I finally had some time to put this together.

For additional background information, see here, here and here. As a reminder and summary, according to the published methods in the USAID funded National Academy of Sciences paper (here) that I based this work off of, an ideal “fair” election should look like one or two (depending on how split the electorate is) clean, compact Gaussian distributions (or “bulls-eye’s”). Other structural artifacts, while not conclusive, can be evidence and indicators of election irregularities. One such indicator with an attributed cause is that of a highly directional linear streaking, which implies an incremental fraud and linear correlation. Another known and attributed indicator is that of large distinct and extreme peaks near 100% or 0% votes for the candidate (the vertical axis) that are disconnected from the main Gaussian lobe which the authors label a sign of “extreme fraud”. In general, for free and fair elections, we expect these 2D histograms to show a predominantly uncorrelated relationship between the variables of “% Voter Turnout” (x-axis) and “% Vote Share” (y-axis).

The source data for this analysis comes directly from the VA Department of Elections servers, and was downloaded shortly after the conclusion and certification of the 2021 election results on 12/11/2021 (results file) and 12/12/2021 (turnout file). A link to the current version of these files, hosted by ELECT is here: https://apps.elections.virginia.gov/SBE_CSV/ELECTIONS/ELECTIONRESULTS/2021/2021%20November%20General%20.csv and https://apps.elections.virginia.gov/SBE_CSV/ELECTIONS/ELECTIONTURNOUT/Turnout-2021%20November%20General%20.csv. The files actually used for this analysis, as downloaded from the ELECT servers on the dates mentioned are posted at the end of this article.

Note that even though the republican (Youngkin) won in VA, the y-axis of these plots presented here was computed as the % vote share for the democratic candidate (McCauliffe) in order to more easily compare with the 2020 results. I can produce Yougkin vote share % versions as well if people are interested, and am happy to do so.

While the 2021 election fingerprints look to have less correlations between the variables as compared to 2020 data, they still look very non-gaussian and concerning. While there is no clearly observable “well-known” artifacts as called out in the NAS paper, there is definitely something irregular about the Virginia 2021 election data. Specifically, I find the per-precinct absentee [mail-in + post-election + early-in-person] plot (Figure 6) interesting as there is a diffuse background as well as a linearly correlated set of virtual precincts that show low turnout but very high vote share for the democratic candidate.

One of the nice differences about 2021 VA data is that they actually identified the distinctions between mail-in, early-in-person, and post-election vote tallies in the CAP’s this year. I have broken out the individual sub-groups as well and we can see that the absentee early-in-person (Figure 9) has a fairly diffuse distribution, while the absentee mail-in (Figure 7) and absentee post-election (Figure 8) ballots show a very high McAuliffe Vote %, and what looks to be a linear correlation.

For comparison I’ve also included the 2020 fingerprints. All of the 2020 fingerprints have been recomputed using the exact same MATLAB source code that processed the 2021 data. The archive date of the “2020 November General.csv” and “Turnout 2020 November General.csv” files used was 11/30/2020.

I welcome any and all independent reviews or assistance in making and double checking these results, and will gladly provide all collated source data and MATLAB code to anyone who is interested.

Figure 1 : VA 2021 Per locality, absentee (CAP) + physical precincts

Figure 2 : VA 2021 Per locality, physical precincts only:

Figure 3 : VA 2021 Per locality, absentee precincts only:

Figure 4 : VA 2021 Per precinct, absentee (CAP) + physical precincts:

Figure 5 : VA 2021 Per precinct, physical precincts only:

Figure 6 : VA 2021 Per precinct, absentee (CAP) precincts only:

Figure 7 : VA 2021 Per precinct, CAP precincts, mail-in ballots only:

Figure 8 : VA 2021 Per precinct, CAP precincts, post-election ballots only:

Figure 9 : VA 2021 Per precinct, CAP precincts, early-in-person ballots only:

Comparison to VA 2020 Fingerprints

Figure 10 : VA 2020 Per locality, absentee (CAP) + physical precincts:

Figure 11 : VA 2020 Per locality, physical precincts only:

Figure 12 : VA 2020 Per locality, absentee precincts only:

