Type I versus Type II errors in election security

You likely first encountered the “Type I versus Type II error problem” in grade school and didn’t realize it. Perhaps some kid in the class played a practical joke on the teacher, and because nobody confessed, the entire class got detention. In some situation or another, you were likely punished undeservedly as a group for the actions of a small number of people.

In non-math terms, a Type I error happens when an innocent person is caught in a “detection net.” With a Type II error, a guilty person escapes the “detection net.” This same concept also applies to Covid-19 testing. In a Type I Covid test error, the test comes out as “positive” for a person who is really uninfected. Likewise, a Type II error occurs when a Covid-infected person gets a “negative” test result. Which type of error do you think is worse?

This also describes quite well the ham-handed approaches we most often use in trying to detect and prevent this scary thing, harped on by the President daily, called election fraud. In practice, many thousands of eligible voters are obstructed from voting in order to catch a small handful (if any) of “criminal voters,” who most likely do not total to enough to sway the election anyway.

The statistics definition

Unless your city is in full crisis mode, more than 90% (currently greater than 93% nationwide) of the people currently tested for the coronavirus are not infected by it. And so, the more reliable of the several available tests should come back negative for most people. This is called the null hypothesis in statistical terms. But some of these uninfected people will get a “false positive” on the test, which is that Type I error. In statistical terms this is called rejecting a true null hypothesis.

On the other hand, some unknown number of people are receiving false negatives from that same test. In other words, they really are infected, but the test says that they are not. This is a Type II error (technically the “non-rejection of a false null hypothesis,” which is a mouthful). In the case of Covid-19 testing, a Type I error wrongly inconveniences uninfected people, requiring them to quarantine when they are, in reality, not a threat to anyone. A Type II error, however, frees an infected person to continue to walk around in public, potentially infecting more people.

Which is worse? The Type II error lets the disease spread more than it would if the test were more accurate. The Type I errors, on the other hand, do not cause physical harm in this case, but could well cause economic harm, unnecessary fear and family disruptions from the false positive. There is your ethical dilemma, with no easy answer.

The problem is best solved by better tests, which would reduce both types of errors. But as Ohio Governor Mike DeWine recently found out, time constraints and cost tend to push us toward less-reliable tests, so the problem will not go away. If the tests are faster and cheaper, however, you can minimize Type I/false positive errors by retesting all positive “hits” with more accurate tests, and minimize Type II/false negative errors by more frequent testing and group testing.

Back to voting

Most “voter identification” laws generate far more Type I errors than Type II errors. In other words, we likely exclude from voting several “orders of magnitude” (perhaps 1000 times or more) multiples of legal voters through ID laws (these are false positives/Type I) than people we miss who are committing intentional “voter impersonation fraud” (false negative/Type II) . The “null hypothesis” here is that, if you randomly “collect a sample” of American adults, they are indeed in the large majority eligible, legal voters, though perhaps unregistered in their current locality. And yet these laws disenfranchise thousands in each major election.

While it seems unlikely to many middle-aged, middle-class, white American citizens, there are thousands of people found in most locales who do not have an identification document approved by their state that shows an accurate address for their current place of residence. For starters about 10% of the U.S. population moves their domicile each year. An ID with an old address is sufficient for most commerce or travel in the United States, but not for voting in many places. These “frequent movers” are heavily skewed toward the bottom end of the socioeconomic scale, and because of that, also skewed to racial minorities. It is not a crime to move. People should not lose their right to vote because their address is unstable.

Older Americans, especially those living in eldercare housing, frequently let their identification documents lapse. They are also mostly legal voters. College students usually have an up-to-date photo ID, but many states like Texas prohibit its use, as well as making it harder for legal residents to vote absentee, or even just to register to vote. In short, the state is forcing massive numbers of Type I errors, blocking many thousands of citizens from the polls, in order to “catch” a few, mostly mythical, “illegal voters.”

Signature matching

I have written recently about why well-designed mail-in voting is much more auditable than many electronic balloting systems currently in place. These are often mischaracterized as “absentee” voting systems, but in many states, such as my current state of Florida, there is absolutely no requirement that you be absent from your precinct on election day. Indeed, the word “absentee” is nowhere to be found on the forms. A Florida resident simply has the right to vote by mail, period.

The primary place in mail-in voting where Type I errors do occur in large quantity, however, is in the signature verification process. Note that these ballots are encoded with multiple “audit points” already before any signature match. Print formats and paper types are not easily replicated. Each ballot is usually bar-coded to an individual eligible voter for tracing. Addresses and postmarks can be audited either before or after any election with a simple audit question to a statistical sample of voters: “Did you submit a ballot in this election?” Post-election ballot data can be also analyzed for inconsistent trends indicating suspicious vote counts. Basic statistical math can uncover almost any large effort at intentional mail-in ballot fraud.

However, people’s signatures do vary over time, and most people likely have no idea as to where the election officials have obtained their signature. For instance, my signature likely entered the Florida system via a computer entry pad that I signed when I got my Florida drivers’ license and registered to vote at the same time. That is the signature I try to match in each election.

