Two weeks ago, the conservative media personalities Diamond and Silk falsely claimed on their Facebook page that people who were not eligible to vote were receiving ballots in Georgia’s special elections next month. Their post was shared more than 300 times.

A week later, the right-wing commentator Mark Levin shared a post on his Facebook page falsely suggesting that the Rev. Raphael Warnock, one of the two Democrats running in the Georgia Senate runoffs, once welcomed Fidel Castro to his church. The misleading claim was shared more than 3,000 times.

At the same time, a drumbeat of misinformation about the presidential election count in Georgia droned on. Lara Trump, President Trump’s daughter-in-law, and the Hodgetwins, a bodybuilding duo who have turned to pro-Trump political comedy, shared several false stories on their Instagram and Facebook pages that claimed suitcases filled with ballots were pulled out from under tables during the November vote count. Tens of thousands of people shared their posts.

As Georgia prepares to hold special elections that will determine which party will control the U.S. Senate, the state has become the focus of a misinformation campaign that is aimed at discrediting the results of the November elections and convincing voters that Democrats are trying to steal the upcoming vote.

A small group of “superspreaders” is responsible for the vast majority of that misinformation, according to new research by Avaaz, a global human rights group. Not only are those accounts responsible for most of the misinformation swirling around the vote, they are drowning out accurate reporting by mainstream media outlets on Facebook and Instagram.

The research indicates that, despite efforts by social media companies to curtail misinformation, the viral nature of false news continues to take advantage of the algorithms that gin up what people see on those platforms. The algorithms often reward outrage over accuracy, and telling people what they want to hear or what gets them angry can easily overwhelm the truth.

Americans are “being drowned in misinformation in Georgia by these superspreaders,” said Fadi Quran, a director at Avaaz.

The Avaaz study also calls into question Facebook’s recent decision to roll back a change that elevated news from authoritative outlets over hyperpartisan sources. The change, which the company said was intended to be temporary, had resulted in an increase in Facebook traffic for mainstream news publishers including CNN, NPR and The New York Times, while partisan sites like Breitbart and Occupy Democrats saw their numbers fall.

Many of the “superspreaders” have previously been named by researchers as playing central roles in spreading misinformation about voter fraud in the November presidential elections.

“Facebook has gotten a lot of pressure over claims that they are censoring the right or conservatives, but what the data shows is that they may be favoring these actors,” Mr. Quran said. “These accounts regularly spread misinformation. The question is: Why doesn’t Facebook demote their reach per their policies?”

Other misinformation spreaders included Eric Trump, the president’s son, and Sebastian Gorka, the president’s former deputy assistant. President Trump also continued his barrage of misinformation about Georgia’s elections, according to the research by Avaaz.

The top 20 Facebook and Instagram accounts spreading false claims aimed at swaying voters in Georgia accounted for more interactions than mainstream media outlets. Using CrowdTangle, a Facebook-owned research tool, Avaaz examined social media posts between Nov. 8, when most news outlets called the election for President-elect Joseph R. Biden Jr., and Friday. They found that the top 20 “superspreaders” averaged 5,500 interactions on their Facebook posts, while the 20 largest news outlets averaged 4,100 interactions per post.

These users saw more people interacting with their posts, despite having fewer followers on Facebook than the mainstream news outlets. Combined, the news outlets had more than 208 million followers, while the top “superspreaders” had 85 million followers.

Mr. Quran said the numbers showed how Facebook’s algorithms favored the sensational, and often false, posts.

A Facebook spokesman, Kevin McAlister, said the company was still cracking down on misinformation, despite the recent rollback.

“We’re taking every opportunity to connect people to reliable information about the election,” Mr. McAlister said. He said the company was also “deploying the teams and technology we used in the general elections to fight voter suppression, misinformation and interference in the Georgia runoff elections.”

None of the top misinformation spreaders responded to requests for comment.

Their claims ran the gamut from insults — that the Democratic Senate candidates, Mr. Warnock and Jon Ossoff, are corrupt — to the often-repeated false claim that voting machines that run on software from the company Dominion Voting Systems flipped votes from President Trump to Mr. Biden.

Mr. Quran said the accounts also appeared to be “professionalized” in how they spread misinformation.

“We see them regularly testing new narratives to see where they can hit a certain nerve, and then acting on it,” he said. Misinformation that successfully targeted Latino voters during the November presidential election, for example, was also being repurposed for Georgia, he said.

One claim, that Mr. Warnock, a pastor in an Atlanta church where the Rev. Dr. Martin Luther King Jr. once preached, “celebrated Fidel Castro and welcomed him to his church” was not accurate. The claim refers to Mr. Castro’s appearance at a New York City church where Mr. Warnock was a pastor 25 years ago, and there is no evidence that Mr. Warnock was involved in arranging the visit. There is also no evidence that he welcomed Mr. Castro.

It was a variation of claims that circulated in Florida during the presidential election that linked Democratic candidates to the Communist Party in Cuba. Some of those claims have also been translated into Spanish to target the more than 300,000 voters with Latino backgrounds in Georgia, Mr. Quran said.

Voters in Georgia are also being targeted with misleading information by new media start-ups. A conservative local news network, Star News group, which already runs news sites in Tennessee, Virginia and Minnesota, announced in November that it was opening a venture called the Georgia Star News, according to the liberal media watchdog group Media Matters for America.

Since then, the website has published misleading news about the presidential election and the coming runoff election, according to an assessment by NewsGuard, a start-up that examines false stories.

The Georgia Star News said in a response that NewsGuard’s assessment included “subjective, nonspecific generalizations that lack any meaningful context” and that it “rejected their assessment as baseless”

A Dec. 5 headline promised a “bombshell” story, reprinting an allegation that an audit of election results in a Georgia county revealed that Dominion voting machines flipped ballots from Mr. Trump to Mr. Biden, in spite of overwhelming evidence to the contrary.

The article was shared more than 2,000 times on Facebook, according to CrowdTangle data, reaching up to 650,000 people on the social network.

Kevin Roose contributed reporting.