One Milwaukee Ballot Curiosity & One New Theoretical Voter Fraud Tool

One Milwaukee Ballot Curiosity & One New Theoretical Voter Fraud Tool


Milwaukee is comprised of a number of wards, almost 500, from which was collected the number of votes each candidate received in both the 2016 and 2020 Presidential elections (official source link). A copy of that was given to me (I take it as is) from which comes the following analysis.

In 2016, 8 parties ran for President, including, of course, Trump and Hillary. The other 6 were minority candidates, including write-ins (I call these “Offvote” in the code). In 2020, there were 6 parties, 4 of which were minority.

In each ward, votes went to one or more parties. Some wards voted for more for one party than another. Here is the across-ward distribution of the ratio of total minority candidate votes to total ward votes.

In 2016 (red), the fraction of votes minority candidates received had a large spread. In 2020, the spread was much less. Meaning in 2020, more votes in wards went to either Biden or Trump than in 2016 when votes were more spread out.

This is curious because there were more total votes cast in 2020 than in 2016; 458,935 to 440,992, a 4% increase. Further, the largest fraction of minority candidates in 2020 was 0.000168, whereas in 2016 the largest was 0.000515, a difference of 3 times. One might have expected that with the 4% increase in total votes, there would at least be some wards which had more variability. Especially if there was an increase in mail-in ballots, in which people had all the time in the world to make their choice.

Further, there were 9 wards which only voted either Biden or Trump or no candidate at all, but there were only 5 wards which voted only Hillary or Trump or no candidate. Perhaps the increase in minority choices accounts for this. In these wards, in 2016, Trump got 9 total votes, Hillary none, and in 2020, Trump got 124 votes and Biden got 423. Every vote counts!

Looking at the picture suggests a break point of 0.0001 fraction of minority candidate support. Examining the data for just those wards, the following picture looks at the distribution of (Trump – Democrat) ward vote totals. Positive numbers are Trump gains; negative numbers are Democrat (Hillary or Biden) gains.

Seven wards stick out as curious in 2020, which are listed on the figure. These represent 12,093 total votes in Biden’s favor, whereas in 2016 those same wards were only 120 votes in Hillary’s favor, and even one ward that went Trump’s way. All wards therefore represent large increases for Biden over Hillary.

Now 12 thousand votes is a lot, so the suggestion is to examine these wards more closely.

This is, I emphasize, not proof of fraud. But they are amazing jumps: a lot higher than the 4% increase in total votes would predict.

The data and code for this are here: MilwaukeeVotes2020.csv, MilwaukeeVotes2016.csv, Milwaukee.R. The code was done in a hurry and is uncommented—you’re on your own.

Predictive Analysis

In earlier posts, I explained a terrific way to identify fraud is to examine the frequency of ballot markings, comparing early and late or in-person or mail-ins. If there are noticeable changes in these distributions, it could be evidence of ballot stuffing.

For example, suppose, as some (unconfirmed) reports said, that huge caches of Biden-only mail-in ballots were discovered, I mean ballots on which the only markings were for President and nothing else. This is improbable even if every single one of the ballots were filled in by earnest people wanting to select Biden.

There is some error rate in filling out ballots, or in any paperwork, and the larger the cache, the larger the chance of at least one error, i.e. at least one Trump vote made by mistake. Any cache over even in the large hundreds is deeply suspicious, and anything over 1,000 suggests these were not natural ballots.

Barring that kind of easy evidence, we can still look at distributions of markings where positions other than president were marked.

Here is some unverified, unofficial data, collected by an anonymous contributor to illustrate how this can be done using the method of predictive statistics. This is for illustration only.

In Michigan we have the following statistics of the number of votes cast for President and those, on the same physical ballot, for Supreme court:

Supreme court winner votes = 2,316,459
Presidential winner votes = 2,279,543

Supreme court winner votes = 2,369,012
Presidential winner votes = 2,790,648

In 2016, 98.4% of ballots had marking for both offices, showing a true civic spirit. But in 2020, only 84.9% of the ballots had markings for both offices, and there was also a distinct increase in the number of votes. In Michigan, because of the coronadoom, there were a gargantuan number of mail-in ballots sent out. We await the final numbers. The Secretary of State’s site does not yet have 2020 data posted.

