You could do it in relation to other news outlets. That won't give you absolute bias, but you could say something like "CNN is much less likely to report about X topics than Fox." It would be interesting as well to add in other factors - i.e. how often do certain outlets report about the wars in the middle east when the president is republican vs democrat?
I would go farther and make it relative to clusters of people on, say, Twitter. If an outlet is concerned with a lot of things that the progressive cluster of Twitter users is talking about (more so than many other outlets), that’s a strong indicator that the media outlet (and other outlets in its media cluster) is also progressive.
I'll just throw out a comment (even though this is mostly a thought experiment) that doing any type of twitter analysis is either nearly impossible (in the scraping case) or prohibitively expensive (e.g. using their API). They've really shut off access to third parties in the last few years. (Just thought I'd mention it since the parent post continues this pre-2015-ish idea that still floats around that using twitter for projects could be a thing.)
Fair enough, yes, Twitter was intended to be an example of a mine-able medium where people express political opinions, but to your point mining Twitter data may be more difficult than I imagined.
But you would still expect them to fluctuate together. How the different news agencies ramp up and down coverage in response to the same events is what's interesting.
