TRUMP PRESIDENT UNTIL JAN 20, 2021 – evidence of Democrat Voter Fraud, means he will continue for another 4 years.


Something very strange happened in America’s democracy in the early hours of Wednesday November 4 and the days that followed. It’s reasonable for a lot of Americans to want to find out exactly what.

Americans awake to learn Pennsylvania mailed out 1.8 Million Mail-In ballots, and we find there were 2.5 Million of them included in the count. Nobody in the Government the Media or the Courts seem interested to find out how that works, let alone let us the people know.

Trump has won the Vote in over 2500 Counties while at the same time Biden wins the vote in less Counties at 524 than anyone other winning candidate, Clinton lost while winning 500 Counties, Obama won with 873 Counties in 2008.

Despite Biden underperforming Clinton and Obama in almost all majority Black Urban Precincts, Biden somehow gets enough votes out of Majority Black Precincts in crucial Swing State Cities Milwaukie, Atlanta, Philadelphia and Detroit, to tip the Rust Belt, Win the Electoral College and achieve a Record National Vote at a claimed 80 million. And Pigs Might Fly too.

Biden has declared victory in the presidential election and many news outlets have been referring to him as president-elect. Some more honest News Media agencies have refrained from calling the race until all litigation contesting the election results plays out.

Current tallies show that, outside of a few cities, the Rust Belt swung in Trump’s direction.

Yet, Biden leads in Michigan, Pennsylvania, and Wisconsin because of an apparent avalanche of black votes in just a few Democrat run cities such as Detroit, Philadelphia, and Milwaukee, an avalanche that occurred between Midnight on election day November 3 and 7.00 am the next day November 4th.

On Election night, Trump was well ahead and in any other election would have been entitled to be declared the winner, but instead someone announced an end to the count for the night. Everything about what has happened since that moment has had a big smell about it.

We are supposed to believe that despite Obama doing better than Biden in comparatively similar Black Urban precincts across the rest of the country, Biden was so popular with Black Voters in rust belt swing states and particularly in Detroit, Philadelphia and Milwaukee, that he was able to beat Obama’s popular vote by 13 million.

The behavior of the media suggest strongly that they were briefed and have been working with the Democrats to put pressure on Senior Republicans to desert Trump, their plan is to horas, pressure and threaten people helping or supporting Trump, to force him into conceding.

So we have those who committed the serious crime of stealing an election, being supported by the Media in their attempt to get away with the crime.

No President Elect until Electoral College Votes are counted Jan 6, 2021.

A self-described fact-checking website Politifact recently issued a correction after labeling a post by Candace Owens saying Democratic presidential nominee Joe Biden isn’t president-elect as “false.”

PolitiFact, which receives funding from Facebook, is one of about a dozen websites utilized by the social media platform to perform fact checks, which have been widely criticized for their oft-subjective nature.

In the video, Owens discussed how Biden isn’t president-elect until the Electoral College decides who to vote for and those votes are counted in a joint session of Congress on Jan. 6, 2021.

“Joe Biden is literally and legally not the President-elect. So why is the media pretending he is?” Owens wrote in an accompanying caption.

PolitiFact rated the assertion false, prompting the threat of legal action from Owens.

“Weeks ago, @Facebook censored a post of mine which truthfully stated that @JoeBiden is NOT the President-elect. So I got lawyers involved. Conclusion? @PolitiFact uncensored the post & admitted that they LIED by rating my post false. The fact-checkers are lying for Democrats,” Owens wrote on Nov. 28, after the correction was issued.

PolitiFact issued a statement following a threat of legal action from the popular conservative commentator.

“Correction: PolitiFact originally labeled this video false in our capacity as a third-party fact-checker for Facebook,” PolitiFact said. “On Nov. 20, an appeal to that decision was made on behalf of Ms. Owens. PolitiFact approved the appeal on Nov. 20, determined that a correction was appropriate, and removed the false rating.”

The correction wasn’t added to PolitiFact’s website.

Most Facebook fact-checkers are dominated by left-leaning funding, personnel, and organizations.

PolitiFact published an article earlier this month saying Biden “is president-elect of the United States,” although the website acknowledged that there is still more left in the process and that the declaration is subjective.

Biden’s Vote Looks more like a Voting Miracle

So lets consider some facts. President Trump received more votes than any previous incumbent seeking reelection. He got 11 million more votes than he did in 2016, the third largest rise in support ever for an incumbent President.

By way of comparison, President Obama was comfortably reelected in 2012 with 3.5 million fewer votes than he received in 2008.

Trump’s vote increased so much because, according to exit polls, he performed far better with many key demographic groups.

Ninety-five percent of Republicans voted for him. He did extraordinarily well with rural male working-class whites.

He earned the highest share of all minority votes for a Republican since 1960.

Trump grew his support among black voters by 50 percent over 2016. Nationally, Joe Biden’s black support fell well below 90 percent, the level below which Democratic presidential candidates usually lose.

