Each transaction includes its own proof-of-work. If there are two parallel streams containing incompatible transactions, the stream with the greatest cumulative proof-of-work in its history becomes valid, and the other is dropped.
Ryan
Wouldn't this be the same as having only one transaction per block?
Yes. That's the way he reduces the delay in confirming transactions. There's less time between blocks/transactions.
My idea is to have transactions added to the block chain individually, rather than in blocks. What would happen is that multiple transactions would simultaneously be added to the head of the chain, which ought to be fine as long as they are all mutually compatible. All that's needed is for further transactions to be able to build on multiple compatible transaction streams and merge them, rather than just picking one. It's possible that a transaction gets merged into several different streams, but that actually helps its odds should it ever end up in a stream that ends up getting rejected.
How that merge would be made?