We eschew all statistical tests! P-values are lousy evidence, as discussed endlessly here. Instead, we will make a prediction conditional on the 2016 data of how many ballots would have both positions marked, given we know there are 2,790,648 ballots in 2020.

In other words, it could be that in 2020 all 2,790,648 ballots had only one position marked. We can calculate the probability of this, assuming nothing other than the 2016 data and that there are only two possibilities, that the ballot has two markings or one. The math suggests the prediction of both positions marked is a beta-binomial distribution over the numbers 0, 1, …, 2,790,648 (see this marvelous book or this page for why).

If we do that, we get this picture of the probability of every possibility, from 0 to 2,790,648.

The spike to the right predicts we’d most likely see that many ballots with both positions filled out. The red vertical line shows the actual number of matching ballots.

Here, for fun and for people who haven’t seen these kinds of things, is a blow up of the same picture on the meat of the prediction.

The prediction was that we’d most likely see 2.74 and 2.75 million matching ballots. We saw 2.37 million.

The prediction was, of course, conditional on the old data, but it was also conditional on the assumption that people’s behavior would be the same. It clearly was not.

One possible change in behavior is an increase in cheating, i.e. ballot stuffing with Biden-only ballots (assuming the data is real!). There are, naturally, many other explanations besides this, such as marked disinterest in the Supreme court in 2020. Plus, we only looked at two ballot positions, when we could look at others, too.

This example is only to show you that hard probabilities, and not flawed p-values, can be used in detecting potential fraud.

Since the code to do this is so simple (in R), I paste it here:

newdbinom = function(x,, k.old, n.old){
   # New observables for predictive distribution given old data and guess of how many new data points there will be
   # beta-binomial
   a = k.old+1
   b = n.old-k.old+1
   (ans = exp(lchoose(,x)+lbeta(x+a,,b)))

# used like this:

newdbinom(0:2790648, 2790648, 2279543, 2316459)

Technical update Lot of newcomers, and so some misunderstanding of the shorthand I used in the second section. The model is not “binomial”: it is a parameter-free deduced model using only the premises that there are two states, matching or not, and there are a known number of ballots. The beta-binomial function has no parameters in the usual model sense; all its inputs are known with certainty. You’ll have to read the book or linked page to discover why.

Second, for excellent, unassailable reasons, I deprecate all “testing”, such as p-values and the like. Go to that page and read the articles on the subject, particularly “Everything wrong with p-values under one roof.” Or read the book (not light reading).

For the others who commented/emailed that this post was too technical, all I can say is that some things are not so easy. I’ll try and explain things more simply next time.

To support this site and its wholly independent host using credit card or PayPal (in any amount) click here


  1. Sheri

    Come on. It’s just a big “get the vote out” effort. Well, actually, it’s cheat and mail-in votes effort, but close enough. Everyone knows you can increase votes by a factor of a thousand in a mere four years. Dems have always done that. And no one cared before…..Why so upset now????? Seriously, Democrats have been stealing elections for decades—LBJ in ’48, JFK from Nixon, Al Franken in Minnesota. Those midnight boxes of ballots have been going on and on and on and now, suddenly, someone’s upset. Little late for that. It has been established that election laws have ZERO meaning in the US. Good luck with pretending they suddenly should.

    Statistics may prove this unlikely, but common sense and an IQ above that of my dog says this is cheating AND THE DEMOCRATS ANNOUNCED THEY WOULD CHEAT. Why the indignation??? Everyone had a chance to fix this, no one gave a damn until Trump “lost”. So, apathy had a huge price. Welcome to the real world.

    People like to think America is the prize example of free voting. People like to believe in UFOs too. Voting was NEVER, EVER free and untainted in this country and if history hasn’t’ been rewritten too much (I have hard copies, so I can tell), we can certainly tell this.

  2. Sheri

    The Democrats also told you for four years they were going to hack voting machines. That was what the Russia interference garbage was about. They were shouting their intentions for 2020. Again, zzzzzzz from the people and the government….Too busy defending Trump to actually pay attention to the message.

