So some Democrats were discomfited by the revelation that the first of the Alabama efforts was explicitly devised to try out the tactics of the Russian operation, according to an internal report on the project obtained by The Times. Rather than Russians working in St. Petersburg posing as Americans, this time Democrats — most of them far from Alabama — pretended to be conservative state residents.

The first of the Alabama efforts was funded by Reid Hoffman, the billionaire co-founder of LinkedIn, who apologized and said he had been unaware of the project and did not approve of the underhanded methods. The second was funded by two Virginia donors who wanted to defeat Mr. Moore — a former judge accused of pursuing sexual relationships with underage girls — according to a participant who would speak about the secret project only on the condition of anonymity and who declined to name the funders.

The two projects each received $100,000, funneled in both cases through the same organization: Investing in Us, which finances political operations in support of progressive causes. Dmitri Mehlhorn, the group’s managing partner, declined to comment on whether he approved of the tactics he had helped pay for. But after the Times report in December, he acknowledged, in a post on the online forum Medium, a “concern that our tactics might cause us to become like those we are fighting.” He declared that “some tactics are beyond the pale.”

Another organizer of the project, according to two participants, was Evan Coren, a progressive activist who works for the National Archives unit that handles classified documents. He did not respond to requests for comment. Beth Becker, a social media trainer and consultant in Washington who handled Facebook ad spending for the Dry Alabama page and the project’s other Facebook page, called Southern Caller, said in an interview that a nondisclosure agreement prohibited her from saying much about the project.

But, she added, “I don’t think anything this group did crossed any lines.”

That may be true in the sense that neither law nor regulations set any clear limits on social media activity in elections. “The law has clearly not caught up with social media,” Ms. Becker said.