From Risk Analysis of Nuclear Deterrence by Martin Hellman. See also http://nuclearrisk.org/

A full-scale nuclear war is not the only threat to humanity’s continued existence, and we should allocate resources commensurate with the various risks. A large asteroid colliding with the Earth could destroy humanity in the same way it is believed the dinosaurs disappeared 65 million years ago. Such NEO (near earth object) extinction events have a failure rate on the order of 10-8 per year [Chapman & Morrison 1994].

During one century, that failure rate corresponds to one chance in a million of humanity being destroyed. While 10-6 is a small probability, the associated cost is so high—infinite from our perspective—that some might argue that a century is too long a delay before working to reduce the threat. Fortunately, significant threat reduction has recently occurred. Over the last 20 years, NASA’s Spaceguard effort is believed to have found all such potentially hazardous large asteroids, and none is predicted to strike Earth within the next century. With a hundred-year safety window in place, resolution of later potential impacts can be deferred for a few decades until our technology is significantly enhanced. Comets also pose a threat, and their more eccentric orbits make them harder to catalog, but their lower frequency of Earth impact makes the associated risk acceptable for a limited period of time.

[...]

While much less accurate than the in-depth studies proposed herein, it is instructive to estimate the failure rate of deterrence due to just one failure mechanism, a Cuban Missile Type Crisis (CMTC). Because it neglects other trigger mechanisms such as command-and-control malfunctions and nuclear terrorism, this appendix underestimates the threat. This simplified analysis uses the time-invariant model described in footnote 3. It also assumes that the experience of the first 50 years of deterrence can be extended into the future.

[...]

Since conditional probabilities were used, they can be multiplied, yielding an estimated range of (2•10-4, 5•10-3) for [...] the failure rate of deterrence based on just this one failure mechanism. The upper limit 5•10-3 is within a factor of two of my estimate that the failure rate of deterrence from all sources is on the order of one percent per year, and even the lower limit is well above the level that any engineering design review would find acceptable.

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The asteroids vs nukes comparison isn't quite apples-to-apples. "Failure of deterrence" does not necessarily imply human extinction, or temporary collapse of civilization, or most people dying. One needs further premises about escalation, spread, nuclear winter, human social resilience, etc.

I agree. If you haven't already done so see my comments at this thread (which I wrote before coming across the article above, HT utility monster). I plan on taking a closer look at the nuclear winter issue in particular (which seems unusually susceptible to quantification).

Nuclear Autumn seems much more likely. This article does a soft comparison of likely nuclear exchange scenarios with the K-T strike. I haven't looked up their references but they sound applicable.

[-]satt30

That Skeptoid article's references are quite old. Encyclopedia of Earth's nuclear winter article discusses more recent scientific work.

Thanks to you too!

HT utility monster

Didn't I tell you about the Hellman piece in SF?

If you did I have no memory of it; maybe you pointed it out to utilitymonster when he was in SF? He just sent me a link to the piece today.

I pointed it out to utilitymonster a number of months ago, when he was not in SF. No worries.

Note also that Hellman's calculation (however rough) is for a Cuban Missile crisis type scenario which would be more likely to escalate/spread than e.g. a terrorist attack.

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Unknown to Kennedy and his ExComm, the Russians had battlefield nuclear weapons in Cuba and came close to giving permission for their use against an American invasion, without further approval from Moscow [Chang & Kornbluh 1998; Blair 1993, page 109; Fursenko & Naftali 1997, pages 212, 242-243, 276]. Not knowing of these weapons, there was strong pressure within the ExComm and from Congress [Fursenko & Naftali 1997, pages 243-245] to invade Cuba and remove Castro once and for all. Another ominous aspect of the crisis was uncovered when key players from both sides met on its 40th anniversary. A Soviet submarine near the quarantine line had been subjected to signaling depth charges, commanding it to surface, which it eventually did. Not until 40 years later did Americans learn that this submarine carried a nuclear torpedo and that the Soviet submarine captain, believing he was under attack, had given orders to arm it. Fortunately, the submarine brigade commander was on board, over-ruled the captain, and defused the threat of a nuclear attack on the American fleet [Blanton 2002].

...today, we are in the process of deploying a missile defense in Russia’s backyard (Poland and the Czech Republic) over strenuous Russian objections. A possible Russian response would be to threaten deployment of a similar missile defense in Cuba, much as our Jupiter missile deployment in Turkey was the stimulus for Khrushchev deploying his Cuban missiles [Burlatsky 1991, page 171].7 While these Cuban missiles would be defensive in nature, many Americans would see them as intolerable. Among other concerns, there would likely be fears that these were offensive weapons disguised as defensive ones. (The Russians have voiced a similar concern over our deployment.)