Trump increased his share of the national Hispanic vote to 35 percent. With 60 percent or less of the national Hispanic vote, it is arithmetically impossible for a Democratic presidential candidate to win Florida, Arizona, Nevada, and New Mexico.

Bellwether states swung further in Trump’s direction than in 2016.

Florida, Ohio and Iowa each defied America’s media polls with huge wins for Trump.

Since 1852, only Richard Nixon has lost the electoral college after winning this trio, and that 1960 defeat to John F. Kennedy is still the subject of great suspicion.

Midwestern states Michigan, Pennsylvania, and Wisconsin always swing in the same direction as Ohio and Iowa, their regional peers. Ohio likewise swings with Florida. And they did on the election day, but then just these few important states took a sharp change in direction after the Media and Democrats announced a suspicious halt to the count in the early morning.

Current tallies show that, outside of a few cities, the Rust Belt swung in Trump’s direction. Yet, Biden leads in Michigan, Pennsylvania, and Wisconsin because of an apparent avalanche of black votes in just a few Democrat run cities such as Detroit, Philadelphia, and Milwaukee, an avalanche that occurred between Midnight on election day November 3 and 7.00 am the next day November 4th.

Biden’s ‘winning’ margin was derived almost entirely from such voters in these cities, as coincidentally his black vote spiked only in exactly the locations necessary to secure victory. He did not receive comparable levels of support among comparable demographic groups in comparable states, which is highly unusual for the presidential victor.

We are told that Biden won more votes nationally than any presidential candidate in history. But he only won a record low 17 percent of counties; he only won 524 counties, Obama won 873 counties in 2008. Yet, Biden somehow outdid Obama in total votes.

Victorious presidential candidates, especially challengers, usually have down-ballot coattails; Biden did not.

The Republicans held the Senate and enjoyed a ‘red wave’ in the House, where they gained a large number of seats while winning all 27 toss-up contests. Trump’s party did not lose a single state legislature and actually made gains at the state level.

Lets look at Non-Polling Metrics –

Another anomaly is found in the comparison between the polls and non-polling metrics.

The latter include: party registrations trends;

the candidates’ respective primary votes; candidate enthusiasm;

social media followings; broadcast and digital media ratings;

online searches; the number of (especially small) donors;

and the number of individuals betting on each candidate.

When the polls err, non-polling metrics do not; they have a 100 percent record.

Every non-polling metric forecast Trump’s reelection.

For Trump to lose this election, the mainstream polls needed to be correct, which they were not.

Furthermore, for Trump to lose, not only did one or more of these non polling metrics have to be wrong for the first time ever, but every single one had to be wrong, and at the very same time; not an impossible outcome, but extremely unlikely nonetheless.

Atypical voting patterns married with misses by polling and non-polling metrics should give observers pause for thought. Adding to the mystery is a cascade of information about the bizarre manner in which so many ballots were accumulated and counted.

The following peculiarities also lack compelling explanations:

1. Late on election night, with Trump comfortably ahead, many swing states stopped counting ballots. In most cases, observers were removed from the counting facilities. Counting generally continued without the observers

2. Statistically abnormal vote counts were the new normal when counting resumed. They were unusually large in size (hundreds of thousands) and had an unusually high (90 percent and above) Biden-to-Trump ratio.

In the early hours of November 4th, 2020, Democratic candidate Joe Biden received several major “vote spikes” that substantially — and decisively — improved his electoral position in Michigan, Wisconsin, and Georgia.

Much skepticism and uncertainty surrounds these “vote spikes.” Critics point to suspicious vote counting practices, extreme differences between the two major candidates’ vote counts, and the timing of the vote updates, among other factors, to cast doubt on the legitimacy of some of these spikes.

While data analysis cannot on its own demonstrate fraud or systemic issues, it can point us to statistically anomalous cases that invite further scrutiny. 

3. Late arriving ballots were counted. In Pennsylvania, 23,000 absentee ballots have impossible postal return dates and another 86,000 have such extraordinary return dates they raise serious questions

4. The failure to match signatures on mail-in ballots. The destruction of mail in ballot envelopes, which must contain signatures

5. Historically low absentee ballot rejection rates despite the massive expansion of mail voting. Such is Biden’s narrow margin that, as political analyst Robert Barnes observes, ‘If the states simply imposed the same absentee ballot rejection rate as recent cycles, then Trump wins the election’

6. Missing votes. In Delaware County, Pennsylvania, 50,000 votes held on 47 USB cards are missing

7. Non-resident voters. Matt Braynard’s Voter Integrity Project estimates that 20,312 people who no longer met residency requirements cast ballots in Georgia. Biden’s margin is 12,670 votes

8. Serious ‘chain of custody’ breakdowns. Invalid residential addresses. Record numbers of dead people voting. Ballots in pristine condition without creases, that is, they had not been mailed in envelopes as required by law

9. Statistical anomalies. In Georgia, Biden overtook Trump with 89 percent of the votes counted. For the next 53 batches of votes counted, Biden led Trump by the same exact 50.05 to 49.95 percent margin in every single batch. It is particularly perplexing that all statistical anomalies and tabulation abnormalities were in Biden’s favor. Whether the cause was simple human error or nefarious activity, or a combination, clearly something peculiar happened.

