My question: Do the blocks in a blockchain without proof-of-work (i.e. a permissioned blockchain) have to be linked together via a cryptographic hash?
Longer version of my question:
(Please correct me if some of my remarks contain mistakes)
The blocks of a blockchain are linked to each other so that after proof-of-work their content cannot be easily faked, right? If several new blocks were created on top of a block which contains my transaction, I can be pretty sure that I'm on the longest blockchain and my transaction can't be faked (i.e. the double spending problem is solved).
However, in a permissioned blockchain there's no proof of work. As far as I know, in permissioned blockchains agreement on the longest chain (i.e. consensus) is reached by having a majority of blockchain participants agree on the longest chain. But since there's no proof-of-work, 51% attacks (pretending to be the longest blockchain while containing blocks with tampered transactions) are much easier to achieve, or am I wrong?
So why would you need to add a hash of the preceding block to a new block in a permissioned blockchain since there's no proof of work and thus linking the blocks in this manner does not provide any help to solve the double spending problem?