When he tried to vote in 2015, he had lived in the same place for about 16 years.

“I’ve been living in Ohio my whole life,” he said. “I pay property taxes and income taxes. I register my car. They obviously had all the data to know that I was a resident. They could have looked it up, but they were too cheap.”

The question for the justices is whether two federal laws allow Ohio to cull its voter rolls using notices prompted by the failure to vote. The laws prohibit states from removing people from voter rolls “by reason of the person’s failure to vote.” But they allow election officials who suspect that a voter has moved to send a confirmation notice.

The United States Court of Appeals for the Sixth Circuit, in Cincinnati, ruled in favor of Mr. Harmon last year, saying that Ohio had violated the National Voter Registration Act of 1993 by using the failure to vote as a “trigger” for sending the notices.

Without that decision, “the ballots of more than 7,500 eligible Ohioans would have gone uncounted in the November 2016 election,” Mr. Harmon’s lawyers at Demos and the American Civil Liberties Union wrote in a Supreme Court brief.

There are other ways to calculate the impact of Ohio’s approach. A Reuters study last year found that at least 144,000 people were removed from the voting rolls in recent years in Ohio’s three largest counties, which are home to Cleveland, Cincinnati and Columbus.

“Voters have been struck from the rolls in Democratic-leaning neighborhoods at roughly twice the rate as in Republican neighborhoods,” the study found. “Neighborhoods that have a high proportion of poor, African-American residents are hit the hardest.”

State officials say they sent Mr. Harmon a notice in 2011. He said he never saw it.

“I don’t remember getting that, and I don’t know why they sent it in the mail,” he said. “I’m out in a rural area, and sometimes I get other people’s mail. Sometimes other people get my mail.”