President Obama just called for cuts in America's nuclear arsenal, down to 1,000 warheads from a Cold War high closer to five figures. The plan follows earlier rounds of reductions, under both the Obama and George W. Bush administrations, that set a limit of 2,200 weapons for Russia and the U.S. The Bulletin of Atomic Scientists estimates that Russia has 4,500 nuclear warheads, of which 1,700 are deployed on airplanes and missiles (the rest are in storage). The group's estimate for the U.S. was 4,650 warheads, with 2,150 deployed. How do we decide how many nuclear bombs is the right number?
Enough to retaliate should someone bomb you first. Following a round of cutbacks in nukes during the first Obama term, scholars at the National Defense University ran models of nuclear arsenals of various sizes to determine the point where potential enemies were no longer deterred from launching attacks on each other. The idea was to challenge Cold War-era beliefs that forces sufficient to cause human extinction—"unthinkable" was the common term—were necessary to prevent devastating conflicts between superpowers.
The idea behind Cold War deterrence was that if one side (say, the U.S.) decided it could fire a nuclear attack at the other side (say, Russia) and destroy it so totally that retaliation will be minimal, deterrence falls apart. So does arms control: The vulnerable side has an enormous incentive to build more bombs. The expensive, dangerous solution to that is to build nuclear forces so large that even if a small percentage survived an attack and could fire back, the results would be catastrophic.
Obama appears to be following the more recent thinking of "minimum deterrence." Minimum deterrence suggests, rather than each side stockpiling an overwhelming force, that it's possible to establish the least number of bombs necessary. You need enough to scare the other guy into never bombing you in the first place. What's that number?
The NDU team modeled a nuclear war between sides with 1,000 warheads each and 500 each. They concluded that a devastating retaliation capacity was still viable even at 500 warheads. With retaliation a possibility even with each side having far fewer weapons than previously imagined, deterrence remained in place—that is, everyone remained scared out of their minds, so no one shot first ... at least in the model.
Either the 1,000 maximum-minimum deterrence regime or the 500 maximum alternative provides for sufficient numbers of second strike surviving and retaliating warheads to guarantee unacceptable retaliation under each of four operational conditions. Russian and American forces provide for several hundred retaliating weapons under a deployment limit of 1,000....
The conclusion was that if both the U.S. and Russia reduced their nuclear forces to levels far below what either side has ever proposed, they'd still be deterred enough to avoid starting a nuclear war with each other, or anyone starting one with them.
When the prewar deployed forces are reduced to a maximum of 500 weapons, each state still retains enough second strike retaliatory power to inflict socially and politically unacceptable damage regardless of the force posture or condition of operational readiness.
No one appears to have tested models in which the number of nukes necessary for deterrence was just one, despite anecdotal evidence suggesting that could be true.