At Fox News, there was little drama over the decision to project Joseph R. Biden the winner of Arizona. But the relationship between Trump and the network was never the same.Shortly before 11:20 p.m. on Nov. 3, 2020, Bill Sammon, the managing editor for Fox News in Washington, picked up the phone in the room where he and others had been reviewing election returns. On the other end of the line was the control room.Mr. Sammon informed the producers and executives listening in that the network was calling Arizona for Joseph R. Biden Jr., effectively declaring an end to one of the most contentious presidential elections in modern times. He clicked a box on his computer screen, and Arizona turned blue on the map that viewers saw at home.Inside Fox News, the moment unfolded with little drama despite its enormous implications. To the people in the room with Mr. Sammon, the result was clear. On the outside, it immediately provoked a fury with President Trump and his supporters, who maligned Fox News, the country’s most watched cable news channel and his longtime stalwart defender, as dishonest and disloyal.The relationship between the former president and the network would never be the same.The events of that night were the focus of a congressional hearing on Monday that peeled back the curtain on the decision-making process at Fox News. The hearing, part of the House investigation into the Jan. 6 Capitol riot, featured testimony from a former senior editor at Fox News who explained how there was never any doubt that his team was making the correct call on Arizona — even though most other news outlets would not call the state for days.“We already knew Trump’s chances were very small, and getting smaller based on what we had seen,” Chris Stirewalt, who was the politics editor for Fox News until he was fired two months after the election, told the House committee. Mr. Stirewalt described the cautious, analytical approach they took to determining that Mr. Trump could not come from behind and overtake Mr. Biden in Arizona.At Mr. Sammon’s insistence, he said, they took a vote of the people who worked on Fox News’ so-called decision desk. And only after the group agreed unanimously did Mr. Sammon issue it.“We looked around the room. Everybody says, ‘yea.’ And on we go,” Mr. Stirewalt testified before the committee, adding that they had already moved on to looking at calling other states by the time they heard of the backlash their decision created.Read More on the Jan. 6 House Committee HearingsMaking a Case Against Trump: The committee appears to be laying out a road map for prosecutors to indict former President Donald J. Trump. But the path to any trial is uncertain.The Meaning of the Hearings: While the public sessions aren’t going to unite the country, they could significantly affect public opinion.An Unsettling Narrative: During the first hearing, the panel presented a gripping story with a sprawling cast of characters, but only three main players: Mr. Trump, the Proud Boys and a Capitol Police officer.Trump’s Depiction: Mr. Trump was portrayed as a would-be autocrat willing to shred the Constitution to hang onto power. Liz Cheney: The vice chairwoman of the House committee has been unrepentant in continuing to blame Mr. Trump for stoking the attack on Jan. 6, 2021.Mr. Stirewalt’s testimony was part of the second televised hearing by the committee, which is aiming to refocus the country’s attention on the horrors of that day and to make a compelling case that Mr. Trump continued to lie about voter fraud and “stolen” votes despite being told by the family and aides closest to him that he had lost.On Monday, the hearing centered on people who said they did not believe that any hard evidence or data supported the former president’s contention that he must have won because the early vote returns showed him ahead on Election Day.At issue was what political observers have called the “Red Mirage.” On Election Day, Mr. Trump was widely expected to appear far ahead as polls closed across the country, because the first votes counted are primarily those from people who voted in person that day — the method favored by Republicans. But that, warned political experts, would probably be a “mirage.” Mr. Trump’s lead would shrink, they said, or perhaps evaporate entirely, as states tallied the mail-in ballots, which were favored by Democrats and take longer to count.For several weeks before the election, a group of advisers, including Stephen K. Bannon and Rudolph W. Giuliani, had encouraged Mr. Trump to declare victory on the night of the election, arguing that he could easily dismiss mail-in ballots as riddled with fraud regardless of whether he had any evidence for the claim.Fox’s Arizona call blew a hole in that strategy. A projected loss in traditionally red Arizona — which a Democratic presidential candidate had won only once since Harry Truman — coming from a presumably loyal outlet, augured a bad night.But Fox News