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by Simon Fish
Executive Summary
We find considerable evidence consistent with the possibility of electoral fraud in vote counts in Montgomery County, PA.
In particular, we examine a highly anomalous update to mail vote totals in the NYT/Edison data which enormously benefited Biden, and which looks suspicious on a number of dimensions.
At a high level, our results are suggestive of a new and highly suspicious batch of mail ballots being added to the count sometime between Wednesday early morning and Thursday morning. These ballots are drawn from an implausible distribution that enormously favored Biden and simultaneously harmed Trump (the latter being done in addition by allocating more votes to Jorgensen). Said mail ballots end up being extremely different both from the mail ballots that came before (as measured in NYT data), and the mail ballots that came afterwards (as measured in the county’s own data).
The key evidence is as follows:
⦁ On Thursday November 5th at 9:09am a large batch of 90,022 mail/absentee votes get added that has over 95% support for Biden, but total votes to go up by only 9,534, implying that in-person votes actually went down by 80,488. On its own, this is a very strange irregularity, as ballots cannot disappear, and in-person ballots cannot become mail ballots. Something is wrong in the reported data, the only question is what.
⦁ The new batch of 90,022 mail ballots looks nothing like existing mail ballots. If the update is a data error, it must be a complicated error along multiple dimensions and is unlikely to be a simple typo. The new batch is improbable on four separate dimensions:
⦁ It has a level of support for Biden (over 95%) that is statistically impossible to have come from the same distribution of mail ballots counted up to that point (74.9% for Biden)
⦁ Every comparison of pairs of candidates shows improbable changes. This is important, as it helps rule out the possibility that a single typo in the data drives the pattern.
⦁ Irrespective of the old distribution, the new batch is extremely unlikely on its own terms, as it has a ratio of support for Jorgenson relative to Trump (20%) that is higher than virtually every county in America. The last fact is consistent with aiming to get Biden’s vote share “high but not impossibly high” while simultaneously trying to not give any more votes to Trump than absolutely necessary.
⦁ The distribution of the ballots being removed from the in-person counts is even more implausible (98.1% Biden), making it difficult to explain the overall vote update as being due to genuine mail ballots having been previously incorrectly classified as in-person.
⦁ Anomalies of this magnitude are extremely rare in the NYT database. Montgomery’s reduction of 80,488 in-person votes is the fourth highest vote reduction in the entire database. Over half of these involve changes of less than 100 votes, and 28% involve changes of just one vote. Of the remaining errors, many can be easily understood as examples of exactly the phenomena ruled out above (e.g. simple vote-type misclassifications).
⦁ Independent confirmation of the two numbers suggests Edison’s numbers are accurate reflections of the County data. Edison’s report of total absentee ballots counted in their update at 5:43am Wednesday November 5th is very close to (and slightly below) media twitter reports of total absentee ballots counted a few minutes later in the county data, suggesting that these early Edison absentee vote totals are likely accurate reflections of the underlying county data. Meanwhile, Edison snapshots on November 8th precisely match County snapshots on November 10th.
⦁ To test this hypothesis further, and to help rule out the possibility that this is all due to NYT/Edison data errors, after the initial anomaly was uncovered, we scraped multiple snapshots of the county’s own data at the precinct level. The changes between the two snapshots reveal that the earlier arriving mail ballots (which included the anomalous update) show a significantly higher vote share for Biden than the mail votes which were counted later in the same precinct. This shows that something is changing in the distribution of mail ballots counted within each precinct, and the earlier ballots showed a stronger tendency to favor Biden.
Adding all this evidence together, there is a strong case for the following interpretation:
-Some time after election night, a very large batch of mail ballots were counted that showed an enormous advantage for Biden-This batch looks nothing like the mail ballots counted up to that point in the NYT data, and also looks different from the mail ballots counted later in each precinct as measured using the county’s own data
-The batch looks implausible on its own face, in terms of relative vote shares of Libertarian and Republican votes
-The updates are difficult to reconcile with simple data errors like genuine mail ballots being mis-classified as in-person, or a single candidate total being incorrectly entered as a typo.
