If you flip a coin and it comes up heads, do you have any new information about whether it is a fair coin or not? If you thought the odds of MAD working were 50/50, do you have any new information on which to update?
If you flip a coin and it comes up heads, do you have any new information about whether it is a fair coin or not?
Yes. If you started with a uniform distribution over the coin's probability of heads being 0 to 1, your new posterior distribution will tilt toward the 0.5-1 half and the 0-0.5 will shrink. Sivia's Data Analysis on page 16/29 even includes an illustration of how the distribution evolves for some random choices of probability and possible coinflips; I've screenshotted it: http://i.imgur.com/KbpduAj.png Note how drastically the distribution cha...
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