Fraction Magic — Part 2: Context, Background, Deeper, Worse


2 — Totals dropping mid-count; poll tapes don’t match; missing single-votes like round-off errors; e-mails from programmers; and voters being personally “weighted” for unequal value —

In August 2014 Bennie Smith was approached by a number of candidates who insisted that their elections had been stolen. He disagreed with the group and offered to look into how the system works.

halbertIn October 2015, Smith received a report from a candidate named Wanda Halbert. On Election Night, she had noticed that as votes accumulated, the number of votes in her race were somehow getting subtracted as new votes were added.

poll tape anomalyA

On Election Day, as a part of his continuing research, Smith had taken a photo of a precinct 07701 poll tape (a results total printed from the memory card in a voting machine). In comparing the poll tape to the GEMS central tabulator report, Smith saw that the totals did not match. More votes were shown on the voting machine tape on Oct. 8 than on the GEMS central tabulator on Oct. 13.  Smith brought this to the attention of Shelby County elections officials but only after Halbert pressed the issue was the inconsistency corrected.

Smith began to research how votes that originate from the same source can change once they get into the GEMS program, beginning with the premise that sophisticated election theft would be near impossible, difficult at best; perhaps achievable in a crude or one-shot or localized way, but certainly not on a national scale, or as part of a plan to capture repeat elections. For that, one would need a system that is configurable, quick, precise, and usable by persons who are not master programmers.

His combined his political acumen with database expertise, a way of considering voting technology that contrasts with traditional studies (which tend to analyze voting systems academically, isolated from political metrics to focus on theoretical penetration and reliability tests).

The question

A viable business model for election control needs repeat customers. The most frequent purchase pattern would involve local elections, which select tens of thousands of public officials every year, and enact thousands of public policy choices. The amount of money at stake is far greater with local than national elections, though this might seem counterintuitive. National and state elections generate a large amount of visible spending, but local elections control hundreds of millions in budget expenditures per jurisdiction, the U.S. has over 3,000 different jurisdictions, and there are elections every year.

Smith examined the question of whether election results could be controlled in a single way under various election circumstances. Could the mechanism be subtle enough to alter results without being detected? Could it function a way that was configurable? Could it work for different “customers” across geographic areas? Does such a mechanism exist?

The Detective Story

His approach was to consider design requirements for what a person with inside access would need to alter election outcomes in a marketable way. Smith often refers to passage from a book by Gary Kasparov:

“Too often we set a goal and head straight for it without considering the steps required to achieve it. What conditions are necessary for our strategy to succeed?”

Vote results would have to be customizable and flexible enough to target:

•  Precinct demographics: by ethnic community, college areas, partisan strongholds, religious areas…;

Voting methods: Early Voting, Election Day, Vote-by-Mail, Combined vote centers;

Counting methods: Cumulative counts, precinct counts, central counting;

Different types of voting machines: touch-screens, paper ballot scanners;

Vote counts occurring at different time periods: early votes counted before polls close; polling place votes flowing in throughout Election Night; absentee counting before and after the election

Different batching methods: some votes consolidated by precinct, others in mixed batches.

Most important would be the ability to create a plausible false count to conform to precinct demographics and prior voting histories, along with the ability to customize which vote subsets would be targeted so as to minimize risk under various administrative procedures.

The absolutely essential design feature needed to achieve all of the above specifications is: Fractions. So Smith began his research by looking for just one thing: Floating point capability (decimals). He found them.

What does a decimalized vote look like?

One person, one vote: “1”
One person, 3/5 of a vote: “0.60”
One person, one-and-a-half votes: “1.5”

Smith contacted former Shelby County Election Commissioner George Monger for an introduction to all things Shelby and GEMS. While looking at GEMS he saw the floating point command for decimals: “DOUBLE.” This term tells GEMS to treat votes as decimals, or fractions, rather than as whole numbers.

The next step was to take a modeled concept for a test run using GEMS. He tested alteration of election results by controlling vote percentages. Vote outcomes could be controlled. Smith set percentages for vote results for each candidate. Vote totals changed to match the results he selected.

