Taken from a discussion in Advogato.
Trust metrication criteria
Bram - I think your ideas about criteria are the Right Thing and I've been thinking some of the same things myself. However I think I can list three desirable criteria and prove you can't have all three.
One is the "Adding Certification Criterion" you define. The second is the "Isomorphism criterion" which states that trust metrication should be a function on graphs, and that isomorphic graphs should get isomorphic trust ratings. The third is attack resistance as raph defines it.
If the attacker has total control over a subgraph, they can duplicate trusted parties, trust links and all. The "Adding Certification Criterion" says that this must not reduce the trust of the duplicated parties, while the "Isomorphism Criterion" means that the duplicates must get the same trust. Thus the attacker has increased the total trust in their part of the graph. They can do this indefinitely for unlimited trust; thus they have violated attack resistance. I'm pretty sure your most recent proposal falls to this attack.
I'll try and write more on this when I get more time...