These facts present strong circumstantial evidence suggesting fraud in mail votes in Montgomery County, and need to be investigated further.
Raw data of the NYT updates is here:
Raw data of the county data is here:
https://ufile.io/vqmshqo3
https://ufile.io/q5penzjs
⦁ Summary of Facts Consistent with Fraud, but Puzzling Under Alternative Explanations
The facts described below are documented using data available from the New York Times feed of Edison data election results, which was helpfully scraped by other researchers in real time. The unusual nature of this change caused us to begin collecting the County’s own data, to see how the updates since then compared, and for a time period considerably after the initial anomaly.
Second, we consider throughout the possibility that the errors are the result of innocent mistakes being made, either by Edison or the New York Times in collecting or publishing their data, or by the County themselves in their early vote counts. Counting processes have all sorts of innocent errors, and weirdness in data is well understood by anyone who has ever worked with it. Machines can break. Data can get transcribed wrong. Code updating websites, both for governments and data vendors, can be faulty. Genuine ballots may be incorrectly classified as one type or another during the counting process. Corrections of earlier errors, even if well-intentioned, may be incorrectly assumed to be additional errors. We have to consider whether these explanations could explain the same set of facts, both individually, and in combination. We will not shirk this task.
It also bears emphasizing – we know that almost without question, some of the numbers reported in the NYT / Edison database are wrong. That bare fact is effectively beyond dispute. The main question is which ones, and why. A good working definition of fraud is “wrong numbers entered for malicious reasons”, and distinguishing these from “wrong numbers entered for accidental reasons” is the challenge. The additional data from the county helps to confirm this question, making sure that not all evidence relies on the NYT data.
At a minimum, we can state the following with confidence. If all the mistakes are just errors in the data and weird patterns in vote sorting, Montgomery County, PA, is the unluckiest county in America in terms of having so many random errors pointing in the direction of fraud, from multiple different datasets at multiple different points in time.
A brief summary of the nine key facts is given, following by details of their derivation:
Fact 1: On November 5th at 9:09am, an update in Montgomery County NYT-reported election results sees reported mail votes increase by 90,022, but total votes increase by only 9,534 votes. The implied number of in-person votes thus decreases by 80,488.
Fact 2: The new batch of mail ballots voted 95.4% for Biden and 3.7% for Trump, whereas previously reported mail ballots voted 74.9% for Biden, and 24.4% for Trump. It is statistically impossible that these two batches came from the same distribution. In addition, every pairwise comparison of candidates produces unlikely results, implying that the result cannot be explained by merely one error in candidate totals.
Fact 3: In the new mail ballot batch, the Libertarian candidate Jo Jorgensen receives 20.0% as many votes as Trump. If Democrat voters are ignored, the new batch comes from a group of people who would be the second strongest Libertarian-supporting county in the entire United States.
Fact 4: All mail ballots in Montgomery County were instructed to be mailed to the same postal address. This strengthens the reasons for believing that mail ballots should be drawn from roughly the same distribution.
Fact 5: The decreases in the in-person votes that coincide with the suspicious increase in mail votes are also extremely unlikely under genuine distributions of ballots. They run 98.1% Biden, 1.5% Trump, and 0.8% Jorgensen, meaning they look nothing like either the previous mail ballots, OR the previous in-person ballots. This makes it very difficult to believe that these were genuine mail ballots that had been previously mis-labeled as in-person ballots, and were simply transferred over – the decreased batch presents similarly extreme versions of both fact 2 and fact 3.
Fact 6: Edison’s early absentee vote totals are very close to media numbers reported a few minutes later, suggesting that the early Edison absentee counts are accurate reflections of the underlying county data at the time. Meanwhile, Edison snapshots on November 8th precisely match County snapshots on November 10th, so the later numbers are definitely accurate.
Fact 7: The change in mail votes in Montgomery, PA is unusual relative to updates to mail votes among counties in Pennsylvania, meaning that this problem is not a general property of how vote counting works in the state. The combination of both i) a large increase in overall mail votes and ii) a large increase in mail votes for Biden, relative to the previous distribution, is not observed anywhere else. Most updates are small, and centered around zero.