What the RAW DATA tells us

Looking at 8,954 individual vote updates (differences in vote totals for each candidate between successive changes to the running vote totals, colloquially also referred to as “dumps” or “batches”), we discover a remarkably consistent mathematical property: there is a clear inverse relationship between difference in candidates’ vote counts and and the ratio of the vote counts. (In other words, it’s not surprising to see vote updates with large margins, and it’s not surprising to see vote updates with a very large ratio of support between the candidates, but it is surprising to see vote updates which are both). 

Nearly every vote update, across all states of all sizes and political leanings follow this statistical pattern.

A very small number, however, are stark and marked aberrations.

Of the seven vote updates which follow this normal and expected pattern the least, four individual vote updates — two in Michigan, one in Wisconsin, and one in Georgia — stand out, as being enormously influential with respect to this property, the overall count and what the Media called as a result, and to make this all look and sound even more suspicious, all occurred within the same five hour window, in the early morning hours of November 4th after the Media and Democrats had called a halt to the count and Republican Observers had been ejected from vote counting facilities..

We are able to quantify the extent of compliance any update to the vote count accords with this property and discover that, of the 8,954 vote updates used in the analysis, these four decisive updates were the 1st, 2nd, 4th, and 7th most anomalous updates in the entire data set.

Not only does each of these vote updates not follow the generally observed pattern, but the anomalous behavior of these updates is particularly extreme. These vote Vote Count updates are outliers of the outliers in the whole of the national count.

The four vote updates in question are: 

  1. An update in Michigan listed as of 6:31AM Eastern Time on November 4th, 2020, which shows 141,258 votes for Joe Biden and 5,968 votes for Donald Trump
  2. An update in Wisconsin listed as 3:42AM Central Time on November 4th, 2020, which shows 143,379 votes for Joe Biden and 25,163 votes for Donald Trump
  3. A vote update in Georgia listed at 1:34AM Eastern Time on November 4th, 2020, which shows 136,155 votes for Joe Biden and 29,115 votes for Donald Trump
  4. An update in Michigan listed as of 3:50AM Eastern Time on November 4th, 2020, which shows 54,497 votes for Joe Biden and 4,718 votes for Donald Trump

In the following reportwe find that the extents of the respective anomalies here are more than the margin of victory in all three states — Michigan, Wisconsin, and Georgia — which collectively represent forty-two electoral votes.

Extensive mathematical detail is provided and the data and the code (for the data-curation, data transformation, plotting, and modeling) are all attached in the appendix to this document[1].

Background

Late on Election Night 2020, President Donald J. Trump had a lead of around 100,000 votes in Wisconsin, a lead of around 300,000 votes in Michigan, and a lead of around 700,000 votes in Pennsylvania. Back-of-the-envelope calculations showed that in order to overtake President Trump, Joe Biden would have to substantially improve his performance in the remaining precincts — many of which were in heavily blue areas like Detroit, Milwaukee, and Philadelphia. 

On Election Night, conflicting news reports came in that various precincts were stopping their count for the evening, sending election officials home, or re-starting their counts.

There remains a large amount of confusion to this day about the extent to which various precincts stopped counting, as well as the extent to which any state election laws or rules were broken by sending election officials home prematurely. Whatever the case is, various precincts in Wisconsin, Michigan, and Pennsylvania continued to report numbers throughout the night. 

By the early hours of the following morning, Wisconsin had flipped blue, as did Michigan soon after.

A few days later, Georgia and Pennsylvania followed suit. Given the uncertain context, many American observers and commentators were immediately uncomfortable or skeptical of these trends. 

For context, using publicly available data from the New York Times, here is a visualization of  the number of votes by candidate in Michigan from the beginning of election night to 7pm Eastern Standard Time (EST) on November 4th, 2020:

Fig. 1. X-axis is the Month-Year Hour of the time, Y-axis is the number of votes as of that time, expressed in millions of votes.  The red series is the running number of votes for Donald Trump, and the blue series the running number of votes for Joe Biden.

As this graph shows, Joe Biden overtook President Trump’s lead through a small number of vote updates which broke overwhelmingly for Biden in Michigan in the early hours of the morning of November 4th.

The situation in Wisconsin is even more stark: a single update to the vote count brought Biden from trailing by over 100,000 votes into the lead. Here is the comparable graph, over the same time range, for Wisconsin, with the x-axis (time) expressed in Central Standard Time (CST):

Fig. 2. X-axis is the Month-Year Hour of the time, Y-axis is the number of votes as of that time, expressed in millions of votes.  The red series is the running number of votes for Donald Trump, and the blue series the running number of votes for Joe Biden.

While some commentators provided relatively partisan analysis, others merely expressed surprise at the near-vertical leaps in some of these vote updates.

Is it likely this phenomenon would arise organically? In an attempt to address this question, this report assesses how extreme and unusual these spikes are with respect to both other vote updates in the states of Michigan, Wisconsin, and Georgia, as well as those around the nation.

