Researchers from (where else) the University of California Berkeley claim to have conclusive proof that the Fox News Channel gives more votes to Republicans. The study is entitled "The Fox News Effect: Media Bias and Voting."
The conclusion:
Between October 1996 and November 2000, the conservative Fox News Channel was introduced in the cable programming of 20 percent of US towns. Fox News availability in 2000 appears to be largely idiosyncratic. Using a data set of voting data for 9,256 towns, we investigate if Republicans gained vote share in towns where Fox News entered the cable market by the year 2000. We find a significant effect of the introduction of Fox News on the vote share in Presidential elections between 1996 and 2000. Republicans gain 0.4 to 0.7 percentage points in the towns which broadcast Fox News. The results are robust to town-level controls, district and county fixed effects, and alternative specifications. We also find a significant effect of Fox News on Senate vote share and on voter turnout. Our estimates imply that Fox News convinced 3 to 8 percent of its viewers to vote Republican.