Fact 8: Finding vote decreases in the NYT data is rare, and finding large vote decreases is even rarer. Montgomery PA displays the fourth largest vote reduction (of 80,488 in-person votes) in the whole database, out of 169 vote decreases. 28% of such decreases involve a change of only 1 vote, and 52% of decreases involve a change of less than 100 votes.
Fact 9: Using the County’s own data, collected after the anomaly was discovered, we can compare how new mail ballots counted since November 10th compare with mail ballots within the same precinct counted up to that point (which are made up of the suspicious update and previously counted mail ballots). We find that, on average, the old mail votes (including the suspicious batch) shows significantly higher support for Biden even when compared with mail ballots later added to the same precinct.
Fact 10: Previous mail ballots show a striking uniformity in support for Biden, even in precincts that voted very heavily for Trump in Election Day ballots. New ballots show considerably more variation in this relationship.
The Challenges to Be Explained by Alternative Explanations
As a final step before the detailed discussion, it is useful to summarize all in one place which aspects of the above facts are most difficult to explain with other, innocent explanations. Bear in mind that the challenge is not coming up with an explanation that covers one or two of the above listed facts, but an explanation that covers all of them.
– Fact 2 shows that all pairwise comparisons between candidates reveal differences in the new mail ballot batch. For this to be due to an error in the data, it would require the existence of at least two out of six mail candidate totals to be wrong (3 candidates, before and after Thursday morning). This makes the changes in mail ballots very unlikely to be explained by a simple “fat finger” typo, or a transcription error, because any such error must have occurred twice out of six times.
-Fact 3 means that it is difficult to posit that the mail ballot numbers are genuine, but that there is some innocent explanation as to why the ballots ended up sorted in a non-random order. The new ballots are very unlikely on their own terms as any plausible subset of American vote patterns. Non-random sorting, like some mail ballots arriving earlier than others and being stored separately, would not explain why in-person ballot totals should go down in Fact 1, or that the decrease should be so unusual relative to other counties in Pennsylvania in Fact 6.
-Fact 5 shows that the votes being subtracted are also implausible, which means that it is very difficult to explain the suspicious shift as being driven by correcting a prior error whereby a genuine set of mail ballots were originally misclassified as in-person. The votes being removed from the in-person totals look even less like the original distribution of mail ballots than the new mail ballots being added, but they also don’t look like the in-person ballots at the time. If there is an innocent reason why in-person ballots were genuine but incorrectly labeled, the affected ballots must come from a wildly extreme part of the distribution.
-Fact 6 makes it unlikely that the patterns represent some broad problem common to the Pennsylvania regulations or vote counting systems. There are other unusual updates to mail votes in Chester, PA, Erie, PA, and Northampton, PA, and we commend other researchers to explore this more. However, most updates to mail ballots are i) small in size, and/or ii) close in 2 party vote share of the new mail batch to the existing distribution. The later Edison snapshot precisely matches the county numbers, so the error is definitely not occurring at this point.
-Fact 7 indicates that the NYT data does not generally appear to be filled with errors of this type. If this is a data error, it is one of the largest and most surprising in the entire database.
-Fact 8 provides reasons to believe that the Edison total absentee numbers in the early snapshot are likely to be correct, given that they are close to independently confirmed numbers, refer to timestamps a few minutes apart, and we do not know how frequently the county website was being updated. This does not prove that every candidate’s absentee totals are also correct, but it makes it more difficult to simply assert that the Edison numbers are all errors.
-Facts 9 and 10 almost entirely rule out the possibility that the entirety of the unusual vote patterns is just an artefact of errors in the NYT data. In addition, the changes are being observed within each precinct, making it difficult to argue that differences come from counting different precincts in different orders. There is some reason why within a precinct, the new mail votes look different from the old votes, in the county’s own data.
-Facts 9 and 10 also make it very difficult to explain the anomalous update as some error in the county’s own numbers that was later corrected. The unusual changes we observe in later mail ballots occur relative to the distribution starting on November 10th, long after there was time to correct any earlier data errors.
