Updating incrementally is useful, but only if you keep in perspective how little you know and how unreliable your information is based on a single trial. If you forget that, then you end up like the guy who says "Well, I drove drunk once, and I didn't crash my car, so therefore driving drunk isn't dangerous". Sometimes "I don't know" is a better first approximation then anything else.
Of course, it would be accurate to say that we can get some information from this. I mentioned "anything from 10% to 90%", but on the other hand, I would say that the our experience so far makes the hypothesis "99% intelligent species blow themselves up within 50 years of creating a nuclear bomb" pretty unlikely.
However, any hypothesis from "10% of the time, MAD works at preventing a nuclear war" to "99% of the time, MAD works at preventing a nuclear war" or anything in between seems like it's still quite plausible. Based on a sample size of 1, I would say that any hypothesis that fits the observed data at least 10% of the time would have to be considered a plausible hypothesis.
Um... yes. I guess we're on the same page then. :)
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