Right now, on Twitter, I can have a list of people I follow. I assume this is something like saying I "trust" them in some way.

I get a feed full of stuff from them, and stuff they've re-tweeted ie said explicitly that they trust, etc.

The whole "social network" thing really is approximately the same shape as an explicitly reified "web of trust". I would not expect the results to be terribly different, other than the added effort of having additional explicit system entities to manage.