thank you for the ‘Mephistophelian’ use, which was perfect for Trump’s chorus.

      Liked by 1 person

      1. That word was made up, then I checked and found it was real. I have a brain that is so full of useless crap that occasionally a lucid thought erupts like a burp in church and can’t be ignored. 🙉🙈🙊

        Liked by 2 people

  3. “In an attempt to bring mathematical certainty to uncertain situations, some have tried developing “election forensics” tools as a way of evaluating the quality of an election. Most election forensics tools involve applying statistical methods and underlying mathematical principles to official election results. One such tool is the application of Benford’s Law to election results. In this paper, I use election data from the lowest level, that of polling station, to assess whether Benford’s Law, as applied to the distribution of second-digits in vote count data, is an appropriate tool for detecting fraud. Unfortunately, my analysis shows that Benford’s Law is an unreliable tool. And, as one applies more sophisticated methods of estimation, the results become increasingly inconsistent. Worse still, when compared with observational data, the application of Benford’s Law frequently predicts fraud where none has occurred.”

    Liked by 1 person

      1. Keep up the good work of helping to sow so much distrust in our election. That is just wonderful. 😇

        Your conspiracies omit that people voted for Republicans enough to affect Congress but they flipped on Trump.

        If the votes had been rigged, the down ballots surely would have been affected. But conspiracies can’t accept that.

        Plus your link mentions relations to previous elections. Yet that Trump was such an political outlier in words and deeds seems to be overlooked. Why should elections follow a non-traditional candidate with regards to data comparisons?

        5 million more votes for Biden are going to be reflected at the electoral level. Biden’s margins in the states won by Trump in 2016 by only 77,000 (suspicious votes…hmmm?) is greater, as is the popular vote. Not surprising since PA, MI and WI are blue states and the flip in 2016 was the anomaly.

        You and Trump are asking the nation to believe that our whole election system is corrupted. That 10’s of thousands helped cheat on a grand scale from canvassing, sorting, counting, auditing and verifying under the scrutiny of cameras and thousands of poll watchers. And in states with Republicans in charge of the process.

        That you and other supporters of the president are voicing complaints is one thing. For the president himself to declare the election a hoax is truly Third World crap. Dangerous words at a time when we are racked with a pandemic, high unemployment, debt skyrocketing, and sharp partisan divides.

        Liked by 2 people

      2. RE: “You and Trump are asking the nation to believe that our whole election system is corrupted.”

        Nope. We are asking for the election process to follow the rules. There is probable cause to be skeptical of the tallies in some places. There are pre-existing procedures for resolving such disputes, and there is nothing unusual in seeking to have them resolved.

        You and Biden are asking the nation to believe the media, which has no authority to call the election one way or the other. That is corrupt.


        1. “You and Biden are asking the nation to believe the media, which has no authority to call the election one way or the other. That is corrupt.”

          The media only calls what it sees, but the official tallies will be issued by the states on specific timelines.
          Nothing corrupt about that.

          I am sure there will be challenges to a few hundred votes that might not pass muster one reason or another. but that is no reason to call the whole election a hoax, which is what is being spewed by Trump and his inner circle of enablers.

          Liked by 2 people

          1. “That’s debatable.”

            Not in this context – media reporting on the evolving vote tally.

            By the way, it is worth noting that it was Fox News who was very quick to call Arizona for Biden. No other network followed them on that. Were THEY out to hurt Trump or were they “only calling what they saw.”

            Liked by 2 people

          2. So the election officials in these swing states, Republicans and Democrats alike, are feeding secret misinformation on counts to all the media?

            That might explain why pizza is served with this crap.

            Liked by 2 people

        1. Cherry picking? There were enough ‘cherries’ in critical states to maybe make a difference, and in any case, even one ‘cherry’ should send someone to prison.

          But I am troubled that you see no problem with dead people and non-residents voting in battleground states.


          1. Unlike you, apparently, I am not troubled by bullshit pulled from the ass of the most dishonest and corrupt person to ever disgrace the Oval Office.

            So far, seven of Trump’s court cases have been rejected by various courts. Turns out that not liking the result is not a grounds for reversing the decision of the voters. Who knew?!

