So let's say the union of both chains is the rule. The problem becomes how many chains do we allow in the union because it is unbounded. If we place a bound on it, the adversary can Sybil attack the bound.
It has to remain unbounded for it to have any chance of working. In this case, such an attack would bring consensus to a standstill - but would this be a sustainable attack? If you imagine the attacker generating new POW transactions continually to create the bigger union, this is going to get quite expensive for him quite quickly... whereas the minority do not need to expend as much energy, since they are just bundling transactions not fabricating them.
Remember I had mentioned in my vaporcoin thread last month that this was my original idea to defeat 51% attack by including all chains. I mentioned when I started this thread that I had found a fundamental flaw in that design. Now I remember what it is.
The attacker can put a double-spend on every block of the minority chain to invalidate it relative to the longest chain (which also contains the double-spend but confirmed after the minority chain has confirmed the double-spend). This is an example of how elusive the flaws can be. You really have to dig.
I think what I did next was contemplate still taking the union (conjunction) of all non-double spent transactions from all chains. I forget at the moment what was the flaw with that. I should have wrote it down. Edit: now I remember. The attacker simply waits until there are derivative transactions, so no one can trust any transaction is truly confirmed on the minority chain.