-The most plausible but innocent alternative explanation seems to require that the New York Times / Edison data (or the underlying source data on which it is based) is incorrect in numerous surprising dimensions – it lists incorrect counts of absentee and total votes around the update, and that there are multiple errors in the individual candidate absentee vote totals before and after the anomalous update. These errors would need to be incorrect for Montgomery County specifically in a way that is highly unusual relative to other anomalies in the NYT data, and other changes in absentee votes within Pennsylvania. Finally, independent of the above, absentee votes from the county must also show a different distribution before and after November 10th for some innocuous sorting mechanism within precincts, in ways that are independent of any of possible errors in the NYT/Edison data.
Detailed Evidence on Nine Facts
Fact 1: On November 5th at 9:09am, an update in Montgomery County NYT-reported election results sees reported mail votes increase by 90,022, but total votes increase by only 9,534 votes. The implied number of in-person votes thus decreases by 80,488.
See exhibit 1 of Edison/NYT data snapshots, taken from real time snapshots of the election results as reported on the New York Times Website (based on Edison data feeds).
Under absolutely any interpretation, the change in votes between 7:43pm on 11/4 and 9:09am on 11/5 is completely inconsistent with the fair and orderly reporting of ballot counts. The raw data on the history of the election results is included at the end, with the suspicious update in red, and the last prior update in green.
In this suspicious update, the total number of mail votes increased by 90,022.
The total number of all votes, however, increased by only 9,534.
As a consequence, the implied number of in-person votes actually decreased by 80,488.
Even without further elaboration, these bare facts alone represent a glaring irregularity. Existing votes cannot simply disappear, and in-person ballots cannot transform into mail ballots.
The most charitable interpretation is that this was simply some strange glitch – existing votes somehow got put into the wrong category, or the totals were added up wrong, and the error got corrected. This could have been at the county end, or the Edison end. Disentangling these possibilities is the work of this study. However, the more different types of errors the data has, the harder it becomes to simply explain things with one or even two incorrect entries in a database.
Interpretation: These represent a large irregularity that is completely inconsistent with any orderly and fair counting of ballots. Existing votes cannot simply disappear, and ballots that were cast in-person cannot transform into ballots sent by mail.
Fact 2: The new batch of mail ballots voted 95.4% for Biden and 3.7% for Trump. This is implausibly different from previously counted mail ballots, which voted 74.9% for Biden, and 24.4% for Trump. In addition, every pairwise comparison of candidates produces unlikely results, implying that the result cannot be explained by merely one error in candidate totals.
Interpretation: It is statistically impossible that these two groups of mail ballots come from the same pool of voters.
Up until this point, the mail ballots had been 74.9% for Biden (110,944 votes), 24.4% for Trump (36,159 votes), and 0.7% Jorgensen (997 votes).
Based on the updated numbers, if the mail ballots coming in were all genuine, of the 90,022 new votes, 95.4% were for Biden (85,857), 3.7% were for Trump (3,331), and 0.9% were for Jorgensen (834).
In other words, Biden’s vote share in the new batch of mail ballots was almost 20.5 percentage points higher than in the previous mail ballots, while Trump’s was 20.7 percentage points lower.
It is absolutely statistically impossible that these two ballots represent draws from the same underlying distribution. Ignoring the libertarian vote for the time being, if you had a coin that had a 75.4% chance of landing on heads each time (Biden’s two party vote up to that point), the chances you would flip it 89,188 times and get 85,857 heads is so small that Excel doesn’t have enough zeroes to represent just how improbable it is. It just rounds it to “zero”.
Importantly, the same implausibility applies (though not at the significance) when comparing any two sets of mail votes before and after. This is important for ruling out the possibility of some error in one of the mail vote counts, either before or after. If only one number is wrong, then two out of the three comparisons will look glaringly wrong, and one of them will look consistent with chance. If all three pairwise comparisons look suspicious, then any innocent explanation must posit at least two incorrectly entered numbers out of the six (three candidate mail counts, both before and after).
