For real quality you need an editor who knows the subject matter to choose articles and news.
Basing rankings on re-tweets or likes is only useful when the likers and re-tweeters are TAs themselves. If it's everyone else, you might just end up with pages that are interesting for everyone else but not necessarily for TAs.
"Likes" can also work in a negative way. If the likers are just uneducated about a topic, it will not even appear on your radar because it's not liked enough. There was an interesting article on slashdot recently where some folks invented a 8 bit upscale algorith based on splines which was really cool. But nobody else understood it, because to them HQ2x is already good enough, even though it works totally differently. Most people don't "liked" this article because they didn't understand it. Dumbness of the crowds... it's a two sided sword.
The other problem I have with likes is that they often don't produce any real news. Lots of people like the same, so stuff gets posted everywhere anyway. If I've seen it on 10 websites before it's hardly news and you can save your bandwidth and time. Same reason newspapers suck nowadays. They buy all their stuff from AP rather than doing their own digging to come up with interesting and new content that sets them apart and gives them readership.
Now you could do a pre selection based on facebook/linkedin/etc ranking, paired with user submissions, so content that is unpopular with the general internet populace but which may be interesting for us TAs gets posted.
Once the story is in the TAO system, rank it internally by how many clicks it gets. Each click on a news items increases it's lifespan of how long it occupies the headline, before it slowly moves down into the archives.