Actually, it’s not the reputation of the people exchanging credit that matters, but the reputation of the notaries. Just a single notary acting in good faith can stop an invalid transaction from going through. A good reputation system or a very strong application membrane should be able to keep the majority of notaries signing any given transaction as an honest actor.
Even if there is an unreasonably high chance of choosing a dishonest notary by whichever metric the currency chooses (i.e. purely random or random but weighted by reputation) at 30%, it would still take less than 150 notaries per transaction to have a lower chance of accepting an invalid transaction than the chance of two 256-bit hashes colliding.
Here is my math:
Where b is the chance of picking a dishonest notary, n is the amount of notaries we are picking per transaction. (and 2^{-256} is the chance that some random 256-bit number is equal to some other random 256-bit number)
And even such a number as 10%, where only 78 notary entries are required for the same effect, may be a gross overestimation of the possibility of attacks, given that any effective reputation system would completely (or mostly) invalidate an agent’s reputation if they were to validate two competing notary entries (these entries are stored on a hashchain, keeping the chain linear would reveal the conflicting data, but splitting the chain is not allowed, and is protected by a very similar system to the one just described).