But while demonstrating that vote totals could be weighted, Smith saw small fractional vote debris accumulate. The Alaska example, below, shows some of these tiny fractional vote remnants.

The sum of these tiny fractions can add up to 1 or 2 votes and become visible. Smith realized that round-off errors would need to be considered in some way. To reduce these tiny discrepancies, programmers would want to use at least three, preferably more decimals.

Such errors can be cleaned up – or even left as is, since prevailing explanations in the elections industry tend to discount discrepancies if they “did not affect the election.” It is reasonable to assume that one vote should not seem to affect the outcome, but if that one vote is actually the accumulation of thousands of small fractional remainders, the real result may be incorrect by thousands, and even tens of thousands.

The next step was to see if any evidence exists showing one-vote discrepancies. In large vote databases, these accumulated fragments can add up to 1, 2, or even more votes, but a succession of one-off errors certainly should raise concerns. Smith compared:

• Total votes cast minus votes that don’t count (blanks, overvotes etc.)
• Total votes of all candidates

The total votes cast minus no-votes should result in the number of votes counted for candidates. Smith searched for a difference of one or two votes during live results uploads on Election Night and shortly afterwards,, finding what he believed could be round-off errors in a number of races. He found errors in Morrow County, Ohio; DeKalb County, Georgia, and Shelby County, Tennessee, including an error in the race of high profile candidate and television personality “Judge Joe Brown” when he ran for Shelby County District Attorney in 2014. Here is the discrepancy:


# of Ballots cast:                         148,494
# who skipped this race:         3,885
Total votes for this Race     144,609 (148,494 – 3,885)

Votes for Amy Weirich:       94,248
Votes for Joe Brown:            50,161
Write-in Votes:                          199

Total of Candidates            144,608 (94,248 + 50,161 + 199)
Number of votes missing: 1

The Answer

After performing a series of testing iterations on the voting system used in Shelby County, Smith’s opinions as to whether a robust, configurable election tampering mechanism exists evolved from “doubtful” to “maybe” to “yes.”

He began collaborating with Bev Harris of Together they studied a conceptual model and checked voting databases from dozens of locations. Smith, a technical thinker, and Harris, a writer, approached the issue with different kinds of questions.

Smith reasoned that if fractionalized votes were actually used to weight races, GEMS programmers would have discussed issues pertaining to how many decimals to use. Harris wondered if the decision to use decimals was deliberate; whether it had always been in the program and if not, when was it put in and by whom; and whether the decimals demonstrate intention to weight a race.

Smith searched for evidence that GEMS programmers had discussed methods to reduce round-off, truncation, or lost value errors. He began searching online e-mail databases for messages about issues with decimal votes.

These are available because over 13,000 e-mails were leaked in 2003. They were initially published at, resulting in a DMCA takedown order, which produced push-back from students across the U.S. First at Swarthmore University, then at over a dozen more colleges and grass roots Web sites, the blocked, leaked e-mails were re-posted, resulting in successive takedown orders by Diebold, an article in the New York Times, U.S. Representative Dennis Kucinich posting some of the e-mails on his congressional Web site, and a successful lawsuit by the Electronic Frontier Foundation in which a court revoked Diebold’s claim to protection of the e-mails on the grounds that they serve a greater public interest.

Smith entered search term ‘diebold, decimals’ into Google search and found this e-mail thread:





understood by or meant for only the select few who have special knowledge or interest;

The above e-mails indicated to Smith that programmers may have been grappling with lost value errors. To Harris, the same e-mails meant that programmers were weighting votes, and that the fractional vote counting was directly related to the concept of weighting elections.

Harris found the “DOUBLE” setting in all GEMS databases from all states for version 1.18 forward. Looking at older GEMS databases, version 1.17 and before, votes were instead configured as whole numbers (LONG INTEGER).

Smith found instructions in the source code to convert vote counting from whole numbers to decimals.

Therefore it can be shown that a choice was made to convert the system to counting decimalized votes; it is not accidental; and it is directly connected to weighting a race.

