(Creative Commons/Wikimedia, P199)

President-elect Donald Trump claimed on Sunday afternoon that the reason he had lost the popular vote in the election was that “millions of people had voted illegally.” As The Washington Post’s Philip Bump has noted, one likely source of this claim is Infowars, a website known for peddling conspiracy theories (such as the claim that the massacre at Sandy Hook Elementary School in Newtown, Conn., was faked by the anti-gun movement). It’s somewhat appropriate then that there is good political science research that finds that people are as likely to claim that they have been abducted by space aliens as that they have committed voter fraud.

One of the key findings of a 2014 article in the Election Law Journal by John Ahlquist, Kenneth R. Mayer and Simon Jackman is that “the lower bound on the population reporting voter impersonation is nearly identical with the proportion of the population reporting abduction by extraterrestrials.” About 2.5 percent of the population seems to admit to one or the other. What does this finding tell us?

It suggests — as does most political science research on the topic — that there is no evidence of large-scale voting fraud in the United States. Certainly, there is no evidence of millions of people voting illegally as Trump claims. As Ahlquist, Mayer and Jackman describe it:

Virtually all the major scholarship on voter impersonation fraud — based largely on specific allegations and criminal investigations — has concluded that it is vanishingly rare, and certainly nowhere near the numbers necessary to have an effect on any election. … To give one idea of the scale: A review of allegations in the 2008 and 2010 elections in Texas found only four complaints of voter impersonation, out of more than 13 million votes cast, and it is not clear whether any of the complaints actually led to a prosecution (Minnite, 2013:101). By contrast, the 2000 presidential election almost certainly was altered by poor ballot design in Palm Beach County, which resulted in at least 2,000 voters who intended to vote for Al Gore and Joe Lieberman casting their ballots for Pat Buchanan by mistake (Wand et al., 2001).

So what Ahlquist, Mayer and Jackman do is look for evidence on rates of voter fraud from a very different source: survey data. The problem they face is that very few people are going to admit to having committed election fraud. Hence, they use an ingenious trick to make it easy for people to reveal (in the aggregate) whether they’ve committed voter fraud without ‘fessing up to it as individuals. First, they randomly divide the people whom they are surveying into a control group and a treatment group. They ask each group to look at a list, and say how many of the actions on that list they have carried out (without revealing which specific actions they have done). The control group gets a list of purely innocuous actions. The treatment group gets the same list, but with one addition — a question asking them whether they have ever committed voter fraud.

By comparing the average number of actions that people in the treatment group have carried out, with the average number of actions that people in the control group have carried out, Ahlquist, Mayer and Jackman can figure out whether voter fraud is a serious problem. If it is, the average number of actions ought to be significantly higher for the treatment group than the control group. This “list experiment” approach has been applied to voter fraud in other countries, as well as to other sensitive topics that people may have difficulty talking directly about, such as racial attitudes.

Ahlquist, Mayer and Jackman’s findings are unequivocal — “the notion that voter impersonation is a widespread behavior is totally contradicted by these data.” However, a few respondents in the treatment group report that they have committed all the actions listed, including voter fraud. Should this be interpreted as evidence that they have indeed cheated at the ballot box? Or are they simply answering the question carelessly?

There’s some internal evidence to suggest that they are just being careless. But to be sure, Ahlquist, Mayer and Jackman carried out a second set of experiments, which is where the extraterrestrial abductions come in. Few people believe that Americans are not being kidnapped en masse by space aliens eager to conduct experiments on their sensitive bits. So, Ahlquist, Mayer and Jackman did a second list experiment in which members of the control group, instead of being asked about voter fraud, were asked whether they have been abducted by aliens. If people answered yes to all questions with about the same proportions in both the space alien abduction experiment and the voter fraud experiment, then this suggests either that people are rushing through the surveys carelessly, or that alien abduction is a much bigger problem than any of us knew. And this is indeed what the authors found:

The implication here is that if one accepts that 2.5% is a valid lower bound for the prevalence of voter impersonation in the 2012 election then one must also accept that about 2.5% of the adult U.S. population — about 6 million people — believe that they were abducted by extra-terrestrials in the last year. If this were true then voter impersonation would be the least of our worries.

So in short, this research provides exactly as much evidence supporting the claim that millions of people are being kidnapped by space aliens to conduct personally invasive experiments on, as it does to support Trump’s claim that millions of people are engaging in voter fraud.

An earlier version of this post was published on Nov. 14, 2013.