If voters are free to take photos, outsiders could also compel voters to take photos, Mr. Gardner said. Corrupt forces that would seek to buy votes could demand evidence that the bought votes were actually cast. By not allowing voters to record that proof, he said, no one would be foolish enough to try to manipulate anyone else’s vote.

In the past, election fixers trying to eliminate voter privacy might have made people deposit their yes and no votes into different boxes, or link ballots to an identity. Modern voting setups had effectively prevented such behavior for many years, but the ability of smartphones to eliminate the privacy of the voting booth has created a new form of the old trick, Mr. Gardner said. And politicians and their supporters have never been shy about trying to find new ways to win elections.

“Whether an exchange of money, or for having to live with someone or some other fear, you don’t want anyone to go into that booth and end up voting for someone they didn’t really want to vote for, but felt they didn’t want to pay that price for whatever reason,” he said.

Why Should Selfies Remain Free?

Those opposed to photography bans say concerns about vote-buying are overblown.

“There isn’t much evidence, if any at all, that this kind of activity is actually occurring,” said Justin Silverman, the executive director of the New England First Amendment Coalition. It was one of three organizations to file amicus briefs on Friday, along with Snapchat and the Reporters Committee for Freedom of the Press.

No one wants to see vote-buying, but in combating that murky threat, officials have placed real restrictions on First Amendment rights, Mr. Silverman said. Millennials and other active social media users use photos as a fundamental part of how they communicate and ought to be able to express their excitement at participating in democracy, he said. Whether a selfie with a completed ballot or an artistic shot of the booth, an Instagram or Snapchat post can be as much a part of expressing civic pride as an “I Voted” sticker.

Mr. Silverman said the image of a goofy selfie with a ballot has obscured what he described as more serious benefits of allowing photography, like serving as an alert system for confusing ballots.