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. This is an example of how elusive the flaws can be. You really have to dig.
You need a way to make the double spend only affect the recipient of the transaction, and not subsequent transactions which are chained off the double spend.
In block based POW, a single double spend amongst many other transactions doesn't invalidate the entire block?
The LCR insures no double-spend exist. There is no fix for the idea of taking the conjunction of chains. The idea is flawed that is why I abandoned it. Also note I had added to my prior post.