Figure 13 : VA 2020 Per precinct, absentee (CAP) + physical precincts:

Figure 14 : VA 2020 Per precinct, physical precincts only:

Figure 15 : VA 2020 Per precinct, absentee (CAP) precincts only:

Source Data Files:

There’s a (IMO frivolous) lawsuit by Mark Elias (here) against the USPO that is causing people to think that there are > 300K outstanding mail-in ballots in VA. According to the VA Dept of Elections data, this is just factually incorrect. There are not 300K outstanding absentee ballots floating around. There is < 100K as per the 11/01/2021 DAL file entries. (Light blue line, logarithmic y axis)

Of the 3 Localities listed in the lawsuit, from the 11/01/2021 DAL File:

	ALBEMERLE COUNTY	JAMES CITY COUNTY	PORTSMOUTH CITY
Total Registered Voters	81738	61961	66696
Total Outstanding Mail In Ballots	2545	1061	1151
Registered / Outstanding * 100	3.1%	1.7%	1.7%

The graph of the breakouts of these 3 counties over time as the DAL files have been updated during the early voting period is shown below. As we see increases in the number of mail in ballots that are in a status state of “Marked” or “Pre-Processed”, we see corresponding decreases in the outstanding “Issued” ballots in all 3 localities. We are NOT seeing a huge buildup of “Issued” ballots that are backlogged as claimed in the lawsuit corresponding to an “October Slowdown” by the USPO. His lawsuit is bunk.

I have been working with a number of different groups for GOTV efforts for the 2021 VA Election, as as such I have been archiving and trending the Daily Absentee List (DAL) data files for a while now. One curious case that I’d love to get somebody at VA ELECT to explain, is why the set of (“Marked” +/or “Pre-Processed”) Ballots for GALAX City has suddenly been reduced to near zero.

As background, the DAL is effectively a transaction log of the status of all early and absentee ballots in VA. When a qualified voter requests a by-mail absentee ballot and it is sent to them a DAL record is created in an “Issued” state. Once it is received the record is updated to “Marked”, and once the ballot has been opened and scanned into a tabulator it is updated to “Pre-Processed”.

In the chart below we can see the number of issued ballots increasing, then decreasing as ballots are received and updated to “Marked” or “Pre-Processed”, but then suddenly (starting with the Oct 26th DAL files) we see the “MarkedOrPre” trace drop to near zero. The only line in this graph that I would ever expect to see decreasing is the number of outstanding “Issued” ballots. So … whats going on here?

Adding on to my previous report (old version is here).

• Fixed a few typos and formatting issues.
• Added some discussion about the fact that the VA DOE did correct the turnout statistic error I found, but did not make any sort of statement or explanation as to why the error was there in the first place; why did it go undiscovered for nearly a year until I pointed it out; what procedures and policies are in place to make sure errors like this don’t happen again?
• Added a section documenting the discovery that a small number of public records have been retroactively adjusted and specific entries are now missing from the public archives regarding the registered voter totals.

I got asked a question earlier this evening as to how the current 2021 VA election early vote/absentee data was shaping up in comparison to the 2020, so I did some quick processing and plotting of the Daily Absentee List (DAL) from just after the 2020 election (11-09-2020), and the current DAL as of today (10-21-2021).

The below graphs plot the APP_STATUS=”Approved” entries in the DAL, broken out by BALLOT_STATUS and plotted vs their BALLOT_RECEIPT_DATE. One major difference is that we haven’t had any Federal Write-In Absentee Ballots (FWAB) entered into the DAL in 2021 yet that have a valid BALLOT_RECEIPT_DATE, and the 2020 FWAB counts had a very different general curve than the other ballots. We also had a little less than 1000 ballots entered “On Machine” before early voting started in 2020. We see ballots issued earlier in the year for 2021, but no major “On Machine” counts. Note these graphs are logarithmic in the y-axis for easier viewing, and I had to discard 660 entries for 2020 and 11 entries for 2021 because the BALLOT_RECEIPT_DATE was invalid.

Per request by a reviewer of my most recent election irregularities report in VA (here), here’s a little more technical detail as to how the “ideal” model is computed in accordance with the original 2012 National Academy of Sciences paper that I based this work off of.

