Mark Finchem, the Republican nominee for Arizona secretary of state, talks a lot about tracking: procedures, processes, audits, the path a ballot takes from voter to tabulator.He’s a member of the Arizona state House of Representatives, and has a formal way of speaking, full of numerical legislation titles and terminology, but also talks about things seen and unseen. Like a number of other Republican nominees for secretary of state this year, Mr. Finchem claims the last election was fraudulent.“Here’s why we know it didn’t happen,” he told an interviewer who had just suggested Arizona may have actually voted for Joe Biden in 2020. “It’s nonsense intuitively. Leading up to the election, this would be August, September, October. It first started off that you’d see a Trump train of maybe a dozen cars, and this is in my community. It’s one community, but I think it’s fairly representative of Arizona. You’d see a Trump train of maybe a dozen cars.” The hosts start cracking jokes about Biden trains behind gas stations these days, but in the interview, Mr. Finchem remains undeterred and unlaughing: First it was 12 cars, then 24, then 48, culminating in a three-mile Trump train. This is the kind of thing Mr. Finchem will abruptly say amid talk of election procedure.In November 2020, Mr. Finchem was part of a hearing in Arizona where Rudy Giuliani aired claims of election fraud; Mr. Finchem went to Washington on Jan. 6. He wants to decertify the 2020 election and for Arizona to withdraw from the Electronic Registration Information Center, a nonpartisan organization funded by participating states that helps them to find potential voters and determine duplicate active registrations. He also could win in Arizona this year; the state has been decidedly close the last several elections.His public comments tend to be both premised on the possibility of rampant voter fraud — which, in actuality, takes place rarely — and reflect a kind of individualism that’s a part of the tech and society we already have, where individuals routinely arbitrate and police disputes online.Mr. Finchem has called himself “probably an evangelist” for a 2013 book by Matthew Trewhella called “The Doctrine of the Lesser Magistrates.” A favorite of some extreme anti-abortion activists, the book argues that officials have an obligation to stop enforcement of laws that violate, in the author’s view, God’s wishes, specifically laws that legalize abortion or acceptance of homosexuality.The author praises the former Alabama Supreme Court judge Roy Moore in his efforts to defy court rulings about placing the Ten Commandments on government property. “Some of the most important and necessary actions down through history were done without a majority,” Mr. Trewhella writes. “In fact, human nature is such that the majority usually only have an interest in their own well-being and livelihood. In truth, the lesser magistrate does not need any support from the people in order to act.”After his primary victory this summer, in one interview Mr. Finchem brought up an app where people can submit perceived voting irregularities and observed, “We’ve basically turned the entire polity — the entire citizen pool in Arizona — into witnesses, and that’s even more robust than having poll watchers.”In April, a podcast interviewer asked Mr. Finchem if he’d discovered anything “determinative” to Arizona’s close election, which Mr. Biden won by about 10,000 votes. Even the audit of Maricopa, the state’s largest county — which was supported by Arizona Republicans like Mr. Finchem and criticized by elected officials — found Mr. Biden won the county. Mr. Finchem replied, “So yeah, part of that was a Psyop [psychological operation]; they worked very, very hard to convince the American people that, ‘Oh it’s going to be a close race.’ No, it wasn’t; it was a blowout.”How much doubt can the system take on? I really wonder how we get out of a situation where some segment of the population believes people rigged the vote against Mr. Trump, and some other segment believes, maybe a little hazily, that something must have been amiss, given all the noise from Mr. Trump and people like Mr. Finchem. Doubt can be difficult to overcome once it’s in the air.How would you talk someone out of this? Pull out a bunch of maps and charts and show how Donald Trump improved his share with voters in some cities and places like the border, but it was no match for Joe Biden’s performance in the suburbs in enough states, the kind of demographic pattern that you can see in states both won and lost by Mr. Trump? Ask them to get involved and see the process themselves? Hope this just fades, if Mr. Trump fades?If Mr. Trump’s endless refusal to concede has vastly expanded and sustained the universe of fraud believers and election skeptics, the sentiment has begun to detach from his personal fortunes.Kansas officials recently had to perform a recount of the blowout referendum to keep abortion legal in the state; candidates who’ve won primaries this year have suggested there might be fraud inherent in the process; one Texas county election staffer who quit his job recently told The Associated Press, “That’s the one thing we can’t understand. Their candidate won, heavily. But there’s fraud here?” In a town hall this summer, after detailing how Utah’s elections work and its security measures, Republican Gov. Spencer Cox called unsubstantiated fraud claims “dangerous” and “not healthy.” Mr. Cox added, “Making people prove a negative — something that doesn’t exist — is virtually impossible.”One of Mr. Finchem’s big plans as Arizona’s would-be secretary of state hinges on the idea that there’s space for fraud in the unseen. He wants to end Arizona’s early voting program, which the state first implemented in the 1990s and many, many voters in both parties regularly use. He claims that to end fraud, you must end early voting. “Here’s what happened: You received a ballot in the mail,” he told an interviewer this year. “You fill that ballot out. And then you put it in the mail. You have just broken [the] chain of custody. You have just put somebody in between you and the county official who’s supposed to be counting your ballot.”Instead, as a federal judge outlined recently in his dismissal of a lawsuit Mr. Finchem and the gubernatorial nominee Kari Lake filed, Mr. Finchem envisions ballots counted by hand, at the precinct level, “one at a time, by three independent counters” in “full view of multiple, recording, streaming cameras,” with a serial number known to the voter but no other personal identification on each ballot.This is just one thing Mr. Finchem has said, but it’s worth lingering on and considering. In the end, this is a really big country with a secret-ballot system: each vote cast must eventually go someplace to be counted, on your faith and trust. A machine counts the ballot — or sometimes, human hands do, if there’s a recount — and that input gets piled up with all the other inputs and then reported to the public, somewhere beyond each voter’s vision. This would still be true under Mr. Finchem’s livestreamed hand-count system — the secret moment would just be flipped to the front end, where some authority would distribute serial numbers to each voter.But it’s striking where this kind of thinking can lead you and leave you. If you follow this broken-chain-of-custody logic, you could not trust the mail carrier or the guy who picks up the ballot dropbox, even if your own mail shows up every day. If you really commit, you might not be able to trust the mechanism that counts the votes, whether that’s a person or a machine or the official feeding the machine, since it’s easy to imagine how this idea of an individual’s subversion could carry from one civic process to the next, once someone pushes that kind of doubt into the system. If you follow the logic all the way, this kind of thinking could leave you, ultimately, alone vs. everything, surrounded by the eternal possibility of subversion.Katherine Miller is a staff writer and editor in Opinion.The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips. And here’s our email: email@example.com.Follow The New York Times Opinion section on Facebook, Twitter (@NYTopinion) and Instagram.