One fairly exhaustive recent study by the Carnegie-Knight Initiative found the frequency of vote fraud by impersonation to be about 1:15,000,000, or about 0.0000067%.
First of all, its the Carnegie-Knight Initiative on the Future of Journalism Education, which is not a group of scientists.
From their web site, the Knight Foundation, "is a national foundation with strong local roots. We invest in journalism, in the arts, and in the success of cities where brothers John S. and James L. Knight once published newspapers." The Carnegie Corporation of New York from their website, was founded as "a foundation that would 'promote the advancement and diffusion of knowledge and understanding.' In keeping with this mandate, our work incorporates an affirmation of our historic role as an education foundation but also honors Andrew Carnegie's passion for international peace and the health of our democracy."
So what's the initiative then? Well it was a joint effort between the two groups, to “advance the U.S. news business by helping revitalize schools of journalism.” Okay, how did that get us to a study on voter fraud? Well, the initiative funding a project called News21, which is itself a project to bring together, "The nation’s most talented journalism students .... to report and produce in-depth, multimedia projects for major national media. News21 shows the kind of work that journalism students are capable of doing and is helping reshape the news industry."
So News 21, put out a project on voting rights in 2012. Why go into all of this? Because it explains why they conducted their efforts in the manner they chose to do so and why their results are flawed. They literally produced very specific numbers that have been repeatedly cited and that don't mean what they imply. So what did they do? They essentially filed public records requests with every state board of elections, and if they weren't responsive with their attorney generals, and if they had to, with their county level prosecutors offices.
Now this obviously could only ever catch situations where a person was "caught" engaging in behavior that could constitute voter fraud (under that states laws). Not every state or county responded, some places refused to give information, still others expressly stated they don't track voter fraud or compile the data requested. Doesn't appear to have been any effort to ensure that the method of reporting results was consistently applied across states, or metrics provided to explain gaps (for instance, they seemed to find a total of 2600 instances, yet they indicated Connecticut, which gave detailed records, had more than 200 alone, that's the kind of self reporting bias that makes a real scientist cringe).
Did they conduct an actual study? It really doesn't appear so. Though they are referred to as having done so, they're very careful to label their records as a database. They don't appear to have any of the metrics that a real study would include, there's apparent measures of significance or any attempt to evaluate correlation or causation. They did do what
journalists like to do and make multiple conclusions based on the statistics that they were able to compile from their database, but that doesn't magically make it into a study with significance. They certainly never point out the gaps in their data base, when they provide detailed and specific numbers and imply they have a "national" merit. They don't emphasize that they made no efforts to consider if reporting standards differed locally as they relied on what they were given back. And when the source was recited, and recited again, all the problems were completely disregarded and dropped, leading to such crazy quotes as what AI asserted in the quote above, converted it into a "fairly exhaustive study" that found a frequency for voter fraud. Even though, if you look at what they did you'd see they made no effort to actually study the rate, frequency or incidence of voter fraud, and at best have a faulty database for even determining the rate at which voter fraud is prosecuted.
So AI if you have an actual study to cite to, would love to see it. Or you have a defense of why a study focused on prosecutions and charges of voter fraud is meaningful as a response to what I said, you know, that voter fraud is difficult to catch and rarely prosecuted, bring it up now.