The generalized summary in my report for VA reads as follows:

“The upper right image was computed per the NAS paper; the bottom left image shows what an idealized model of the data could or should look like, based on the reported voter turnout and vote share for the winner. This ideal model is allowed to have up to 3 Gaussian lobes based on the peak locations and standard deviations in the reported Virginia results.”

While that description is absolutely accurate, it glosses over some of the implementation as I didn’t want the reader to go all glassy-eyed on me! A more explicit technical definition is as follows: All of the localized maximal peaks in the 2D histogram that are above pThresh (~= 0.7) x the value of the global maximum peak are used as the centroids of a Gaussian Mixture model, with shared covariance matrix equal to 1.5 x sqrt of the covariance matrix of all of the data points. (Thats a lot of mathematics packed into one sentence, but its accurate!) In the case of the VA per county per cong district data this give us either 2 or 3 peaks dependent on the value that is used for the pThresh threshold. The value of 0.7 was chosen after observing results from multiple states data that I have been doing fingerprint analysis on. The MATLAB imregionalmax(…) function from the Image Processing Toolbox is used to find the candidate localized peaks, and the gmdistribution(…) function from the Statistics toolbox generated the final idealized model.

% HBf is the 2D Histogram image
BW = imregionalmax(HBf);
v = HBf(BW);
[r,c] = find(BW.*HBf >=  max(v(:))*pThresh);
mu = [r,c];
s = 1.5;

cv = diag(diag(s*sqrt(cov(rawData))));
GMModel = gmdistribution(mu,cv);

The end result of this is shown below (bottom left) with the Bayesian Information Criterion (BIC) and number of Gaussian components listed in the title of the bottom left “ideal” plot.

Background:

The US National Academy of Sciences (NAS) published a paper in 2012 titled “Statistical detection of systematic election irregularities.” [1]  The paper asked the question, “How can it be distinguished whether an election outcome represents the will of the people or the will of the counters?” The study reviewed the results from elections in Russia and other countries, where widespread fraud was suspected. The study was published in the proceedings of the National Academy of Sciences as well as referenced in multiple election guides by USAID [2][3], among other citations.

The study authors’ thesis was that with a large sample of the voting data, they would be able to see whether or not voting patterns deviated from the voting patterns of elections where there was no fraud. The results of their study proved that there were indeed significant deviations from the expected, normal voting patterns in the elections where fraud was suspected.

Statistical results are often graphed, to provide a visual representation of how normal data should look. A particularly useful visual representation of election data is the election fingerprint. When used to analyze election data, the election fingerprint typically analyzes the votes for the winner versus voter turnout by voting district. The expected shape of the fingerprint is of that of a 2D Gaussian (a.k.a. “Normal”) distribution [4].  (See this MIT News article for a great additional description and primer on the Gaussian or Normal distribution: https://news.mit.edu/2012/explained-sigma-0209)

 Here is an example reprinted from the referenced National Academy of Sciences paper:

The actual election results in Russia, Uganda and Switzerland appear in the left column, the right column is the expected appearance in a fair election with little fraud, and the middle column is the researchers’ model with fraud included.

As you can see, the election in Switzerland shows a range of voter turnout, from approximately 30 – 70% across voting districts, and a similar range of votes for the winner.  

What do the clusters mean in the Russia 2011 and 2012 elections? Of particular concern are the top right corners, showing nearly 100% turnout of voters, and nearly 100% of them voted for the winner.

Both of those events (more than 90% of registered voters turning out to vote and more than 90% of the voters voting for the winner) are statistically improbable, even for very contested elections. Election results that show a strong linear streak away from the main fingerprint lobe indicates ‘ballot stuffing,’ where ballots are added at a specific rate. Voter turnout over 100% indicates ‘extreme fraud’. [1][5]

Election results with ‘outliers’ – results that fall outside of normal voting patterns – are not in and of themselves definitive proof of outright fraud. But additional reviews of voting patterns and election results should be conducted whenever deviations from normal patterns occur in an election.  Additionally it should be noted that “the absence of evidence is not the evidence of absence”:  Election Fingerprints that look otherwise normal might still have underlying issues that are just simply not readily apparent with this view of the data.