Through several investigative mechanisms, we find these four vote updates to be extraordinarily anomalous. While these alone do not prove the existence of fraud or systemic issue, it invites further scrutiny.

The Concept, the Intuition, and the Measurement

Data analysis relies on recognizing and evaluating patterns in data. When we find anomalous data, that is often an indication of underlying differences. This is why in this report we focus on these four vote updates.

There are also a number of general intuitions upon which we draw to direct our research. In general, the larger the sample size, the smaller we expect the deviation from the population average to be. While anomalous vote ratios may occur, the statistical chance of anomalous margins goes down as the size of the sample (or vote update) goes up.

The basic intuition is: big margins are one thing, and so are super-skewed results, but it’s weird to have them both at the same time, as they generally become inversely related as either value increases.

We will demonstrate below that the data overwhelmingly follow this intuition, but that four key vote updates identified by this report cut against this intuition.

In particular, we will show the existence of a very strong inverse relationship within vote updates, across all states and times, between the difference of votes for Joe Biden and Donald Trump (often referred to as the “Biden-Trump margin”) and the the ratio of Joe Biden’s votes to Donald Trump’s votes (often referred to as the “Biden:Trump ratio”). 

As described in more detail in the next section, we take the natural logarithm of the ratios so that they are symmetric, i.e. so that we are not treating the two candidates differently when graphing and analyzing.  These values are often referred to as “Biden:Trump log-ratio.”  Since the logarithm is an order-preserving transformation — i.e. if x is bigger than y, then log(x) will be bigger than log(y), and vice versa — we sometimes use them interchangeably when precision is not required.

At any geographical level, we can test the assumption of an inverse relationship between vote update size and the extremity of the ratio between the candidates’ votes, and, as we will see here, the relationship is extremely strong.  Across states red and blue, where turnout is high and low, there is an obvious inverse relationship between the two.

Measuring This Relationship Between The Candidate’s Margin and their Ratio

Let us now attempt to quantify the nature of the inverse relationship in the context of a particular state. First we take our data set of running vote totals[2] for each state, and, for each state, calculate the vote differential for each candidate between updates. This produces a sequence of vote differences, the sum of which, within any given state, is the total.

To begin, we consider each sequential update in the state of Michigan where the vote totals for both Trump and Biden are greater than zero[3].  For each of these, we compute two values:

  • The difference between the number of votes for Biden and the number of votes for Trump — the “margin”
  • The logarithm[4] of the ratio between the number of votes for Biden and the number of votes for Trump — the “log-ratio”

Note: both of these metrics are symmetrical. If we let f1 be the first metric and f2 the second, the reader will note that, for any positive numbers (X, Y):

And that:

In other words, given X for Biden and Y for Trump, either metric will produce a score which is the opposite of what it would produce if the update instead had Y votes for Biden and X for Trump.  This property is extremely useful, and will come in handy during the statistical analysis.

Readers might ask: Why are you measuring the ratio? Why not measure the difference between the vote proportions (or, equivalently, their percentages). The answer to this lies in what we are looking for, i.e. evidence of fraud or foul play which manifests in extremely unusual outcomes.  In particular, ratios are almost never used in expressing vote counts (one typically hears of percentages or, when a race is close, numbers) and so anyone committing fraud and looking to “cover their tracks” is more likely to be “gaming” the metrics they’re used to, and much more likely to leave tells in metrics they’re not considering.

This obscures critical differences between the two statistics.

  1. Ratios demonstrate an important property: the farther ahead a candidate is, the harder it is to move the next 1 percent ahead. They reflect the relative difficulty of each marginal vote as the pool of remaining votes decreases.As a candidate approaches 0% or 100% of the vote, the rates at which the ratio of that candidate’s votes to the other candidate’s votes converge to zero or infinity are very different.  
  2. Ratios allow us to spot a potential sign of fraud: unusually low ratios between the losing (major) candidate and other, less well-known candidates.  Because those who watch and participate in elections tend not to think in these terms, if there is fraud, they’re much less likely to have covered their tracks in this respect.  A tin-pot-dictator style election where the favored candidate gets 99% of the vote is obviously suspect, but less attention is often paid to details like whether the ratio between the most popular losing candidate and long-shot third-party candidates actually makes sense[5].  Looking at metrics which are less popular in practical use will be tremendously helpful here, as we will see.

This election represents an extraordinary and unique opportunity for election integrity analysts and the application of statistical fraud detection research, as it is likely the first national election in American history, at the very least, where the general public has had access to time-series election data. Even well-respected academic papers which study election fraud in other countries[6] seem to mostly study after-the-fact information about final tallies; analysis is done on statistics about voter turnout, digit frequencies, and other information which is available in after-the-fact official numbers. After all, if reports of widespread fraud and corruption ordered from the top in elections in, e.g., Russia, Uganda, Ukraine, Iran, etc., are to be believed, then those governments, which tend to have much more control over what can and cannot be published than our government, are unlikely to want to increase the number of dimensions along which their claim to legitimacy can be audited.