However, missing and mismatched signatures have sometimes resulted in thousands of rejected ballots, the vast majority of which are Type I errors. My county, however, has an online process to improve on that issue. That barcode allows me to track my individual ballot online from receipt to verification to counting, and I can then contact the office to “cure” any problem. This is basic systems management in the 21st century, but many jurisdictions (intentionally) won’t take that auditing step.

How significant are these errors?

So, how do we know which is larger? Is it the Type II errors, where we fail to catch the criminal masterminds messing with our elections? Or is it the Type I errors, where an old signature, or a missing piece of irrelevant data, or an old address on a drivers’ license, or just being a student in Texas, disqualifies an adult U.S. citizen from casting a ballot?

You have to be pretty much a conspiracy nut to believe the first, even though Donald Trump claimed that California allowed millions of undocumented immigrants to vote in the 2016 election. I wrote a post last year looking at the probability math behind “Deep State” and other similar conspiracies. The successful conspiracies around the Trump administration are more like the math of small-time grift, which I also wrote about in 2018. The smaller the group required and the stronger the Omertà (code of silence) used to stifle squealers, the better the odds that you will pull off your con. But big conspiracies require the silence of too many people to be mathematically sustainable.

Criminals or Doofuses?

And because of that math, those “criminal voters” are often more boneheaded doofuses than masterminds. Kris Kobach’s highly-touted “voting integrity commission” was disbanded after finding no evidence of widespread voter fraud. Which conspiracy nuts, of course, would say “proves” how good the conspiracy is, so good that there is no evidence.

Instead, the incidents that have surfaced have mostly been either (1) caught by the very audit controls that competent states can easily put into effect, or (2) “one-offs” that are too small to matter, or (3) really dumb people doing even dumber things. And, not coincidentally, most of those from the last group uncovered in the 2016 election tried to cast illegal ballots for Donald Trump, not Hilary Clinton.

An example of a problem caught by standard audit procedures was a 2018 case of an elections official altering absentee records, which was caught by a post-election audit of cross-validation procedures. Even then, the intent here appears not to have been an attempt to change election results, but rather to cover up some bad counting mistakes.

In one of the most notorious intentional fraud cases from the 2018 Congressional election, a Republican political operative was caught trying to forge absentee ballots collected from unsuspecting voters. Again, procedures in place uncovered this fraud, and the election was run over again, with a different Republican candidate in place.

Conflicting laws for catching felons who illegally vote after their release despite having their rights taken away fall into the second category of “one-offs.” The tragedy here is that courts have at times imposed sentences far harsher (five years in this case) than “white collar” criminals often get for million-dollar frauds or paying off mistresses to swing a presidential election. There is no evidence that these actions are sufficient to sway elections.

On the “doofus” side, there were several cases of determined Trump voters trying to vote multiple times, including this woman who was apparently convinced by Donald Trump that her first vote would be awarded to Hilary Clinton.

There certainly are confirmed threats to voting processes, but these are far more likely to be associated with the potential hacking of electronic systems without paper ballot backup. Even then, we have yet to see an election-throwing case brought to fruition here.

We need this simple amendment to the Constitution of the U.S. to cut down on the number of Type I voting errors: “The right of adult citizens of the United States to vote in Federal elections in the location of their primary domicile or by the U.S. Mail shall not be inequitably impeded.”

For additional posts on probability, volition and ethics, follow the Dice icon back or forward where it appears.

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1 thought on “Type I versus Type II errors in election security

  1. Bruce Lindgren

    In any investigation, including even scientific investigations, defining the problem correctly is one essential element; and using an effective investigative methodology is an equally important element. I have friends who call up a variety of urban legends that include episodes of large numbers of non-citizens showing up at polling places and demanding to vote. These tales can seldom be verified, and in any case, a person cannot vote without being previously registered to do so. (A hilarious video has been circulating in which the Apprentice-era Donald Trump travels from precinct to precinct in Manhattan with Billy Bush trying to vote and getting turned away each time because his name is not on the roll for that precinct. Finally, he takes a paper provisional ballot and tries to fill it out in the limo with Billy Bush looking on.)

    Kris Kobach has undertaken “voter fraud” investigations, both as Kansas Secretary of State and as the chair of Donald Trump’s Voter Fraud Task Force. In both cases, Kobach does not seek to go after the proverbial non-citizen voters. He’s looking for people registered to vote in more than one state using a multi-state database tool called Crosscheck. Searches tend not to be very sophisticated, so it tends to turn up a lot of duplicate “John Smith” names. (A lot to “Type I” errors.) People have been found to have voted twice through these checks, but they tend to be small in number and often based on a misunderstanding. (Perhaps a neighbor says, “It doesn’t matter if you’ve already voted absentee in Oklahoma; you’re a Kansas resident now, so you can vote here.” The voter says, “You seem to know what you’re talking about, so I’ll do it.”) Of course, these errors (which are still against the law) occur rather randomly, so investigations in Kansas tend to catch more Republicans than Democrats just because there are more Republicans in the state.

    These investigations have turned up a small number of random problems, but findings of systematic voter fraud in which “millions” of votes are cast for one particular party by dogs, non-citizen immigrants, and Islamic terrorists just do not show up. The true voter fraud cases that do occur tend to be localized and reflect a rare display of bipartisanship.


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