Citizens United itself concerned a slashing polemical documentary about Hillary Rodham Clinton paid for by a conservative advocacy corporation that wanted to distribute the film on a video-on-demand service during the Democratic presidential primaries in 2008, when Mrs. Clinton was seeking the party’s nomination.

The five-justice majority in Citizens United said that speech about politics is at the core of what the First Amendment protects, that more speech is better than less and that the government has no business deciding who can speak or how much.

It is a small step from that reasoning to saying, as eight justices did, that it helps to know who is advancing the ideas you are evaluating. You probably trust some sources of information more than others, for instance, and you may examine an argument more skeptically if it happens to align with the speaker’s self-interest.

Richard L. Hasen, an election law specialist at the University of California, Irvine, added that political science research had shown that disclosure could provide voters with useful information. “If all I tell you about a candidate is that he is backed by the N.R.A. or Planned Parenthood, that is all many voters need to know,” he said. “The disclosure serves a shortcut function.”

James Bopp Jr., a driving force behind the Citizens United case and a leading critic of campaign finance regulation, acknowledged that his side had been on something of a losing streak in disclosure cases, including in a pair of decisions last month from the United States Court of Appeals for the First Circuit, in Boston, that upheld laws from Maine and Rhode Island requiring the disclosure of election-related spending.

“It is true,” Mr. Bopp said, “that some courts, particularly most recently the First Circuit, have treated Citizens United’s endorsement of disclosure as novel, which it isn’t, but also as carte blanche for any regulation.”

Mr. Bopp is right that the Supreme Court has long been comfortable with disclosure requirements. But Ciara Torres-Spelliscy, a law professor at Stetson University in Florida, said that lower courts had in the years before Citizens United grown skeptical of compulsory transparency, sometimes saying that it chilled First Amendment rights by imposing burdensome reporting requirements. “Before Citizens United, there was a very alarming trend in this area,” she said.