A Look at Michigan

Let us now calculate these two values for each vote update in Michigan where both Biden and Trump have positive values. If it follows the intuition that there as an inverse relationship between the margins of an update and its ratio, we should expect to see a large cluster of data with a few points above, below, to the left and right, and virtually no points in either the top right (which would represent a simultaneously extreme Biden-Trump margin and Biden:Trump ratio) or the bottom left (which is analogous but favorable to Trump).

Here is that distribution, presented as a scatter plot, with the numerical margins as the X-axis and the log-ratios as the Y-axis.

Fig. 3.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each vote update, and the Y-axis is the natural logarithm of the ratio of the two.

As we can see, most observations follow the basic contour of our hypothesis, i.e. the more extreme an update is in one respect, the less extreme it is in another.  

For example, the update at (-3,622, -6.449), has a fairly extreme ratio of Biden:Trump votes — about 1:632 — but is not very large, producing only a margin of -3,622 votes for Biden, which, as we can see, is not terribly extreme in the context of this distribution.  Similarly, the point all the way to the left, (-66,456, -0.816), is one where Biden’s margin is a significant -66,546, but where the ratio, of about 1:2.26, is not particularly unusual for a vote update which favors Trump.

We can see this pattern as well in almost every Biden-favoring update as well.  For example, the update with the 3rd greatest margin for Biden, at (34,450, 0.296), is 134,326 Biden votes to 99,867 Trump votes, and only has a Biden:Trump ratio of 1.34:1. And the update with the 3rd greatest Biden:Trump ratio, at (6,091, 2.184), in which Biden received 6,863 votes and Trump received 773 votes, has a fairly extreme ratio of 8.884 but only nets Biden 6,091 votes, a relatively small amount compared to what we will examine next.

Two points stand out.

Let us first consider the less extreme of these, i.e. the point at (49,779, 2.447).  This point, representing a vote update which went 54,497 for Biden and 4,718 for Trump and arrived at 3:50am ET on November 4th 2020, is both the second-largest vote margin of Biden’s, at 49,779, and also has the second largest Biden:Trump ratio at 11.55:1. As we can see and as was described above, the update with the next largest margin was an update with merely 7,776 votes, while this update had over 7 times as many votes and broke more heavily for Biden.

The oddness of the update described above pales in comparison to that of the update in the top right corner, however. That update, at (135,290, 3.164), represents the vote update described at the top of this report, and is responsible for the extremely noticeable spike which nearly eliminated Trump’s lead in one shot. It arrived at 6:31am ET on November 4th, and went 141,258 for Biden to 5,968 for Trump — representing both the largest vote margin for Biden of any of the 502 updates we have here, at 135,290, while also representing, by a factor of more than 2, the largest Biden:Trump ratio, at a whopping 23.67:1 (the log of which is 3.16).  As we will see when comparing with other states, by our metric this is the single most anomalous point in the nation.

This update is also particularly interesting for another reason: there are 2,546 non-two-party votes, while Donald Trump only has 5,968. Here is a histogram of vote-total-weighted Other:Trump ratios[7]:

Fig. 4.  The x-axis is, for each vote update, the ratio of other (non-2-party) votes to votes for Trump, multiplied by the number of total votes in that update.  The y-axis is the number of vote updates in that “bin,” where each bin has a range of 500.

As we see, when we weight by the number of votes in any given update, this update is particularly anomalous. The next closest vote-weighted Other:Trump ratio is less than two-thirds of this one, and the median — 137.56 — is smaller by a factor of about 464.5.  For such a large batch of votes to be counted while also showing such an exceptionally poor performance of Trump relative to the non-two-party vote is clearly very surprising.

In particular, it calls into serious question the veracity of this vote update, and is perhaps some of the strongest direct evidence of fraud in this entire report.  Someone looking to fraudulently improve Joe Biden’s margins relative to Donald Trump is likely to be focused on covering their tracks by keeping Joe Biden’s share of the update at a reasonable value.  95% might seem plausible, but 99.9% at this scale becomes prima facie implausible to any honest observer.  One effective way of achieving the desired goal of decreasing Donald Trump’s lead at this point would have been to suppress the Trump vote while artificially inflating the non-two-party vote in an attempt to disguise just how Biden-favoring this update actually was.  Indeed, this is precisely the reason this report uses ratios — because they are a metric virtually never used for any practical purpose in discussing election results, someone committing fraud is far less likely to consider how unusual a ratio might look.  In particular, because the non-two-party candidates received far less media attention than in the 2016 Presidential election, and the Green Party candidate was even successfully sued off of the ballot in one or more states, it is hard to believe that this vote update only favored Trump over the non-two-party vote by less than a factor of 2.5, when the statewide ratio was over 31[8].

Absent a compelling explanation of why this particular update — at such a crucial time, in a crucial state, which improved Biden’s standing in the state so dramatically — also had non-two-party votes performing so unusually relative to Trump votes, it seems unlikely that this vote update reflects an honest accounting of the legitimate votes.

