Maybe it's not reality people differ on so much as their attribution of what is good and bad. For example, differing opinions over what qualities make a person trustworthy, or a good friend.
This suggests a twist on the idea of trust networks which eliminates the "network" part:
Use input from everyone equally to determine what qualities each person has: promptness, honesty, valour, geekiness, work ethic, humour, good instincts, Catholicism, precise manner, etc etc. Possibly using an approval vote, or possibly something else, it doesn't matter too much because we're all talking about the same objective reality. Make sure people can add new qualities easily. If there are specific qualities that tend to cause disagreements and wars, drop them and look for other qualities that people are able to agree on.
Each person then identifies qualities that they look for in friends: aspects of personality, shared goals, shared attitudes, etc. Semantic similarity between qualities can be identified as per my last blog entry. Each person ends up with their own way to compute a level of trust from another person's objective qualities.
One nice thing about this is that it allows for shades of meaning that existing systems miss by lumping everything into one or two numbers. As many people have noted already, terms like "trust" or "friendship" as used in friend-of-a-friend networks are pretty vague, people use the words in different ways. They probably have limited transitivity. Allowing an arbitrarily extensible set of qualities/dimensions seems much more natural.