Using this studies methodology, in late 2020 and 2021, multiple researchers in the US have applied the same analysis to the US 2020 election results, as well as the results of previous elections.

The US 2020 Election – New Hampshire:

Source Data:

1. Registered Voter Data: https://sos.nh.gov/media/00lg4swb/names-on-checklist-general-2020.xlsx
2. Total Regular and Absentee Ballots Cast: https://sos.nh.gov/media/yi4fonny/ballots-cast-2020-general.xls
3. Vote Totals: https://sos.nh.gov/media/yjmp5qmd/president-2020.xls
4. Write-In Totals: https://sos.nh.gov/media/wv3m4jne/presidential-write-ins-2020.pdf
5. Records of Voter Rolls Pre-Election Day, On Election Day, and marked as Absentee.  (Note that due to personal privacy considerations, this raw dataset is not openly published and the raw data must be obtained via request. The summaries of this dataset is included in the “2020-NH-Combined-Data.csv” file included below)

Election Fingerprint:

The upper right image in the following graphic is the computed election fingerprint, computed according to the NAS paper and using official state reported voter turnout and votes for the statewide winner. The color scale moves from precincts with low counts as deep blue, to precincts with high numbers represented as bright yellow. Note that a small blurring filter was applied to the computed image for ease of viewing small isolated histogram hits.

The bottom left image of the graphic shows what an “idealized” model of the data could look like. The upper right image was computed per the NAS paper; the bottom left image shows what an idealized mixture-of-Gaussian model of the data should look like, based on the reported voter turnout and vote share for the winner.

The top-left and bottom-right plots show the sum of the rows and columns of the fingerprint image. The top-left graph corresponds to the sum of the rows in the upper right image and is the histogram of the vote share for Biden across precincts. The bottom right plot corresponds sum of the columns of the upper right image, and is the histogram of the % turnout across the precincts.

Observations/Conclusions:

• There does not appear to be any majorly distinct linear correlations, over 100% turnout precincts, or otherwise major red flags even though there is some patterned noise.  The distribution is very large and diffuse, and has a definite skew, which is curious, but not necessarily indicative.  
• There are a small number of outlier precincts outside of the main distribution lobe, most notably the cluster along the 40% turnout line (Lempster, Newport & Claremont Ward 3), and two precincts above 90% turnout (Randolph & Ellsworth).
• There are at least two major peaks in the main lobe, which is consistent with the theory of a split electorate.
• The % Vote Share for Biden plot (Upper-Left) is “lop-sided” and shows a distinct skew in the data above the 40% Vote Share mark.  
• Looking at the difference between the Total Reported Votes from Source B and Total Votes count from official Source C shows 10,666 unaccounted for votes.  The total number of Write-In votes from Source D was only 1158 and not nearly enough to account for this difference.
• Looking at the difference between the registered voters from Source E and the Registered voters from Source A, there is a difference of 122,248 registrations.

References:

[1] “Statistical detection of election irregularities” Peter Klimek, Yuri Yegorov, Rudolf Hanel, Stefan Thurner Proceedings of the National Academy of Sciences Oct 2012, 109 (41) 16469-16473; DOI: 10.1073/pnas.1210722109 (https://www.pnas.org/content/109/41/16469)

[2] USAID: Assessing and Verifying Election Results: A Decision Makers Guide to Parallel Vote Tabulation and Other Tools (http://web.archive.org/web/20201118021847/https://pdf.usaid.gov/pdf_docs/PA00KGWR.pdf)

[3] USAID: A guide to Election Forensics (http://web.archive.org/web/20210501091306/https://pdf.usaid.gov/pdf_docs/PA00MXR7.pdf)

[4] Multivariate Normal Distribution – Wikipedia (https://en.wikipedia.org/wiki/Multivariate_normal_distribution)

[5] Mebane, Walter R. and Kalinin, Kirill, Comparative Election Fraud Detection (2009). APSA 2009 Toronto Meeting Paper, Available at SSRN: https://ssrn.com/abstract=1450078

Data Files: