Anyone can mine even with no ID in my system - that includes sole mining.
So... if a miner had 51% of the network, couldn't a "bad" mining pool simply set the ID on half of their miners to be "no ID" - so then it would look like they only controlled 25% of the network... when in fact, they would control over 50%.
Which would be effectively the same as the current situation where GHash publicly controls 40% of hashrate - and I've read claims (not saying true or false, just that some people claim) they also control another 10-15% of "unknown" miners.
Sorry if I've misunderstood.
No, because if they are removed from the trust lists then their blocks and all other untrusted / no ID blocks would be counted as one partition w. +50% and these new clients would start to not relay their blocks.
You can still do some double spend attacks in my solution, but there is an upper limit introduced and total control becomes impossible.
You didn't answer the question. A miner holding 60% of hashing power could pretend to be 10 independent miners with 6% power each.