March 2011 research from link-sharing solutions provider Visibli found that among Facebook pages with at least 100,000 “likes,” engagement dropped as the number of fans increased. Each individual post by brands and media organizations received fewer “likes” as a proportion of the page’s fan base.

Similar data from social media engagement firm LoudDoor shows a more complex picture of how page size affects “likes” and comments per post. “Likes” increased with page size, except among pages with 2.5 million to 5 million users. On a per-user basis, “likes” began to decrease for pages with more than 100,000 fans, then rose again for pages with 1 million to 2.5 million followers. Larger pages had fewer “likes” per post per user, but the decrease...Read more at http://www.soldlab.com/maintaining-engagement/