We determine what is fake in the same we we always did. Sanity checking the authors, validating for self-consistency, cross-checking evidence, searching for conflicting interests, and evaluating probable accuracy based on those factors.
The paradigm shift is the Internet as a whole: democratizing dissemination of information. Facebook, email, same thing.
We're now flooded with noise from random anonymous un-credentialed entities, unable to track and filter out low-signal sources. The public is the new broadcast medium... the narrative becomes whatever resonates strongest with some subpopulation, rapidly spread through the wires by people who never critically analyze agreement.
Old news institutions at least held some degree of credibility... plenty of faults, from simple mistakes to missed coverage to occasional outright propaganda (generally corporate) - but there was accountability. John Doe wrote for The City Times, you learned to ignore the bad reporters and institutions, and if we go back far enough you could actually talk to them in-person.
Every democratization comes with a social challenge of creating norms to maintain order. Political democracy is a work in progress, economic democracy currently not viable, I guess this signals it's time for us to face information democracy...
We all went through those lessons in high school, but for a lot of people they just didn't sink in. And they still don't. Talk to a high school teacher about how their students use Wikipedia.
The postal service cannot prioritize letters that encourage banning abortion. Telephone companies cannot subsidize conversations about organizing unions. Facebook, on the other hand, can exert control over how visible a post is based on whether or not it, say, supports Donald Trump.
Many previous mechanisms for sharing do have such central control mechanisms, and exercise them far more enthusiastically than does FB. Dead tree print outlets are a mechanism for sharing with such features. Meatspace social clubs are a sharing mechanism with such features.
Facebook may be unique in the degree of it's reach for a sharing mechanism with the capacity for centralized editorial control, but it is not historically unique in being a sharing mechanism which features the capacity for centralized editorial control.
This hints at mechanisms to deal with such a monopoly (were it to arise) in analogy to how the government has protected its people by dealing with economic monopolies (sometimes creating them deliberately, sometimes monitoring them, and sometimes breaking them up when they abuse that position, etc.).
Imagine if those chain emails from your crazy uncle were always displayed prominently at the top of your inbox depending on the number of forwards.
And like the article points out, the inefficiencies (from the campaign's point of view) of the current targeting may be doing an overall service to democracy by giving populations a message they wouldn't otherwise hear.
There is a lot of hand waving in this argument but I'm convinced we should attempt to solidify what effects are there and whether we find them valuable before dismissing it.
No such mechanism in traditional media. In my country sometimes news outlets can be forced (by law) to publish a correction of a false story, but it is usually done in small print and gets hushed over.
Edit: that said, I think there exists a big problem in attempting to filter these items. How do we determine what is fake vs what simply goes against our preexisting (mis)conceptions?
Edit 2: best course of action might be that a wide diversity of ideas gets a chance to be seen (i.e. show stuff outside of your bubble), rather than trying to artificially manipulate proliferation.