Subsequent sections of this report quantify how extreme it is in other respects and consider the implications if it had been slightly less extreme.

A Look at Wisconsin

Here is the analogous graph for Wisconsin.

Fig. 5.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each vote update, and the Y-axis is the natural logarithm of the ratio of the two.

The patterns in this graph are somewhat more bizarre.  The updates favoring Trump (i.e. those to the left of zero on the x-axis) exhibit an inverse relationship between the margin of victory in a Trump-favoring update and the ratio between Trump and Biden votes.  For example, the update at, (-5,433, -4.564), which is the most extreme in the state in terms of ratio, is from an unusually Trump-favoring batch of ballots which went 5,490 for Trump to 57 for Biden, i.e. a Trump:Biden ratio of about 96:1 for Trump.  This number itself is quite large, but, critically, it is not anomalous with respect to the shape of the distribution. The tell-tale sign of oddity here is not extremity with respect to either value, but co-extremity.

Biden’s distribution looks slightly odd here, but there is one point which especially stands out, i.e. the one in the top right, at (118,215, 1.74).  This was the vote update which arrived at 3:42am CST on November 4th, and went 143,379 for Biden to 25,163 for Trump[9], giving a margin of 118,215 and a Biden:Trump ratio of about 5.7:1 — about 3 times larger than the update with the next largest margin (which was 39,499).  At the same time, only one update — one with a mere 6,435 votes (i.e. about a factor of 18 fewer than the update in question) which went 3,037 for Biden to 495 for Trump — has a larger ratio, at around 6.14:1.

A Look at Georgia:

Fig. 6.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each vote update, and the Y-axis is the natural logarithm of the ratio of the two.

This one seems only slightly more anomalous than other such graphs, but, as we will see, actually contains two of the nine most anomalous vote updates in our combined distribution of 8.954 vote updates. In particular, the point at (136,155, 1.543), representing a vote update which arrived at 1:34am EST on November 4th, is the update with the largest margin of all of the updates in Georgia — it also has the 10th largest Biden:Trump ratio. There are a few smaller updates with more extreme ratios, but, as we will detail later in this report, this point is in fact unusual.

A Short Survey of Other States

We now turn to other states, particularly those with similar characteristics (e.g. a swing or blue state where one or two urban cores offsets an otherwise very Republican population).  These help us establish an initial baseline of what these distributions should look like within any state before we begin comparing updates directly across states.

Pennsylvania:

Fig. 7.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each vote update, and the Y-axis is the natural logarithm of the ratio of the two.

The inverse relationship is immediately visible here.  We have points near the bottom (representing high Trump:Biden vote ratios), a few points far to the left (representing high Trump – Biden values), and a couple (much farther) off to the right, representing a high Biden-Trump margin, but which are not particularly extreme in terms of their Biden:Trump ratio.

Minnesota:

Fig. 8.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each vote update, and the Y-axis is the natural logarithm of the ratio of the two.

While there is an update which is more extreme in terms of how large the Trump:Biden ratio is, and several updates with extremely large Trump-Biden margins, we see the basic shape remains the same.

New York:

Fig. 9.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each vote update, and the Y-axis is the natural logarithm of the ratio of the two.

The vote margins for each update are clustered fairly heavily around zero, while the few updates which have exceptionally large margins for either candidate have ratios which are not nearly as extreme as those of many other updates.

Consolidating, Comparing, and Measuring

Having taken a brief tour of states with similar characteristics, i.e. where Joe Biden is currently in the lead and the Democratic vote comes overwhelmingly from a single urban area (or perhaps two, in the case of Pennsylvania), we can see that the Michigan and Wisconsin graphs both look unusual. In order to more rigorously assess the extent to which this is actually anomalous, it is necessary to accommodate the reality that the typical Biden-Trump margin and Biden:Trump ratio will vary substantially between states. If we merely take these values as they are, then most of the differences between, e.g., Alabama and California would likely just be artifacts of the massive discrepancies between how the candidates each performed in these states.

To achieve this, we can use a data transformation process called standardization.  This is a process by which, for a series of numerical data, the mean of the data is subtracted from each point, and then the result is divided by the standard deviation.  This will produce a series of distributions which permit an apples-to-apples comparison of these values (i.e. per-vote-update Biden-Trump margin and Biden:Trump log-ratio) between states which are both very different in size and lean very differently, politically.  Data standardization is a very common technique in machine learning for training models on data sets with very different numerical magnitudes and means[10], as it provides precisely the functionality we need here.

We can thus standardize each individual (margin, log-ratio) point within its state[11], and plot it as we did before. Here is what that graph looks like. The values for Michigan are in red, those for Wisconsin are green, and the values for all other states are blue:

Fig. 10.  The X-axis is the difference between the number of Biden votes and the number of Trump votes in each update, standardized by the distribution of such values of its state.  The Y-axis is the log-ratio of Biden votes to Trump votes in each update, again standardized by the distribution of such values in its state.

