Sorry to revive this old topic, but this indeterminism still bothers me. The following initial state is used in many PARSEC presentations:
The problem is that this situation is not in the domain of validity of PARSEC because there are two nodes with an estimate of true and two with false. This means there are necessarily two malicious nodes here, which is above the 1/3 PARSEC threshold.
The common coin will allow reaching an agreement, but there is a 50% chance that the decided value will be the one proposed by the malicious nodes. I think this is an obstacle for users to understand the protocol, and this certainly confused me.
Now, I will rephrase my original question: Is the common coin protocol only needed to unblock the algorithm outside PARSEC domain of validity or are there cases where it is also needed within this domain (with less than one 3rd of malicious nodes)?