> and how many people would fall prey to it?
How exactly? I could be wrong, but I believe it won't make things any worse. I see three scenarios:
First, let's say someone is an antivaxer, already subscribed to that belief. If they're reading some posting, the fact that some other antivaxer vouched for that post's author doesn't change much.
If someone had not made any opinion yet - they won't have any trust connections on that matter, so if they're reading an anti-vaccine posting, they won't have any impact. Their query to the web of trust would say "no idea, you don't have any trust anchors set on this matter, go figure out whom you trust first".
It is only if they have a friend they trust on the subject vaccines, and that friend happens to be an antivaxer, they may have a "your friend vouches for this" result. This is the only scenario I see, where someone could be swayed towards a certain opinion, and I'd be damned if this doesn't already happens without any technologies, completely organically. It's their peer group that sways them, so the technology in question here doesn't make it worse or better, it just accelerates the process.
Again, I could be wrong about either or all of those. I readily recognize all of this stems from my beliefs in humanity (in general) as something that can work out its way through any amount of dissenting opinions, finding out the truths. I mean, historically, society had worked this way. And a controversial belief that accelerating this is a good idea - I admit, I don't have a rational arguments for or against this part - it's just a belief. Guess it comes from hatred of seeing all those slow simmering almost-pertpetual memetic wars and being unhappy about their fallout, yet not believing any forcible silencing of opposing forces is a viable approach.
Oh, and just to clarify: it's extremely important that trust must not be ultimate (exceptions apply for closest peers, e.g. partners or parents), but limited to a subject. E.g. I may trust someone on subject X but at the same time know they're avid subscribers to what I think is a false belief on subject Y, so I explicitly distrust them on that matter.