> are public
Ah. What mechanism assures this consistency of this information?
> at one node might or might not be a problem
How could it not be a problem? If that is the totality of the network, and the network is 1-fault tolerant, what prevents spontaneous divergence of the state?
> most likely cause of such a topology is a Sybil attack
"likely"? It's not clear what you mean there. What statistical model have you adopted that allows you to reason about the likelihood of various topologies?
Social networks usually appear to have small word behavior where its usually very easy to draw lines that describe disjoint local-majorities (or fairly large local-super-majorities).
I agree that a sybil sticking on a bunch on a bunch of extra 'nodes' and the sybil nodes diverging as a result isn't interesting case. What I do think is interesting is what mechanism will prevent user's honestly stated trust (much less politically manipulated trust) being a bad topology?
What is the procedure that I can follow, that if everyone else follows it, results in the correct global behavior (with high probability)? What are the additional assumptions required to achieve that and make it secure? Why are they plausible? Do they provide decentralization? (I can suggest on procedure which works: Stellar tells everyone who to trust; but it completely fails at decentralization so I assume that isn't the goal.)
In Bitcoin our security assumption is that the computational majority of participants conform to the protocol ('are honest') and these participants are not completely partitioned from each other. People can then think about-- or debate-- how reasonable those assumptions are.
(There are alternative formulations of Bitcoin's security which also argue about how plausible these assumptions are given economic incentive assumptions; but even this most simple set of assumptions gives people something easy to reason about.)
Can you give a parallel (informally stated, but equally comprehensive) version of the security assumptions for your consensus system?
> But there is certainly precedent for building a robust network out of pairwise relationships, namely inter-domain routing on the Internet.
The Internet is _wildly_ inconsistent. Asymmetric routing is the norm, the internet frequently suffers small partitioning and loops; single malicious parties at the edge can frequently inject bad state that is accepted globally, congestion and blocking happens multiple hops away from users where they have no recourse. The internet is not a consensus system, and these issues are not usually hugely problematic; someones brokenness doesn't involve your traffic generally effect you, you can route around problems locally. Ephemeral routing and ledgers are fairly different problems. Ambiguity about the ownership of a coin eventually effects almost everyone. I'm not seeing the connection you're making there.
I certainly agree that useful systems can be built from pairwise relationships: The original ripple design for pure IOUs without creating its own cryptocurrency prior to opencoin buying the ripple name was such a system, it had no need for a global consensus (except perhaps in certain atomic unwind cases)-- only the participants in a particular IOu transfer needed to be involved. It is not at all clear to me that a safe global consensus system can be built from pairwise trust.