Groups opposed to some U.S. immigration programs claim Facebook has suppressed their content and visibility of their groups. These allegation, if true, could be due to algorithm design errors or deliberate. Either way, these allegations illustrate the potential of social media propaganda:

Patty McMurray says that since her group began covering immigration on its Facebook page, her group’s engagement numbers dropped by around 93 percent — even as her group continued to gain more followers.
“We were seeing engagement levels of 27-32 million people,” she said. “We had 150,000 Facebook followers who were very active [and] if we posted something on our page, within an hour it would have 10,000 shares,” she said. “Now we have more followers than ever before — over 400,000 — but now we’re lucky if we can get an engagement level of 2 million people.”

Source: Exclusive – Immigration Hawks: Facebook Engaging in Deliberate Suppression of Our Content
Some of these groups note Facebook’s CEO Mark Zuckerburg leads a lobbying group that promotes the importation of temporary high tech workers into the U.S., contrary to the interests of the groups that are allegedly being suppressed.
They accuse Facebook of “unsubscribing followers, hiding the groups’ content from their followers’ newsfeeds, deleting posts, and suspending the advocates’ ability to post on their own Facebook pages” and prohibiting such groups from purchasing Facebook advertising.
We already know that Facebook has, in the past, attempted to control users’ feelings and conducts psychology experiments on the FB user population without permission.
Disclosure – Before I was aware of allegations of Facebook censorship, I curtailed my own use of Facebook because Facebook can be a waste of my time. I maintain some online group pages including one on software development, and the Occupy Propaganda web page. However, I no longer read the daily “news feed” of friends’ posts nor do I post much there any more.
If the allegations are true, this could explain my past observation that the quality and quantity of left wings social media propaganda posters seemed high and widely shared, while that of right-wing propaganda posters seem of lower quality and quantity, with limited distribution.