At Kuantero, we develop and launched a new WordPress plugin, called FBtops. With it can be created tops/rankings of posts based on the number of facebook likes, shares and comments the posts are getting.
You can download it from here: http://wordpress.org/plugins/fbtops/
It’s very useful if you want to make a contest, where the articles from specific categories are competing 🙂 This is something we’ve been useing at StartEvo for some time now:
The Top of Most Liked Articles – http://startevo.com/top-articole-startevo/
The Top of The Inspirational Speakers – http://startevo.com/top-vorbitori-inspirationali-startevo/