  3. John Mauer

    Have you done ratio tracking [President, Senate] as discrete channel with noise, looking for spikes? Try MI

  4. Hmmmm

    This is interesting. It would be more convincing if you could show that in other states the voting trends in 2020 still match 2016.

  5. Bryan H

    This article was much more difficult to follow than the others, but I think the following video might be related to this. Get all the raw data while you still can….


  6. JC

    I second the motion from Mr. Mauer. Break out flyover states from swing states too. You take requests, right Matt?

  7. awildgoose

    After years of telegraphing from the Left people really need to stop making fun of movies where the villain explains his plans in great detail.

  8. Yancey Ward

    Briggs, not sure where you are getting the 2020 Michigan Supreme Court voting data. What I find was that the ballot allowed each voter two choices out of seven candidates, and the two winners had 1.97 and 1.23 million votes each. There were a total of 6.19 million votes cast in the election for the MI Supreme Court. In 2016, there were also two seats, but the elections were separated on the ballot that year- each election separately had 3.4 million votes compared to the 4.8 million cast for the presidential candidates that year. So, I think focusing on the winner’s votes in 2016 is the wrong approach.

    I still think the best way to use this approach is to just tally up all the ballots that only selected Trump and left every other race blank, and tally up all the ballots that only selected Biden and left every other ballot blank. I assert that if the ratio of the two is above 2, you have clear evidence of fraud. If the ratio is above 10- iron clad proof, and you can even estimate to a pretty high precision whether or not a state’s outcome was affected by it.

  9. Shecky R

    Keep meandering down the garden of forking paths… ahhh, but do-est no evil whilst picking the cherries.

  10. john

    Hi William, have you looked at the following:

    MIT PhD and his associates demonstrate clear systematic bias in votes being moved from Trump to Biden in republican dominated precincts…You may find it interesting…I’d be curious to read your critique…thanks!
    Love the book “Uncertainty” br, john

  11. John (above):

    Me too .

    (re: Dr.SHIVA LIVE: MIT PhD Analysis of Michigan Votes Reveals Unfortunate Truth of U.S. Voting Systems.)

  12. 1UnknownSubject

    I think Shiva has a really compelling case. He has done a lot of work on voting systems, fraud, etc even prior to this election on Nov 3. The guy he has as guest also did a walk through of fractional voting by using the software and while difficult to grasp, shows how easy it was to alter votes based on the hidden “weighting”. I am not sure how to prove fraud other than doing chain of customer, process, and physical counts. My thought is once the ballots go through the machine, they have already been tidied up and will not show fraud. It will take a lot more analysis to prove fraud, all while the days, hours and minutes slip by.

  13. JH

    The prediction was, of course, conditional on the old data, but it was also conditional on the assumption that people’s behavior would be the same. It clearly was not.

    One possible change in behavior is an increase in cheating… There are, naturally, many other explanations besides this….

    Why don’t you just honestly say that the prediction/model is useless? (The assumption of a binomial model is not valid either.)

    One curiosity after another. LOL. Being a curious statistician, I think I have usually found at least one “curiosity” in all real data sets I have examined. If you want me to demonstrate my claim, send me Florida election results.

    Some oddities in the data can be verified, and some not. Randomness and Uncertainty!

    If you want to show voting fraud, perhaps, you’d need evidence such as reported here: Find a vote counter who would testify. Find a truckful of uncounted votes. Etc.

  14. Vuald Berwy

    Everything you did can also be done equivalently with test statistics and pvalues, beta binomial expected values, bayesian too. ehat you breathlessly call prediction is just expected value from model.

  15. Dennis

    Interesting stuff coming out about Dominion Voting Systems (the Democrat run voting machine firm that runs about 1/3 of all voting machines – Sen. Feinstein’s husband owns a majority share, their chief lobbyist is a former Pelosi staffer, and other top execs. are also former Dem staffers). Supposedly there have been some whistleblowers come forward as well regarding Dominion programming. The alleged “glitches” that switched voters to Biden are a “feature.”

  16. Amateur Brain Surgeon

    Dear Sheri Yes. Why now? This BS has been going on FOREVER especially in dem strongholds

    Now, it has to be proved

    Do we really want a POTUS who took his base for granted while dancing to YMCA at his rallies

    That was gonna rev up his white working class voters?