Out of these 8,954 vote updates across the country, we can see how overwhelming the pattern is.  In particular, we see that — with a few notable exceptions — as one value grows more extreme in any direction, the other tends to become less extreme.

This brings us to the visually identifiable exceptions.

Directing our attention to the points on the far right end of the distribution, i.e. those which have the most extreme Biden-Trump margin with respect to their state, we immediately see one point from Michigan, which is quite far above where the shape of the plot would otherwise predict it being.  This, the point at (15.494, 4.989), is the vote update which arrived at 6:31am EST on November 4th, went 141,257 to Biden and 5,968 to Trump. Recall: this update had both the largest margin (135,290) of any of the 574 updates[12] in Michigan, by about 85,000 votes and a factor of about 2.7 over that of the update with the next-largest update, (5.679, 3.912) — which, critically (and surprisingly, vis a vis what this distribution shows), was both the second largest in terms of Biden-Trump margin and Biden:Trump ratio[13].  It also had the largest Biden:Trump ratio (roughly 23.69:1), by more than a factor of 2 over that of the update with the next-largest Biden:Trump ratio.  The visual discrepancy between that update and the overwhelming pattern followed by the other updates is glaring, and we will shortly quantify just how extreme it is.

Next, consider the green dot just slightly down and to the left of the red outlier.  This is the vote update in Wisconsin which arrived at 3:42am CST on November 4th, which went 143,379 for Biden and 25,163 for Trump, for a margin of 118,215[14].  It was the update with the largest Biden – Trump margin in Wisconsin by a large distance[15] and, in Biden:Trump ratio, was second largest — second only to an update which was 26 times smaller and yet only slightly more extreme in its ratio[16]. 

We also see a red dot at (5.679, 3.912), which corresponds to the vote update which arrived at 3:50am EST on November 4th and went 54,497 for Biden to 4,718 for Trump, for a margin of 49,779 and a ratio of 11.55:1. It is worth noting that, while not nearly as anomalous as the 6:31am EST update, this one was very extreme along both dimensions in its own right.  As we will see, however, it ends up being the seventh most extreme value in terms of its non-adherence with the distribution as a whole.

While both of these points would be unusual on their own, it is exceptionally unlikely that both of them would have come from the same state, critical to the election, less than three hours apart during an overnight counting process — a process subject to great controversy and where there remain, nearly three weeks from election day, many unknowns. Together, these two vote updates  provided Joe Biden with the votes required to deliver him the lead in the state.

Quantifying the Extremity

Having demonstrated visually how anomalous the four key vote updates are, we can now proceed to attempt to quantify how unusual it is that these three points exist at once and that two of them are from the same state.

The below graph has two particularly interesting visual properties:

  1. The graph is presented two-dimensionally, but it’s really three-dimensional. It’s visibly much denser in the center, has what appear to be something like two normal distributions, and as you move farther from the origin along a positive-sloping line which runs through the origin, the lower the density you can expect.
  2. The outer “edges” of the graph, in the top-right and bottom-left quadrants, closely resemble the shape of the line y = 1 / x.

We similarly expect points to be in both the top-right and bottom-left quadrants, and between an outer line which has the shape of y = 1 / x and the origin.  Since these values will thus mostly be either both negative or both positive, we can see that multiplying each point’s x-coordinate with its y-coordinate is a useful way of assessing the extent to which it follows this sort of distribution.  Since there are more points near the origin than there are on the visible “boundary lines” (i.e. the sequences of points on the outer edges in the first and third quadrants which visibly form these lines which look like a graph, if perhaps scaled, of y = 1/x).

We thus, for each (again, both standardized by state) coordinate pair of Biden-Trump margin and the log-ratio of Biden to Trump votes, can multiply these values and examine the distribution of the resulting products. Here, the larger a value is in magnitude, the less it follows the non-co-extremity. Plotting these products gives us: 

Fig. 11.  Histogram of products of x and y values for each coordinate pair in Fig. 10

As we can see, the values are overwhelmingly concentrated near the median, and the graph is profoundly right-skewed — otherwise, the x-axis would not need to stretch all the way to 80.  All but 60 out of 8,954 unique updates have values less than 10, and all but 10 have values less than 20. In other words, an overwhelming share of updates seem to track this rule pretty closely, but a small number of updates are truly extreme outliers.

A quick dive into these ten points reveals data which, by this point in the report, will be very familiar to the reader:

As we can see, four of the seven most anomalous vote updates — which is to say, updates in which the margin and ratio are co-extreme — are in election-critical states and occurred during the same five hour period where the circumstances on the ground were (and remain) contested and highly suspicious.

It is worth noting here that roughly 15% of the vote updates in the data set of 8,954 were from these three states.  If we assumed it equally likely that any particular state should end up at any of these extreme points, there would be about a 1.2% chance that three states are represented in three out of the top four or four out of the top seven spots, and about a 0.99% chance that these three states would occupy five out of the top seven spots. It is thus very surprising to see the states in question be so disproportionately represented in the top 0.11% of the distribution of co-extremity[17].