When comparing Trump votes with Jorgensen before and after, the prior Trump “success” ratio is 97.316% , i.e. (36,159 / (36,159+997). Next, in comes 4,165 new votes for either Trump or Jorgensen. Trump wins 3,331 of these. The binomial probability of such an outcome in excel is also rounded down to “zero”.
When comparing Biden votes with Jorgensen before and after, the prior Biden “success” ratio is 99.109%, i.e. (110,944 / (110,944+997). Next, in comes 86,691 new votes for either Biden or Jorgensen. Biden wins 85,857 of these. The binomial probability of such an outcome in excel is 0.0142. Unlike the other two, this number is not in the “completely impossible” category, but is still in the “highly unlikely” category.
As will be noted below, there are also good reasons to suspect that even under a fraudulent distribution, the Biden/ Jorgensen ratio should be the closest together, but still not equal. In a fraud scheme, it is advantageous to increase both groups (so the comparison between the two will necessarily look less extreme), but also advantageous to increase Biden by more (so the comparison between the two will still be broadly unlikely).
Fact 3: In the new mail ballot batch, the Libertarian candidate Jo Jorgensen receives 20.0% as many votes as Trump. If Democrat voters are ignored, the new batch comes from a group of people who would be the second strongest Libertarian-supporting county in the entire United States.
Interpretation:. Not only is the new batch of the mail ballots inconsistent with the old batch, it isn’t even internally consistent with any reasonable estimate of the relative support given to Libertarians and Republicans. It is however consistent with a desire to balance the desire to get Biden as high as possible while simultaneously giving as few additional ballots to Trump as possible.
If the new batch of mail votes is genuine, then the part of Montgomery County they are coming from is unlike almost anywhere else in America in terms of the ratio of support for Libertarian candidates relative to Republican ones. The Libertarian candidate Jorgensen enjoys 20.02% as much support (834 votes) as the Republican (3,331).
At the last update of our data, on Sunday night, in Pennsylvania as a whole, Jorgensen’s support was 2.3% as large as Trump’s, roughly 1/9 as large. But even this understates how bizarre this ratio is. Let us suppose that this new batch of mail ballots, with its 20.02% Libertarian / Republican ratio, were a separate county – with 90,022 votes, it’s certainly large enough to warrant it in most of the country. Out of the 3,156 counties where we have election data as of Sunday night, this new batch, if it were a county, would be the second highest in America in its Libertarian to Republican ratio, behind only Ogalala Lakota in South Dakota. The 99th percentile of the distribution is only 6.81%.
SIf the new mail ballots are genuine, they manage to draw on a voting population whose relative preferences for Trump and Jorgensen are among the most fringe in the whole country.
This fact is actually the kind of small detail that is actually quite diagnostic of fraud, versus other alternatives. Raising the libertarian vote to such implausible levels seems strange, until you realize that it is the solution to the joint problem of how do you
-Raise votes for Biden to as high as possible, without being ludicrous, but
-Also reduce the votes for Trump, so that the two-party difference goes up?
When you’ve spent all your Biden votes, the only option left is to increase Libertarian votes.
It is difficult to generate credible alternative explanations for this fact, other than a general “the numbers are all garbage” claim, which doesn’t predict anything concretely.
Fact 4: All mail ballots in Montgomery County were instructed to be mailed to the same postal address. This strengthens the reasons for believing that mail ballots should be drawn from the same distribution
If the distributions of counted mail ballots are different before and after (which is almost indisputable), then if both batches are genuine, they must have been subject to some kind of sorting mechanism beforehand, innocent or malign. In other words, the distribution isn’t random and equally distributed before and afterwards.
We don’t know what internal processes Montgomery County has. But one important clue that militates against obvious pre-sorting is the fact that every mail ballot in the county is to be sent to a single address. This is documented on the Montgomery County website, archived here.
If every ballot ends up in the same pile until it’s opened to be checked and counted, then the piles will be random. If this is the case, it is literally impossible to get such a large discrepancy. The calculation is exactly the one above.