had good reason to feel confident about a call no other news outlet was prepared to make at that point in the evening, with roughly one-fourth of the vote still uncounted in Arizona, Mr. Stirewalt said. Its decision desk used data that other networks did not have.After the 2016 election, Rupert Murdoch, who oversees Fox News as part of his larger conservative media empire, urged Fox to pull out of the consortium of news organizations that used polls to project results. Those polls had wrongly predicted a Hillary Clinton victory.That paved the way for Fox News and The Associated Press to go their own way in 2020, according to an account of the decision desk’s process that Mr. Stirewalt gave for the book “Insurgency: How Republicans Lost Their Party and Got Everything They Ever Wanted.” In the weeks leading up to the election, they surveyed 100,000 voters across the country who had cast ballots early, giving them a sense of how misleading the “mirage” might be. On the night of the election, the Fox News decision desk compared those surveys with another layer of data: actual precinct-level vote tallies that the A.P. was tracking.On Monday, Mr. Stirewalt testified that the joint A.P.-Fox News project worked remarkably well. “Let me tell you, our poll in Arizona was beautiful,” he said. “And it was doing just what we wanted it to do.”Some of Mr. Trump’s former aides testified that the Fox call shocked them but also undermined their confidence in his chances of victory. Jason Miller, a senior aide on the Trump campaign, said in video testimony played by the committee that he and others were “disappointed with Fox” for making the call but at the same time “concerned that maybe our data or our numbers weren’t accurate.”Mr. Miller had shared none of that concern on election night, when he tweeted that Fox was a “complete outlier” whose call should be ignored by other media. At Mr. Trump’s insistence, he and other aides immediately reached out to Fox executives, producers and on-air talent to demand an explanation. Jared Kushner, Mr. Trump’s son-in-law, went straight to the top, calling Mr. Murdoch. The scene played out in part on the air as Fox talent commented about the complaints raining down on them from the Trump campaign.“Arnon, we’re getting a lot of incoming here, and we need you to answer some questions,” the network’s chief political anchor, Bret Baier, said at one point, referring to Arnon Mishkin, the person on the decision desk who was responsible for analyzing the data and recommending when Fox issue its calls.On Monday, Mr. Stirewalt did not describe either Mr. Murdoch or Lachlan Murdoch, the Fox Corporation executive chairman, as being part of the decision desk’s process. And network executives have said the Murdochs were not involved.Though Fox News coverage is typically favorable to conservative, pro-Trump points of view, that deference has never been adopted by the decision desk, which is a separate part of the news-gathering operation overseen by Mr. Mishkin, a polling expert who is also a registered Democrat. In the days after the election, Mr. Mishkin was unwavering in his defense of the call as Fox anchors pressed him. Once, as the host Martha MacCallum peppered Mr. Mishkin with a series of “what if” scenarios that could bolster Mr. Trump’s chances of eking out a victory, Mr. Mishkin responded sarcastically, “What if frogs had wings?” (Mr. Mishkin remains a paid consultant for the network, not an employee, and will run the decision desk for the midterm elections in November.)The decision desk was created under the former Fox News chairman and founder Roger Ailes, who relished making controversy and drawing ratings more than he cared about toeing the line for the Republican Party. Its quick calls angered Republicans on more than one occasion, including in 2012, when it was the first to project that President Barack Obama would win Ohio and a second term, and in 2018 when it declared that Republicans would lose the House of Representatives even as votes were still being cast on the West Coast.Though Fox News and the Murdochs stood by the Arizona projection, they paid a price for it.As Mr. Trump’s rally goers took up a new chant, “Fox News sucks,” the former president urged his supporters on Twitter to switch to Fox’s smaller, right-wing competitors instead, Newsmax and One America News Network.With anchors who steadfastly refused to acknowledge Mr. Trump’s loss, Newsmax saw a ratings bump as Fox, the No. 1 cable news network for two decades, showed some rare — if short lived — slippage.Soon, various Fox opinion hosts were giving oxygen to false assertions that the election was stolen, several of which were methodically debunked at Monday’s hearings, including by one former Trump aide, who called them “nuts.”Mr. Stirewalt, who was among the Fox News journalists who defended the Arizona call, was notified of his firing on Jan. 19, 2021. 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