Important Considerations

It is important to note one crucial indicator of why these results are bizarre.  In virtually all other cases, areas which are very pro-Biden or pro-Trump have vote updates of varying size, and so a large vote update heavily favoring one candidate is almost always accompanied by even smaller updates which have a higher variance in the ratio, and at least some of them will favor the candidate who won the largest batch.

In particular, to accept the results as seen in Michigan as legitimate, one would need to believe that the one or two most possible pro-Biden areas of the state were somehow each counted their ballots entirely in one or two vote updates.  If they were counted incrementally and released in smaller batches, as is typically the case, we would expect to see smaller updates with higher variance in outcome, and would almost certainly see updates with a higher Biden:Trump ratio than the two Michigan updates discussed in this report.

Indeed, if it is subsequently discovered that these did not comprise the entire count (for either mail-in votes or all votes) in these areas, then these results should be regarded with extreme suspicion.  While vote counts are by no means a random sample nationally, given a small enough sub-population at which votes are counted, they eventually are.  If it can be shown by those with access to time-series county-level (or precinct-level) data that, for whichever counties or precincts reported in this update, that there were other updates (or other updates with mail-in ballots), then these results become almost impossible to believe.  

This is to say, the believability of these updates relies on the premise that the one or two most Biden-favoring parts of the state (perhaps by ballot type) were counted entirely in these two batches. 

If it cannot be shown that the ballots counted during these spikes were qualitatively different from all other vote updates in Michigan, then the results are likely too extreme along multiple dimensions to be accepted at face value.

One would also need to believe that mail-in ballots, which have generally been understood to be more pro-Biden, sometimes substantially so, were counted in their entirety in these regions.  While this data set does not provide breakdowns of how many votes in each update came from different types of votes, it is extremely surprising that we do not see smaller vote updates with mail-in votes which favor Biden more heavily.

This is also the case in Wisconsin, there the update discussed in this report, which had the largest Biden margin by far, also had the second-highest Biden:Trump ratio, by only a small amount.  Accepting this at face value requires the belief that the most pro-Biden subset of the votes — by geography and vote type — was counted entirely in one batch.  It would be extremely surprising if all mail-in ballots in the two most favoring Biden counties in the state, Dane and Milwaukee County, were entirely contained in this batch, and so it raises the question as to why we didn’t see even more pro-Biden updates in smaller, higher-variance vote updates in these heavily Democratic areas.  If we are to accept that these votes were counted entirely in one batch, this raises serious questions as well.  In particular, given the ambiguity — to this day — about where the vote-tabulation process was stopped and why, it makes little sense why these votes would be released in such an unusually large batch.

All of this is especially surprising when viewed in contrast to the prevailing analysis of the election, i.e. that Joe Biden’s victory was the result of improved performance in suburban areas. Looking at a map of final results by county, it is highly likely that these vote updates came from more densely-populated urban counties where Biden’s ratios were much higher.  The findings here call that into question, however, as we can see that he relied heavily on four extremely aberrant vote updates which were almost certainly in heavily pro-Biden urban areas to provide a much-needed boost in the early hours of November 4th.

Conclusion

This report studies 8,954 individual updates to the vote totals in all 50 states and finds that four individual updates — two of which were widely noticed on the internet, including by the President — are profoundly anomalous; they deviate from a pattern which is otherwise found in the vast majority of the remaining 8,950 vote updates. The findings presented by this report [28]suggest that four vote count updates — which collectively were decisive in Michigan, Wisconsin, and Georgia, and thus decisive of a critical forty-two electoral votes — are especially anomalous and merit further investigation.

In particular, the finding that the broader data follows general patterns and our ability to measure just how much any individual vote update does — or doesn’t — follow this pattern allows us to make concrete claims about both how extreme any given vote update is and about what any particular vote update might have looked like, had it been less extreme one one axis or another.

We further find that if these updates were only more extreme than 99% of all updates nationally in terms of their deviation from this generally-observed pattern, that, holding all else equal, Joe Biden may very well have lost the states of Michigan, Wisconsin, and Georgia, and that he would have 42 fewer Electoral votes — putting Biden below the number required to win the Presidency.  Either way, it is indisputable that his margin of victory in these three states relies on four most anomalous vote updates identified by the metric developed in this report.

We once again note that this analysis is largely restricted to four individual vote updates out of a sample of nearly 9,000. This report by no means suggests stopping investigations in Michigan, Wisconsin, Pennsylvania, Georgia, or elsewhere; it is merely that these four key ballot updates are both profoundly anomalous with respect to a metric which removes any component of different states having different partisan leanings or a different number of voters. Furthermore, this analysis does not require that we regard the final vote totals in any of these states (or counties thereof) as suspicious, nor, critically, does it require that we accept that the observed data should follow any particular distribution a priori.  We merely show that the data, adjusted appropriately to remove differences in size and political leaning between states, does follow a certain pattern, and that four key vote updates deviate profoundly from that pattern.

It is our belief that the extraordinarily anomalous nature of the studied vote updates here, combined with the staggering political implications, demands immediate and thorough investigation.

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