Sean Hannity of Fox News. (Rick Scuteri/AP)

Suppose your favorite network TV show wraps up at 10 p.m., and you decide to go channel surfing for a little news before bed. If you're not terribly picky about the source, you might just click your way up the dial and stop at the first news show you see.

In this scenario, the order of channels in your cable package will determine whether you arrive at Fox News, CNN or MSNBC — whether the voice that tells you what's happening in the world belongs to Sean Hannity, Don Lemon or Lawrence O'Donnell.

That's a big difference — big enough to change voting habits, according to researchers at Emory University and Stanford University. Here's an excerpt of a study by Gregory J. Martin and Ali Yurukoglu, shared with The Fix in advance of its publication in the September issue of the American Economic Review:

We demonstrate that a one-standard-deviation decrease in Fox News's channel position is associated with an increase of approximately 2.5 minutes per week in time spent watching Fox News. We estimate that watching the Fox News Channel for this additional 2.5 minutes per week increases the vote share of the Republican presidential candidate by 0.3 percentage points among voters induced into watching by variation in channel position.

There's some math jargon in there, so let's break it down.

One standard deviation, in this case, is about 17 channels. Martin and Yurukoglu found that if Fox News is, say, channel number 500 in your cable lineup, instead of 517, you will watch an extra 2.5 minutes of Fox News in a week, simply because you will encounter Fox News at an earlier point in your channel surfing.

If 1,000 people watch an average of 2.5 minutes per week of additional Fox News coverage for this reason, three of them will be persuaded to vote Republican.

Three votes out of 1,000 might not sound like a ton, but consider that many people are firmly committed to one party or the other. According to Gallup, 41 percent of Americans call themselves independents and only 11 percent say they do not lean in either direction.

An extra few minutes of Fox News probably isn't going to make committed Democrats — or even people who lean left — vote for a Republican presidential candidate. If these people are politically engaged, they probably seek out other news sources, also.

What we're really talking about here is Fox News's power to influence people in the relatively narrow middle. Three votes out of 1,000 is actually pretty impressive.

Notably, the researchers found that CNN and MSNBC do not wield the same power. In other words, improving the channel positions of Fox News's competitors in the same way described above does not translate into additional votes for one party or the other.

Fox News, it seems, is uncommonly convincing.

A side-by-side look at how President Trump and Fox News pundits discussed the Charlottesville violence. (Thomas Johnson/The Washington Post)