There are some models that are a bit better than trust by royalty (app-stores) and trust by hirarchy (TLS). One of them is trust flowing along flow limited edges in a graph (as in Advogato). This model however isn't free from fault, as when a highly trusted entity gets compromised, there's no quick or easy way to revoke that trust for that entity. Also, a trust graph such as this doesn't solve the problem of stake. We trust say, the twitter API, because we know that twitter has staked a lot into it. If they violate that trust, they suffer proportionally more. A graph doesn't solve that problem, because it cannot offer a proof of stake.
Interestingly, there are way to provide a proof of stake (see various cryptocurrencies that attempt to do that). Of course proof of stake cryptocurrencies have their own problems, but that doesn't entirely invalidate the idea. If you can prove you have a stake of a given size, then you can enhance a flow limited trust graph insofar as to make it less likely an entity gets compromised. The difficulty with that approach of course is, it would make aquiring high levels of trust prohibitively expensive (as in getting the priviledge to access the filesystem could run you into millions of $ of stake shares).