The polls were off this election by about 2 percentage points, and it seems that much of this was from differential nonresponse: Survey respondents included too many Clinton supporters, even after corrections from existing survey adjustments.
Maybe Republicans would be more likely to respond to a Fox News poll. According to FiveThirtyEight.com, Fox polls were +0.5 Republican this year. That’s not a lot, but it’s something.
What if Fox were to collaborate with some politically neutral organization — say, Gallup — and do a joint poll, where they agree ahead of time on the questions and then they just start off the phone call with, “We’re calling from the Gallup Poll . . .” or “We’re calling from the Fox News Poll . . .”? And similarly with callbacks: “This is the Gallup Poll. We called yesterday and left a message. Is Mary Smith at home?” Or the same thing but with Fox. They simply randomly assign each phone number to be Gallup or Fox, they do a large poll, and then they compare the results.
What would happen? I’m guessing that conservatives who might not respond to the Gallup poll would be more likely to answer the Fox interviewers, while liberals and moderates might get turned off by the Fox label. But it would be interesting to see how large this effect is, given the concern that polls in key swing states were off this year in part because of nonresponse from Republican voters.