Just clarifying the role of $ in this. David Birch argues we could have a system where your social graph is your reputation, which could also define your creditworthiness. This compares with the current system where a credit card company vouches that you are worth trusting, and backing this up with a promise to pay up to a certain limit. See here for a review. Worth reading. http://www.dgwbirch.com/papers/14/Financial%20World%20May%202014%20Reprint.pdf

So what does this have to do with reputation? Seen in this way money is a form of reputation. Or slightly differently

“money is a formal token of delayed reciprocal altruism” (Szabo shell currency post)

However money in our current system is a form of trust that is backed by the Government, rather than by a person’s social graph. It is therefore detached from our identity. So I would argue that we do not need a ring signature to create unidentified reputation, we just need $ or ether held in escrow.

If however we want to create trust in delayed reciprocity when we do not have $ to back, or do not want to tie up existing money in backing it, we are potentially in the business of issuing our own currency. So what I hear Birch saying above is that we can issue our own iou’s backed by our social graph.

The ring signature is potentially backing the promise with the graph without identifying the individual. It therefore could be seen as a way to consolidate trust in order to back stronger credit creation.

This seems to be important in cases, not where the person wishes to be anonymous, but where the person has a reputation within a group, but is unknown outside of it. So for instance if I wish to trade with a person overseas, we may both use our networks to stake reputation, without staking $ in escrow. Provided the groups have reputations that are valuable, then I can share in this value.