For years now, Fox News has been the most-watched cable news channel in America. While it lays claim to neutral reporting, its coverage has typically been more sympathetic toward Republican candidates in general elections. But the 2016 presidential race hasn’t exactly been typical. The Republican Party is set to nominate a figure in Donald Trump who has divided his own party and been at odds with Fox News, too, since squaring off with anchor Megyn Kelly at a debate last August. Lately, however, there have been signs of a possible détente—including a soft-focus interview with Kelly in March—suggesting that Trump may get the same enthusiastic support Fox has provided to Republican candidates in elections past. How much would the full-throated backing of Fox mean to Trump?

A great deal, given the findings of a pair of studies analyzing Fox’s impact on vote share. The studies find an effect that’s sufficiently important that it’s earned a name: researchers who study the influence of mass media on politics call it the “Fox News Effect.” Far from simply preaching to a conservative choir, Fox, the researchers find, has been winning ever more hearts and minds for the Republican Party over the past 15 years. If we take the studies’ estimates of the Fox News Effect seriously, it could easily prove pivotal in deciding the 2016 presidential election.

Measuring how much Fox—or any other source of information—affects what people believe is no easy task because so many viewers come to Fox—or its left-leaning competitor MSNBC—with their political views already firmly established. One way of trying to get over this hurdle is to look at how voting patterns change when Fox News comes to town. This is the approach taken by economists Stefano DellaVigna and Ethan Kaplan in the 2007 study that gave the Fox News Effect its name. Fox News was only founded in 1996. In the next four years, it expanded rapidly to reach many—but by no means all—cable subscribers across the country. So it’s possible to compare how Republican vote share changed between 1996 and 2000 in places that got Fox News in time for the George W. Bush–Al Gore election, as compared to places that still lacked access. The study’s authors found a modest impact: Republican vote share was 0.4 to 0.7 percentage points higher in locales with Fox News. (There weren’t any other significant differences between places with and without Fox News, which somewhat alleviates the worry that Fox News was targeting areas poised for a Republican upsurge.)

Of course, it’s not possible to use this approach to measure Fox’s impact in more recent years: These days, Fox News is just about everywhere. Instead, Gregory Martin of Emory University and Ali Yurukoglu of Stanford University revisited the Fox News Effect in a May study using an entirely different method. Their approach takes advantage of the fact that channel order varies by local cable provider. Why should channel order matter? Because, it turns out, inertia acts powerfully on channel surfers, so the order of channels has a powerful influence over how many subscribers watch a particular station. Many viewers turn on the TV at channel 1 and just starting clicking upward till they find something they like. In some places, Fox News has a coveted slot in the low 20s (the first 15 to 20 spots tend to go to broadcast networks); in other places, Fox might be channel 50, so you need to click through many more options to get to Fox. (Fox News’ channel assignment isn’t related to viewer demographics that might otherwise predict its popularity—for example, Fox didn’t get a better channel in areas that have traditionally voted Republican.)

Martin and Yurukoglu use the differences in audience size that come from Fox’s random positioning in the cable lineup to calculate how much impact the channel had on voting in the 2000, 2004, and 2008 presidential elections. For 2000, they generated an estimated impact pretty close to what DellaVigna and Kaplan calculated a decade before. But they also found that Fox’s impact took off during the decade that followed: It increased Republican vote share by more than 3.5 percentage points in the 2004 election and more than 6 percentage points by 2008. These gains, the economists argue, come from an increase in Fox viewership combined with what they calculate to be an increasingly pro-Republican bias at the network, based on an analysis of Fox transcripts. These are huge numbers: Since the U.S. has a two-party system, one more vote for the Republican nominee is typically one vote less for the Democrats. So an extra 6 percent share for the Republicans means 6 percent less for the Democrats, suggesting Fox News’ support could erase a 12-percentage point Democratic lead in the popular vote.

Let’s assume Martin and Yurukoglu’s estimates capture something close to Fox News’ actual influence today (the channel’s viewership has held steady since 2008). A Reuters poll in early June had Clinton leading Trump by 11 percentage points: Fox’s support could make such a race a dead heat. Support from Fox could even help Trump climb out of the hole he’s dug recently with poorly received statements on the mass shooting in Orlando and his attack on a federal judge overseeing the fraud case against Trump University. Of course, Trump has surely already benefited from the Fox News Effect—he’s enjoyed the support of Sean Hannity and Bill O’Reilly, among others, for months. But if he commands the full support of the network in the general election, Fox could play a pivotal role in deciding the victor.

Then again, if there’s one lesson from the 2016 election cycle it’s that predicting its outcomes is a fool’s game. Trump is a unique figure whose rise has befuddled even the most practiced prognosticators. But given the influence of Fox News in prior elections, we can’t rule out the possibility that the network’s attitude toward him could decide who becomes the next U.S. president. Trump himself may have already come to this conclusion, given recent reports that the candidate is in talks with top Fox executives because, according to what one insider told the New York Daily News, Trump realizes he “can’t win the general election without Fox.”

Of course, Fox is hardly the only media outlet with sway in this election. There’s a parallel story to be told, we’re sure, about MSNBC’s effect on its viewers. We focused on Fox because of its scale. They may face increasing competition from online options like Facebook, which faced recent accusations of giving a liberal bias to its news feed. But there is still no other US news source—news channel, newspaper, magazine, or social media—has the attention share that Fox News commands. That is, not only does Fox have a far greater viewership than its competitors—it has three-times the audience of MSNBC—its viewers are also less apt to seek news from other sources.

Donald Trump has made no secret of his disdain for the media, and the press is right to be concerned about the steps a President Trump might take to curtail its powers. Those powers are essential to keep elected officials accountable to voters. But the power of news outlets like Fox to swing elections should also give the public pause. If it is true that Fox News has the potential to anoint a winner, how do we know that they will not use it to secure favors or assurances from presidential hopefuls? If media moguls are communicating with presidential hopefuls outside the spotlight, what are they asking for, and what are they promising? We, the electorate, have the right to know.

Read more from Slate on the 2016 campaign.