In the current scenario, there are still other possible ways that mail ballots can be sorted, such as those arriving early and late (which might happen just by normal processes) or by location (which would seem to be difficult to do without first opening the individual envelopes). However, this explanation has difficulty explaining Fact 3 above – the vote share in the new batch looks implausible even on its own terms.
Fact 5: The decreases in the in-person votes that coincide with the suspicious increase in mail votes are also extremely unlikely under genuine distributions of ballots. They run 98.1% Biden, 1.5% Trump, and 0.8% Jorgensen. This makes it very difficult to believe that these were otherwise genuine mail ballots that had been previously mis-labeled as in-person ballots – the decreased batch presents similarly extreme versions of both fact 2 and fact 3.
This fact primarily helps rule out a specific alternative – that the simultaneous increase in mail ballots and decrease in in-person ballots was due to some of Wednesday’s counts being legitimate mail ballots that had been misclassified. The evidence so far shows that the final mix of what was added to the mail total is highly implausible. This fact shows the mirror image of this – that the distribution of what was taken out of the in-person ballots is also extremely implausible.
SThe Trump versus Jorgensen success ratio of 844 wins out of 1517 has a p-value of “0” (i.e. lower than excel’s ability to display) under both the mail and in-person distributions of the previous candidates’ votes totals. The Biden vs Trump win rate of 78,971 out of 79,815 trials also similarly has a p-value of “0” under both in-person and mail distributions. In terms of Biden vs Jorgensen, Biden’s win rate of 78,971 out of 79,644 has a p-value of “0” under the in-person distribution, and a p-value of 0.081 under the mail distribution, the only number corresponding to “reasonably unlikely” rather than “flat out impossible”.
In terms of the Libertarian vote share relative to Republicans, 44%, is a number that has assuredly never been seen outside of the Libertarian National Convention.
For an example of what a ballot decrease that does look like a simple misclassification is like, Chester, PA (shown below) removed 41,695 Biden in-person votes, 9,622 Trump in-person votes, and 377 Jorgensen in-person votes. But these are almost exactly the number of in-person votes that had been added in the previous updates. In other words, it may be considered suspicious for votes to be added to the wrong category, but at least there is no difficulty accounting for the total number of votes being transferred. By contrast, in Montgomery the numbers don’t seem to add up at all. If we examine the sum of all prior additions since 5:43am, Biden had added 80,722 votes (and then lost 78,971), Trump had gained 22,166 (and then lost 844), and Jorgensen had gained 1121 votes (and then lost 673).
Fact 6: Edison’s early absentee vote totals are very close to media numbers reported a few minutes later, suggesting that the early Edison absentee counts are correct. The earliest update to the Edison data on absentee vote counts is 148,100 absentee ballots counted, timestamped at 5:43am on Wednesday 5th (in the Edison data, not the timestamp of underlying county data). Media twitter accounts report the county numbers as of a few minutes later (5:45am) as being between 149,358 and 149,382 absentee ballots counted (taking into account rounding errors). Given the uncertainty of when exactly the Edison snapshot was drawn (as opposed to when it was pushed to their database), this gives independent confirmation that the early Edison snapshot absentee vote totals looks at least approximately correct.
The following tweet by @MontcoCourtNews, made at 7:36am, refers to a 5:45am county snapshot of 239,336 mail votes total, of which 62.41% had been counted. Given rounding in the final digits, this corresponds to between 149,358 counted absentee ballots, and 149,382 counted absentee ballots as of 5:45am.
As of 5:45 a.m. all in-person votes from the county’s 431 precincts have been reported.
Count of mail-in votes continues. 239,336 mail-in votes were received so far & 62.41% have been counted as of 5:45 a.m. #montcovote
— Carl Hessler Jr. (@MontcoCourtNews) November 4, 2020
Edison’s earliest timestamp that we have was pushed to their database at 5:43am, and records 148,100 counted absentee ballots. Given it is unclear how frequently they scraped/refreshed the county website, or how often the county updated their underlying data, it seems very plausible that the reported count as of some time shortly before was indeed the Edison number.
For the last NYT/Edison snapshot on November 8th (which we use for out comparisons), our numbers from the NYT on Sunday November 8th precisely match the County’s total numbers on November 10th, for both in-person and absentee/mail ballots, and for all three candidates. These numbers assuredly are the County’s own numbers.
