If nuclear war is the Great Filter it may take a while. One could conceive for example if it takes on the order generally of a few hundred years to get substantially off-planet from when one develops nukes (note that this requires among other details no near Singularity) then it starts looking a lot more plausible. Similarly, global governments may not be stable in that time frame.
Note also that there's been discussion here of how much the age of the planets could matter, and whether planets where intelligent life arises earlier are more likely to wipe themselves out (from easier access to uranium 235), and the consensus seemed to be that this was not a significant enough different to be a major part of the filter. See discussion here when I last brought it up.
Possibly an explanation for the great filter, but if it only applies after we move off-planet, then it doesn't explain why we survived our own cold war on our own planet (and means we are still at risk of hitting the great filter ourselves, and not a rare technological civilization among the stars like we thought.)
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