The arrival of former Republican Sen. Jon Kyl to advise Facebook on political bias comes not a moment too soon for conservatives struggling to maintain a foothold on social media amid charges of politically motivated purges.

Facebook revealed Wednesday that Mr. Kyl, a three-term senator from Arizona who retired in 2013, and his law firm have been brought aboard to examine claims of discrimination against the right. A day earlier, 63 conservative leaders declared that the social media situation had “reached a crisis level.”

As if to prove their point, Facebook accidentally released, and then disabled, a reporting button Tuesday asking users if certain posts contain hate speech. Turning Point USA, a mainstream conservative advocacy group, prompted the flagging.

The same day, Facebook CEO Mark Zuckerberg said the company had begun its effort to promote “quality news” by ranking outlets on their trustworthiness and then boosting or suppressing pages based on their scores.

“We put [that data] into the system, and it is acting as a boost or a suppression, and we’re going to dial up the intensity of that over time,” Mr. Zuckerberg said, as reported by BuzzFeed. “We feel like we have a responsibility to further [break] down polarization and find common ground.”

Conservatives fear both initiatives are ripe for free speech abuses — not to mention the targeting of politically incorrect thought — but were nonetheless heartened by Facebook’s willingness to reach out to the right.

In addition to Mr. Kyl, the conservative Heritage Foundation has been brought in to convene meetings on conservative bias with Facebook executives, according to an announcement on Axios.

“Facebook has at least reached out to the conservative movement,” said Dan Gainor, vice president of business and culture at the Media Research Center. “The fact that they’re bringing in Kyl is good news.”

That is more than can be said for Google, Twitter and YouTube, the other social media kingpins long accused of discriminating against conservatives by banning and suspending them.

In a joint statement, 63 conservative leaders led by Media Research Center President Brent Bozell urged the four companies to provide equal treatment by enacting nondiscriminatory social media policies and providing greater transparency when deleting accounts and removing content.

“They have skewed search results and adjusted trending topics in ways that have harmed the right,” said the statement. “Firms have restricted and deleted videos, even academic content. Conservative tech employees have found their speech limited and their careers harmed.”

Other signers included Rep. Lamar Smith, Texas Republican and chairman of the House Media Fairness Caucus; former Attorney General Edwin Meese; Live Action President Lila Rose; Citizens United President David N. Bossie; Tea Party Patriots co-founder Jenny Beth Martin; and former Republican Rep. Allen West.

House and Senate Republicans pounded the bias theme at hearings last month featuring Mr. Zuckerberg. They called on the Facebook founder to address free speech and privacy issues.

House Majority Whip Steve Scalise, Louisiana Republican, said he was encouraged by Facebook’s effort to address biases in its algorithms.

“I’m encouraged that they’ll conduct a full review & I’ll closely watch what steps they take to ensure their platform doesn’t discriminate,” Mr. Scalise tweeted.

Meanwhile, liberals were miffed that the effort to root out conservative bias included Mr. Kyl and Heritage but no one from the left.

ThinkProgress called it “a bias study with one side represented.” Gizmodo called Mr. Kyl, now with the Washington law firm Covington & Burling LLP, a “fake news huckster.”

“There’s no evidence that any examples of conservative bias at Facebook are anything more than cherry-picked instances that fail to demonstrate a pattern of politically motivated censorship,” said Gizmodo’s Rhett Jones. “But Facebook wants to get over this … and move on.”

Joel Kaplan, Facebook vice president of global public policy, responded with a statement saying, “Getting outside feedback will help us improve over time — ensuring that we can more effectively serve the people on Facebook.”

The Media Research Center released a report April 16 detailing examples of discrimination against conservatives. It included a 2016 Gizmodo report quoting former Facebook workers who said they “routinely suppressed conservative news.”

The conservative Western Journal issued a March 13 analysis showing that liberal publishers gained about 2 percent more web traffic prior to Facebook’s latest algorithm change in February, while conservative publishers lost an average of 14 percent.

A March 5 study by The Outline using engagement data from 20 publishers found that conservative outlets’ totals dropped by as much as 55 percent after the change, while engagement numbers for most liberal publishers were not affected.

“This change has ramifications that, in the short term, are causing conservative publishers to downsize or fold up completely, and in the long term could swing elections in the United States and around the world toward liberal politicians and policies,” said The Western Journal’s George Upper.

Facebook also launched a civil rights audit Wednesday to be led by civil rights leader Laura Murphy and conducted by the law firm Relman, Dane & Colfax PLLC, with feedback from groups such as the Leadership Conference on Civil and Human Rights.

“We are encouraged by Facebook’s commitment to conduct a civil rights audit of the company and its products and the team they have selected to do it,” said Vanita Gupta, president and CEO of the conference.

Facebook has come under fire for allowing advertisers to exclude minority viewers from seeing housing ads and targeting their pitches to anti-Semitic audiences.

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