Why do you need a blockchain at all then? This is what I really don't get. If you have your "majority" available at all times they just agree on account balances and call it a day. Just like WebMoney did circa 1998.
Also majority in a decentral system is not that simple. It can be done with FBA (Federated Byzantine Agreement). If that's the case, then yes, account balances are simply agreed on and they call it a day (or technically its called a closed ledger). Then they add the next. Now ledger are blocks of data and the best way to order them is to chain them with hashes depending on the previous ledger (block). And we are back to "blockchain". Its still misleading the "magic" part isn't the chain of blocks. Its the fact that the double spending problem can be solves without an arbiter of truth.
>Just like WebMoney did circa 1998.
I dont know about the technical way this was implemented back then but most likely the system was operated by a single entity. There is some kind of master balance database and the all other sync with that. A double spending can be prevented by rules applies to the master DB. AKA a write-sync is denied if it violates the balance rules. This is easy to do centralizes and obviously who ever controls it can circumvent the rules if he wants to.