An examination of GEMS release notes shows that this change shows up on June 27, 2001:


GEMS USER MANUAL documents weighted race feature:


But what exactly did they mean by “weighted race”? Further research shows that ‘weighted race’ is defined in a way that removes the one-person, one-vote expectation from elections:

“Weighted voting systems are voting systems based on the idea that not all voters should have the same amount of influence over the outcome of an election. Instead, it can be desirable to recognize differences by giving voters different amounts of say (mathematical weights) concerning the outcome.”

Harris researched use of weighted voting in U.S. elections, and did locate one example, found in California and used for small “special district” elections.  This could appear to explain the next e-mail clip:




However, further research showed that Sacramento didn’t and still does not use GEMS; that California law specifies how weighted races are to be conducted, and that they do not involved decimalization of votes.

The Decimals Toggle

In the GEMS “race” table is a field called “Race Type.” By experimenting with different settings, Smith found that by inserting the number “10” (a mostly undocumented setting), decimals appear in results reports for viewing. To be clear, ALL votes are counted as decimals whether or not the “10” flag is set. Toggling “10” on and off simply allows the user to view decimals, or not, in results reports.

Below we show a results report for Alaska which we weighted to ensure Kerry would win. (See Part 4 and Part 5 of this series.) We turned on the ‘show decimals’ feature, demonstrating that: a) votes can be counted with decimals; b) fractional “debris” can accumulate, with very small remnants being stored, such as 1/50th of a vote for Cobb. It is these fragments which can accumulate to produce very small telltale errors of one or two votes; and c) the existence of this “show decimals” option demonstrates that programmers clearly intended to enable vote values containing decimals.







It is unnecessary to embed a weighted race feature into every election in America to accommodate minor special district elections (which sometimes involve less than 10 voters and can easily be hand counted). The fractional vote capability is built into GEMS for all races, whether they are weighted or not; it is embedded in all locations including states which do not have weighted elections, and it is the default setting for all races everywhere.

The risk clearly out-weighs any obscure potential benefit that might be anticipated. Undocumented features are not allowed in voting systems. Some acknowledgement of the weighted vote feature however cryptic, had to be provided to voting system certifiers should they ask about it.

The issue of intentionality

GEMS programming has often been referred to as amateurish, sloppy, and unsophisticated, explanations used whenever its high-risk features are exposed. Such explanations provide deniability of intent. But GEMS is more sophisticated than most researchers realize. It contains subtleties, showing obvious functions anyone can see in its MS Access tables, but hiding other functions within its executable. Still other functionality seems to appear only when connected to external parts. As far as we could determine, some of these are undocumented in the GEMS system and are unviewable when looking at GEMS databases.

For example:

“Bar codes are assigned by the voter registration system, containing encoded information identifying the voter, tags identifying races as well as weight values for every voter and every race. .. Weighted results are reflected in the election results reports in candidate totals as well as votes cast … Since GEMS does not contain the weight information …”

The above excerpts indicate that GEMS interacts with an external module containing encoded information which assigns a weighted value to each voter.

Each individual voter’s vote assigned a weight

Our vote-weighting example involved reallocating votes, It can be done and it presents a grave risk to voting rights. The actual weighted race function, however, is much worse. We did not, and will not attempt to create a working demo for what follows.

We have documented that weighted race functionality is fully available in GEMS, but documentation pertaining to how it works seems to be missing in user manuals. We did, however, locate documentation in a development version of the GEMS manual.

In a document called “GEMS 1.18 Users Guide Revision 4.0” we find the following on page 158:




This indicates that votes are being tied to voter names.

The weighting of the voter is contained in “encoded information” stored outside of GEMS.

This leaves no doubt that the intent is to allow votes for some voters to be counted less than votes for other voters. Particularly in the South, where voters’ race is identified in the voter registration system, this quite literally allows each Black voters’ vote to count as, for example, 3/5, while White voters’ vote would count as 1+ 2/5. Whatever the claimed reason for doing this, it is a voting rights abomination.

