Iota doesn't do total ordering. Even more, iotas can be spent before they were acquired. "Total number of iotas can't exceed some constant (1 billion without 10^-9)" - this is the rule Iota nodes stick to. There are some lesser rules used for transaction validation but they are not important in this context.

By using that simple rule Iota protocol gives a lot of freedom, the system can be in any state in points where total supply is not important. This gives a big boost to transaction processing speed.

I see parallels between Iota ledger and a quantum system. The quantum tunneling allows particles to pass through potential barriers => double-spendings can exist at some moment. Iota users "vote" on one particular state of the ledger at some moment making the ledger to "collapse" like a wave function.

PS: I think I'm starting to get your problem. You construct models in classical world, maybe it's a good moment to get your feet wet in the quantum world?