            Liked by 1 person

          2. Have you seen ANY evidence that fraud has taken place. Every time Trump officials, campaign officials and a few GOP supporters are asked they cite no evidence. And just repeat the mantra off fraud.

            Dead people? Where and how?

            Graham has said they need to change our election system because Republicans will never win.

            WTF? They won a boatload of down ballot races.

            Sorry but what Trump is doing, personally and through lackeys, is designed to be a scorched earth policy to destroy our democracy.

            Of course that might explain you glee in the propaganda of a stole election. We know you don’t like democratic participation by the unwashed. Or that is what you professed many times.

            Liked by 2 people

          3. The unwashed are welcome, as long as voting is important enough to them to make some effort.

            That is the threshold for me.

            The people here, and those we know, make effort to be informed and vote based on our view of the public good. But it is a mistake to think that everyone is like that.

            Too many people put no thought at all into the good of the country, and if you go to them and place a ballot in their hands they will vote based on the most clever Facebook meme they saw that day.

            They are the assassins of republics.

            They are the ones who elect Hitlers and Maduros.

            So, yes, I don’t want voting to be too easy. I would like to hide the polling places at the end of a short scavenger hunt, starting at the location of the last election.

            The unwashed are welcome, but the lazy we don’t need.


          4. So I was correct. Democratic elections are not approved by you. You know we used to have poll taxes, literacy tests and billy clubs that kept out the “wrong people” from the polls. Your suggestions are that they were right and those that did not fit your elite club deserved nothing in the participation of our country.

            The problem of course is who decides who is worthy. And here is a clue: it is not you, or me, or Molly McGee.

            Democracy is messy. But as often posited, it is far ahead of any other forms of governance that we have experienced in the world.

            Remember, that many of your unworthy voters have also put their life on the line in military conflict so you could sit here at home and complain about their laziness and lack of intellect.

            One of the great inequities we experienced in history recent enough to still have millions of people who experienced it either first hand or through parents is they way we treated Blacks coming home from the war.

            Good enough to die to protect us, but not to vote or even participate in our country as full citizens.

            Keeping that in mind, you can see that your premise has some very unsavory history as well as being a dangerous route to go.

            Why don’t you dismiss all natural born citizens from voting. After all, they did nothing to gain their status except by the fortune of being born here. Whereas naturalized citizens, like me, took classes, tests, an oath and paid a fee. Perhaps that is what everyone has to do when they reach the age of majority and then earn the right to vote.

            Liked by 3 people

          5. “Democracy is messy. But as often posited, it is far ahead of any other forms of governance that we have experienced in the world.”

            I disagree, A democratically elected representative republic can, with appropriate safeguards, be an excellent form of government, but an actual democracy is just a short, ugly road to a dictatorship.


          6. “Too many people put no thought at all into the good of the country, ” …

            Lots of Trump voters fall into your category. If you don’t believe that, you are just being delusional,

            Liked by 2 people

          7. OK, if that is true and verified then remove his single vote. Unless he voted for Trump, of course.

            Don. there are always going to be errors in casting and counting ballots from 150 million people in thousands of precincts over seen by tens of thousands of people. And we processed the bulk in just a few days. Plus people move, die, change names and you know that it takes time to update the voter registration rolls. Except by Republicans who just toss out Democrats, minorities, young people, ex-felons until someone notices. That should be a concern for all Americans.

            So far every lawsuit has been shown to be bogus based on nothing. Oh yeah, a closer distance was granted to all poll watchers in some place. So there is that.

            There will be recounts in a state or two. Georgia for one which is run by Republicans. And that is not going to toss ten thousand votes.

            What I think should be done is for a few judges to recognize frivolous suits then charge the attorneys with filing them and start jailing and fining a few.

            We know for a fact that the 2016 election was rigged. How could Trump win in those 3 key states without cheating. It is a proven violation to this day. Didn’t you know that? Everybody knows that. They say…

            And yet… there probably wasn’t any fraud. Poop happens, and it did in 2016.

            Great things can happen too. Witness 2020 election.

            PS: I remind you that the two most egregious voter fraud and rigging efforts were by Republicans in the last 2 years. Taylor, whose people pleaded guilty to fraud and in NC where an entire election was tossed after voter fraud by the GOP candidate’s campaign.

            Liked by 2 people

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