Page 158, continued:




They provide an example using whole numbers, as required by law for California’s few oddball special elections.

However, they implement the weighted race function using decimals, not whole votes. Then they insert programming to achieve this, strip out reference to how it works, and make fractional votes the default setting for every race in every election.

Here is the entire section as originally written on page 158:


Weighted races are tallied by weights, assigned from the voter registration system, and may be counted in Central Count vote centers only.

Bar codes are assigned by the voter registration system, containing encoded information identifying the voter, tags identifying races as well as weight values for every voter and every race.

The tag defined for each weighted race should correspond to the race tag in the voter registration system.

Race types

A weighted race has the same attributes as a candidacy, and other than being weighted, is counted in thesame manner as candidacies. In order to configure a question as a weighted race, two candidates are defined as positive and negative values in a vote for one race.

Preference and endorsement races control weighted races in the same manner as candidacies.

Election results

Weighted results are reflected in the election results reports in candidate totals as well as votes cast, and results are reported with two decimal places. Likewise, weighted results are manually entered in decimal amounts. Note that totals are not verified when manually entering the results of weighted races.

Since GEMS does not contain weight information, it is not possible to perform verification of manually entered weighted results, so that it is critical that these results entered be verified independently both prior to and following manual entry.


Voters vote on two propositions in a weighted election, Proposition A and Proposition B. Three voters vote in the election, John Doe, Jane Doe, and Bill Smith. John Doe is defined in the voter registration system with weight 25 for Proposition A and 50 for Proposition B, Jane Doe with weights 33 and 45, and Bill Smith with weights 20 and 40, respectively for the two propositions.

The three voters then vote as follows:
Race Selection Voters Tallies Total
Proposition A Yes John Doe 25
Jane Doe 33 58
No Bill Smith 20 20
Proposition B Yes Jane Doe 45 45
No John Doe 50
Bill Smith 40 90

All this for a special district election in which GEMS was never used, or maybe it was. Which did not use decimalized votes, or maybe it did.

Which brings us back to the question we set out to answer in this report: Does a mechanism exist that is precise, configurable, quick, and usable by persons who are not expert programmers, which can control results of elections? The answer is “Yes.”

What we do know for certain is this:

– Fractionalized counting is exactly the feature needed in order to rig the state of Alaska in four seconds, and many other jurisdictions as well. (See Part 4 and Part 5 )
– The design of GEMS contains the most important design requirement for a business model based on selling elections.


Part 3: Proof of code


Part 1: Votes are being counted as fractions instead of as whole numbers


Part 1: Votes are being counted as fractions instead of as whole numbers
Part 2: Context, Background, Deeper, Worse
Part 3: Proof of code
Part 4: Presidential race in an entire state switched in four seconds
Part 5: Masters of the Universe
Part 6: Execution capacity – coming –
Part 7: Solutions and Mitigations – coming –


* * * *

bev-harrisBev Harris is a writer and founder of Black Box Voting. She has researched and written about election transparency and computerized voting systems since 2002. Harris was featured in the Emmy-nominated HBO documentary Hacking Democracy, and is the author of Black Box Voting: Ballot Tampering in the 21st Century, a book purchased by the White House Library and also reportedly found on Osama bin Laden’s bookshelf. Harris’s research has been covered in The New York Times, Vanity Fair, Time Magazine, CNN and several international publications, including the Philippine Daily Inquirer and Agence France Presse. Contact by text or phone 206-335-7747 for media inquiries.

bennie-smithBennie Smith is a Memphis-based application developer for an electrical manufacturing company. He is also a political strategist who has developed a micro-targeting application that predicts voter turnout. In August 2014 he was approached by a number of candidates who insisted that their elections had been stolen. He disagreed with the group and offered to look into how the system works. After discovering a number of irregularities, Smith began to research how votes that originate from the same source can change once they get into the GEMS vote tabulation program. Smith’s attention to these anomalies uncovered an extraordinarily high-risk tampering mechanism and ultimately provided a new infrastructure for analyzing questionable election results.



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