Fact 7: Among Pennsylvania counties that updated their mail ballot counts since election night, there are no other counties that see anywhere near such a large change in the growth of mail votes for Biden versus mail votes for Trump.
Interpretation: This update is not the result of some arcane aspect of Pennsylvania election law or state-wide counting procedures, since Montgomery County is a huge outlier relative to the rest of the state. To see this, we can compare within the NYT/Edison data every update made to mail/mail votes. We can compare how unusual a given update is in terms of how it changes along two dimensions simultaneously:
-How large is the overall size of the increase in all mail votes, relative to the total number counted so far?
-How different is the two-party vote share for Biden in the new batch of mail votes relative to mail ballots counted so far?
In the data, most changes in mail ballot totals are small in their overall number. That is, after election night, there isn’t a massive change in the number of counted mail ballots.
Second, whatever changes that do occur generally show a distribution of new mail votes that looks similar to old mail votes.
Third, violations of the above are more unusual when they occur simultaneously. It is easy to have an unusual deviation of vote share in a new batch if you’re only counting a very tiny batch. Counting a very large batch that also is different from the old batch becomes more surprising.
Most observed PA changes in mail ballots don’t exhibit this joint property of being both a) a large increase in total mail votes, and b) a large deviation from the percentage of mail votes already counted, in terms of two-party support for Biden. For instance, Chester PA, discussed above, looks more like a genuine classification error, because (in addition to being able to account for the total number of votes), the additional ballots appear to come from a very similar distribution as before. Montgomery PA displays neither fact.
Fact 8: Finding vote decreases in the NYT data is rare, and finding large vote decreases is even rarer. Montgomery PA displays the fourth largest vote reduction (of 80,488 in-person votes) in the whole database, out of 169 vote decreases. 28% of such decreases involve a change of only 1 vote, and 52% of decreases involve a change of less than 100 votes.
It is also worth getting a sense of how error-filled the NYT data is in general. Are these kinds of errors common? The answer is no. In general, egregious errors like vote tallies decreasing in some categories is very rare, with only 169 cases in total. Within that set, the sheer size of the current anomaly is also striking. Montgomery is the fourth largest, behind Erie NY, Westchester NY, and Queens NY. There are indeed errors in the NYT/Edison data, but very few of them are as glaring as the current one. Most of the corrections are very small – 28% of such decreases involve a change of only 1 vote, and 52% of decreases involve a change of less than 100 votes.
Finally, it is worth observing that some of the other large NYT vote decreases in particular categories do look like exactly the kind of simple mis-classification of genuine votes that we ruled out in Fact 5. Maricopa County, AZ, sees two large updates (~40,000 votes) where exactly the same number of Biden, Trump and Jorgensen votes get simultaneously added to mail ballots and removed from in-person in the same update. Such errors look like simple misclassification, whereas the current one does not.
Fact 9: Using the County’s own data, collected after the anomaly was discovered, we can compare how new mail ballots counted since November 10th compare with mail ballots within the same precinct counted up to that point (which are largely made up of the suspicious update). We find that, on average, the old (suspicious) batch shows significantly higher support for Biden even when compared with mail ballots later added to the same precinct.
We wanted to get independent confirmation of the unusual nature of the earlier batch of mail ballots in two key respects. First, we wanted to test it using the County’s own data, to make sure this isn’t something odd about the NYT/Edison data. Ideally, we could have gone back in time and started scraping the County data since the start of the election, to observe the actual anomalous update directly but that ship had already sailed. Instead though, we took two snapshots of the county’s own precinct-level data after we had become suspicious. The first was on November 10th, the second on November 14th. The advantage of looking at the data in such a later period, however, is that there has been plenty of time since the first update to correct any errors. Secondly, the county-level data is much finer than the Edison data, because it zooms all the way into individual precincts. How do the changes in mail votes between November 10th and 14th compare with the distribution up to November 10th?
