I don't think you need to invoke the anthropomorphic principle here.
The fact that we survived the cold war without a nuclear war doesn't really tell us that much about the odds of doing so. It is basically impossible to estimate the probability of something with a sample size of 1. It could be that we had a 90% chance of getting through the cold war without a nuclear war, or it could be that we only had a 10% chance and just got lucky; based on our current data, either seems quite plausible.
So, for your question "did MAD work"; well, in some sense, either it worked or we got lucky or some combination of the two. But we don't really have enough information to know if it's a good policy to follow or not.
That doesn't sound right to me. Sure, with a sample size of 1, your estimate won't be very accurate, but that one data point is still going to be giving you some information, even if it isn't very much. You gotta update incrementally, right?
The standard view of Mutually Assured Distruction (MAD) is something like:
Occasionally people will reply with an argument like:
This is an anthropic argument, an attempt to handle the bias that comes from a link between outcomes and the number of people who can observe them. Imagine we were trying to figure out whether flipping "heads" was more likely than flipping "tails", but there was a coin demon that killed everyone if "tails" came up. Either we would see "heads" flipped, or we would see nothing at all. We're not able to sample from the "tails: everyone-dies" worlds. Even if the demon responds to tails by killing everyone only 40% of the time, we're still going to over-sample the happy-heads outcome.
Applying the anthropic principle here, however, requires that a failure of MAD really would have killed everyone. While it would have killed billions, and made major parts of the world uninhabitable, still many people would have survived. [1] How much would we have rebuilt? What would be the population now? If the cold war had gone hot and the US and USSR had fallen into wiping each other out, what would 2013 be like? Roughly, we're oversampling the no-nukes outcome by the ratio of our current population to the population there would have been in a yes-nukes outcome, and the less lopsided that ratio is the more evidence that MAD did work after all.
[1] For this wikipedia cites: The global health effects of nuclear war (1982), Long-term worldwide effects of multiple nuclear-weapons detonations (1975). Some looking online also turns up an Accelerating Future blog post. I haven't read them thoroughly, and I don't know much about the research here.
I also posted this on my blog