One of the reasons people use social media is to get a feel for the generally environment of opinion, even if we disagree with it. We want to know what "people are saying" and understand the rapidly-changing boundaries of what is socially acceptable. That's why I follow people on Twitter and Facebook that I don't trust at all. I would not want to use a decentralized trust system to consign myself to an echo-chamber, even if it is full of believable truthful people.

But the system TimJRobinson describes is flexible: you don't have to simply filter out the less trustworthy posts. You could simply flag them somehow as low-trust.

Right now the major social sites are designed to amplify the voices of users that produce content that drives engagement, even though the most engaging content tends to be offensive or inaccurate. That's why the people I least trust on Facebook always show up on the top of my feed: I sometimes engage with them by telling them I think their posts are inaccurate.

So I can see your system being used not just as a filter for what the users sees in their feed, but as a feedback mechanism for people's posts.

I think a more responsible social site would optimize for positive outcomes, and not just engagement: employing algorithms and techniques to optimize for accuracy, quality, and civility. I think decentralized moderation could be one of those techniques.