    Taking advice from Jared to support and then blabber about prison reform?

    Yes! There is nothing that will rev up the white working class voter like letting blacks out of jail.

    The POTUS not talking about The Wall?

    Yes, the white working class voter as so sick of thank about The wall and stopping illegals crossing the border.

    I guess his base did get tired of winning

  17. Rick C.

    Dr. Briggs — You were magnificent today on Dennis Prager’s national radio show! Thank you once again for your clarity of thought and communication!

  18. Bryan H

    Dr. Shiva’s formula, or his conclusion drawn from it, is regrettably completely wrong.

    X-axis: Percentage of Straight Party Ballots that were Republican/Trump (RSP)
    Y-axis: Percentage of Trump votes on the mixed ballots (MBT) MINUS the Percentage of Straight Party Ballots that went Republican/Trump (RSP)
    His formula is as follows:
    (MBT – RSP) / RSP

    As you increase RSP, you will go into negative territory…..Guaranteed.
    Call out the video wherever your see it…..

    Personally, I would be very careful about using Dr. Shiva as a source of conservative information.

  19. john

    A 100% hand count would remove the algo and also permit and audit of signatures, dates, address, whether voter was alive…etc. Dr. Shiva’s work, leads to the conclusion, let’s hand count the votes!

  20. Yancey Ward

    Yes, that would be the method I would investigate. My question is this, though- were did those numbers come from? That greater than 100 to 1 is sure proof that most of those 95801 votes were fraud votes. I just want to know where the numbers came from.

  21. Dennis

    This might be the most interesting thing I’ve seen yet about Dominion Voter Systems – particularly when looked at in conjunction with an odd “typo” in a Trump tweet on October 2, when he was being treated for Covid. This guy has been reading the Dominion user manual and looking at ways stealthy code could be inserted to help Biden, then compares that with the Oct. 2 Trump tweet:

    “Going welI…” (different font here than Twitter default, but same thing – and actually looks less obvious in the Twitter sans serif default). A very odd and suggestive “typo” in light of that Dominion info, since l/L & i/I are not adjacent letters on the keyboard, so Trump had to make a conscious effort to switch to capital I at the end from the 7 preceding small letters. People naturally made fun of the tweet at the time, the “typo” supposedly demonstrating Trump’s idiocy – and the optimism just seen as typical Trumpian bluster while the media was hoping he was really on his deathbed – though it was quickly forgotten and no one really thought it too meaningful. Or was he actually signalling with that “welI,” a month before the election, that they already knew the kind of shenanigans going on with Dominion’s code to game the results (and surely already had some moles inside feeding them info that they’ve just been compiling since, waiting for the right time to release it all and blow the whole fraudulent system up)?

    Stay welI everyone! Feeling more white-pilled tonight!

  22. Bryan H

    The vote switching software must be investigated, BUT you have to be careful with using numbers that only go to the thousandths place. Rounding can become a big factor here.

    This is probably going to show up ugly in this post, but I calculate the most defensible number of switched votes to be a much smaller number than the article does by including rounding. It may be enough to explain a lot of states where you wouldn’t expect fraud.

    Reported % Low Possible % High Possible % Total Votes Reported Lowest Highest Max Range Lowest possible switched
    0.578 0.5775 0.57849 573857 331689.346 331402.4175 331970.5359 568.11843 -4852.09717
    0.568 0.5675 0.56849 574417 326268.856 325981.6475 326550.3203 568.67283
    0.401 0.4005 0.40149 573857 230116.657 229829.7285 230397.8469 568.11843 2528.24657
    0.406 0.4055 0.40649 574417 233213.302 232926.0935 233494.7663 568.67283

    Assuming the raw numbers are right, this still would prove some funny business, but not by as big of a margin (Minimum of 7,380 vote change during a 560 vote update). This can be calculated more exactly by looking at the adjacent updates, but it’s enough to hopefully illustrate my point about being careful about rounding, particularly when you’re dealing with larger numbers later in the counting process.


Leave a Reply

Your email address will not be published. Required fields are marked *