I said measure. We need to understand if we're being manipulated, and if so, figure out what an appropriate response should be. Maybe it's as simple as releasing a report and letting the media talk about it. Knowing gives us the ability to develop a response.
Filter bubbles are relatively new, and it's not yet clear the extent to which they can be used to shape a democratic society.
We don’t need to find that out because we are being manipulated. These are algorithms designed to maintain attention and sell ads. It is impossible for that to not be manipulative. The goal shouldn’t be to understand the algorithms, but to stop them from ruining our lives.
My understanding (vastly simplifying) is that the current standard is: does not infringe on rights of protected classes, does not incite imminent violence, & subject to national security concerns.
All of which are fuzzy lines, subject to court interpretation on a case by case basis, as they should be. (Even national security, which courts have traditionally granted wider latitude to)
All three are plausible rationales under which to bring a hypothetical "antidemocratic" case (to use a catch-all term that encompasses what people seem to be implying).
At core, and first principles, what "we" probably want as a nation is a sliding scale that moves from primacy of shareholder / owner to primacy of public, according to user count & market percentage.
Aka if you're a 10,000 user app, and you think (non-inciteful) racist content will make you the most money, that's your (terribly immoral) business.
But if you're a 100,000,000+ user multi-app company, then public and democratic interest takes primacy over your shareholders. Don't like that? Spin off some products.
Beyond that, I'm not sure how easy it would really be to detect. Seems like the method for that kind of thing would more likely be to have networks of users/bots/whatever that take advantage of facially neutral recommendation algorithms. So would you catch that by auditing the algorithm?