We find that, on average, the Biden vote share in the earlier batch of mail votes is unusually high relative to the later additions in the same precinct. All the points in the graph are located on the right hand side, but show considerable vertical variation.
In other words, early mail counts showed a striking uniformity in terms of voting for Biden. The absolute lowest Biden fraction across all 431 precincts in the County data is 59.7% for Biden. Ignoring one precinct that had only counted 5 mail votes by November 10th, the highest support for Biden in mail votes up to November 10th is in “Norristown 2-2”, where Biden won 98.7% of the 150 mail in votes that went for the two major parties, a number that Saddam Hussein would be proud of. Incidentally, Norristown 2-2 shows exactly 2 votes apiece for Republicans and Libertarians, again consistent with the very strange Libertarian to Republican ratio discussed earlier.
Meanwhile, new votes come in. How high do they run for Biden? They show both significantly lower support. For instance, Norristown 2-2 had previously counted 148 Democrat mail votes, 2 Republican mail votes, and 2 Libertarian mail votes. Between Republican and Democrat alone, this is like a coin that has a 98.7% chance of landing on heads. Three more votes are added. One of them comes up Republican, two for Democrat (66.6% Biden). This is somewhat surprising, but is a very small number of new votes, and a single precinct. “Cheltenham 5-3” had previously counted 361 Democrat mail votes and 26 Republican mail votes (i.e. 93.3% Biden). 18 new votes get added. 12 of them are Democrat, 6 are Republican (i.e. 66.7% Biden). Individually, each new addition is only a small number of new votes, and only one precinct at a time, but a lot of them look quite unusual, with the old batch showing more Biden support than the new batch. We can repeat the same analysis for all the precincts, and compare how different the proportions look before and after for all precincts as a whole. For the statistically inclined, we’ll compute the precinct-level z-scores for the Pearson test of differences in means at each precinct. Then we convert them to p-values, and add the sum of –ln(p-value) together into a single Chi-squared test statistic with 2n degrees of freedom.
The probability of all these changes being jointly drawn from the same distribution for precincts as a whole is less than 0.0001, when using the precinct-level changes. If we take the simpler test of just comparing all county mail votes before and after, we get 196,801 Biden votes before versus 39,490 Trump votes before. In the new votes, we get 3,283 Biden votes and 752 Trump votes. The probability that these came from the same distribution, using a Pearson test, is 0.00058. However the within-precinct test is more powerful, because it shows that the change is occurring even within votes counted in the same very small geographic areas.
This shows with very high likelihood that something continues to be unusual about the distributions of mail votes even late in the counting, and in a way that suggests that earlier batches showed unusually high support for Biden, even within the small location of a precinct.
It is also worth noting that we are not comparing the anomalous batch to the new votes. We are comparing the sum of mail votes before Wednesday morning plus the anomalous batch, with the new votes. We are also only observing the tail end of mail vote increases, and not every update after the initial suspicious batch. So the test above is much weaker than the ideal test, which would be just to test the new batch of mail votes that came in on the morning of Thursday 5th. But even so, the differences are still apparent.
Fact 10: Previous mail ballots show a striking uniformity in support for Biden, even in precincts that voted very heavily for Trump in Election Day ballots. New ballots show considerably more variation in this relationship.
Another way of showing how unusual the early distribution of mail ballots is to compare them with the distribution of votes on the day of the election in the same precinct.
When looking at votes counted up to November 10th, the mail ballots show a striking consistency in votes for Biden. The lowest precinct in terms of election day in-person vote share for Biden is Franconia 5, where only 16.3% of votes went for Biden. But even here, apparently 60.4% of mail votes up to November 10th went to Biden! The crazily heavy Republican precincts nonetheless all sent in strong majorities of mail votes for Biden. When plotting the same relationship with vote shares afterwards, there is a lot more variation. Admittedly, these come from smaller batches, so more noise is expected. But this is why we perform the formal tests above, to rule out the fact that merely small vote totals in the updates are driving the results (as the individual z-scores take into account exactly this fact). The most striking thing is simply the disconnect in the levels, whereby mail ballots assigned to extremely heavy Republican precincts still voted overwhelmingly for Biden.
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