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The Arizona Senate’s Contractors Fail to Understand Basic Probability and Voter Data

Items identified in the partisan review by Cyber Ninjas as problems are easily explained.

October 1, 2021

Last week, the company Cyber Ninjas finally released a “report” on their partisan review of the 2020 elec­tion that the Arizona Senate commis­sioned. The firm’s top three find­ings, accord­ing to its own rank­ing of import­ance, are text­book examples of how purvey­ors of voter fraud myths misun­der­stand data — if there were a text­book about data illiter­acy.

The most facially naïve of these find­ings is the one titled “Voters That Poten­tially Voted in Multiple Counties” — labelled as one of two find­ings of “high” import­ance, just below the so-called “Crit­ical” find­ing of “Mail in Ballots Voted from Prior Address.” It even went so far as to claim “5,295 ballots impacted.”

But it turns out that this “find­ing,” and the attend­ant recom­mend­a­tion that a list of 10,342 voters be “fully reviewed,” is based on fail­ure to compre­hend basic prob­ab­il­ity and patterns of name popular­ity. Cyber Ninjas simply looked for Arizona voters who shared a first, middle, and last name and birth year with another voter in the 2020 elec­tion, and it found 10,342 of them.

The Cyber Ninjas thinks that warrants a “full review,” and goes so far as to claim these people may repres­ent the same person, voting more than once in the elec­tion. But their suspi­cion is completely base­less, and just evid­ence that they are ignor­ant of the “Birth­day Prob­lem,” a basic stat­ist­ical concept.

If we look at a group of people with a common name, such as Robert Smith, we should­n’t be surprised that two of them share a birth­day. In fact, we should expect it.

A lot of people find this coun­ter­in­tu­it­ive, hence the name “Birth­day Prob­lem,” or some­times “Birth­day Para­dox.” But Cyber Ninjas did some­thing even more outrageous. It only checked for birth year matches among Arizona voters who share a full name and parti­cip­ated in 2020. It is even more common to share a birth year with someone than to share a full birth­d­ate includ­ing the month and day.

If we assume that any group of voters who share a full name contains people evenly distrib­uted from 18 to 75, the group only has to be 10 voters for the odds of a birth year match to be over 50 percent. We’d expect a match among just 16 voters 90 percent of the time. But it’s even more common than that, when you remem­ber that there are vari­ations in birth rates and popu­lar baby names over time.

The Bren­nan Center analyzed Texas’s voter file, and we found 41 people named “David Alan Smith.” More than two-thirds were born before the 1970s, though, when the baby boom was over and the popular­ity of the name “David” began to decline. In the 1950s, we found 10 “David Alan Smiths” who share the same birth year as another David Alan Smith. In the 1960s we found seven. But by the 1970s, there were just two.

For fun, we checked on James Richard Perry, the former governor. There were just two people with that name in the Texas voter list, so the odds weren’t good they would share a birth year, and indeed, they didn’t. But changes in name frequency make a big differ­ence. There were seven people named James Richard John­son who share a birth year with another voter of the same name.

Of course, Texas is big. But Arizona isn’t small, with over 4 million registered voters. When we analyzed Arizon­a’s registered voter file we found that nearly 30,000 voters share a full name (first middle and last) and birth year with another. That’s consist­ent with what basic stat­ist­ics predicts, not a sign of elec­tion miscon­duct.

It’s also unclear if Cyber Ninjas took the trouble to exclude intra-county matches, as their “find­ing” implies. An intra-county match is, of course, virtu­ally impossible to repres­ent someone voting twice, since Mari­copa County uses elec­tronic check-in lists that update in real time to avoid any acci­dental or inten­tional double voting.

In another example of the company’s lack of exper­i­ence with voter data and elec­tion law —the find­ing that Cyber Ninjas labelled as “crit­ical,” supposedly “impact[ing]” 23,344 ballots — is that this number of people voted in the 2020 elec­tion in Arizona but also showed up on a list of people who had moved provided by a commer­cial address veri­fic­a­tion service. This service is used by compan­ies that want to find custom­ers, so it would not have reason to distin­guish between a tempor­ary move and a perman­ent one — local furniture stores and restaur­ants want you as a customer whether you plan to stay at your new loca­tion forever, or just the fall semester. But tempor­ary moves do not change a voter’s eligib­il­ity to vote in the juris­dic­tion of their perman­ent resid­ence.

The other find­ing of “high” import­ance accord­ing to Cyber Ninjas was the alarm­ing claim that in thou­sands of cases, “More Ballots Returned by Voter Than Received.” But when Mari­copa County records that a ballot was returned, that does­n’t mean it is neces­sar­ily going to be veri­fied and coun­ted. For instance, a voter may have forgot­ten to sign the envel­ope. If this happens, elec­tion offi­cials will contact the voter to “cure” the prob­lem and will not count the ballot until the inform­a­tion neces­sary has been received. County offi­cials have confirmed that this is the most common reason for a voter to appear multiple times in the file that Cyber Ninjas looked at.

Another of the senate’s contract­ors, Shiva Ayyadurai, simil­arly failed to under­stand (or acknow­ledge) this notice and cure proced­ure, when, in a senate hear­ing he made a rambling present­a­tion that raised suspi­cion about duplic­ate envel­ope images from the 2020 elec­tion and at one point erro­neously described the duplic­ate envel­ope images as “two ballots.” The report was then ampli­fied by elec­ted offi­cials and candid­ates in Arizona who falsely called them “duplic­ate votes” and “duplic­ate ballots.” But there is noth­ing suspi­cious about an envel­ope being processed twice if the first time, the signa­ture can’t be veri­fied. Once the prob­lem has been fixed, the envel­ope is ready to be rescanned and the ballot inside removed and coun­ted.

In short, the contract­ors’ most atten­tion-grabbing find­ings fit the pattern: remain ignor­ant of basic prob­ab­il­ity, voter data, and elec­tion law, in the service of rais­ing base­less suspi­cions about one’s fellow citizens and the dedic­ated public servants who admin­is­ter elec­tions. It would be boring if it weren’t so danger­ous, as these suspi­cions lay the ground­work for future sabot­age of our demo­cracy.