I make the following assumptions:
* Forks are the only thing which make a double spend attack possible
* A forkless blockchain has no need for an amortised consensus
A forkless blockchain is only possible where all nodes are aware of who the block producers are, because otherwise you could have islands of nodes with separate consensus from the main group with their own block producers. If a node finds itself cut off from all the block producers, it must wait to reconnect - consensus stalls for such a node.
Network latency can cause forks in an amortised consensus because the set of candidate transactions can be different between block producers at block production time. However, if consensus happens simultaneously, picking the majority common transaction set between block producers would eliminate the problem with latency - all delegates come to an agreement about their common transactions, which get put into a block, and the remaining transactions are simply postponed.
Under this model, there is no possibility for a fork to form, either consensus continues to progress, or it stalls completely. With no forks, there can be no double spends and transactions can be accepted with confidence as soon as they enter a block.
Thoughts?