I'm not sure you can expand the theorem to deal with that issue. Arrow's theorem essentially says even if you as an individual or society as a whole had perfect news sources, there is no voting method (edit: no ordinal voting method), or method of choice (other than dictatorship, which is bad for obvious reasons), which can accurately register preferences. All voting systems fail at some point, though some are better than others.

To be cynical, in the context of voting, consume news however you want to because to some extent it doesn't matter.