Thanks for this series—it’s very interesting so far.
Whether a counterforce second strike by Russia would actually cause fewer deaths than a first strike is conditional on 1) the US striking first, 2) Russia choosing not to launch on warning, and 3) Russia being substantially under-prepared for a first strike. My best guess is that the probability of all three of these being the case is fairly low. If we naively assume that the probability that the US strikes first is 50%, the probability that Russia chooses not to launch on warning is also 50%, and that the US counterforce strike destroyed the ‘center value’ of the range for the number of nuclear weapons that might be destroyed (870), or 79% of the number of warheads I expect Russia would use against the US during a counterforce _first _strike (1,100), I would expect that about 5% fewer deaths would be caused by a Russian second strike than by a Russian first strike (0.50.50.21).
There’s a good chance I’m just misunderstanding this, but shouldn’t that be 19.75% fewer deaths in expectation? 0.5 * 0.5 * 0.79 (=0.1975), rather than 0.5 * 0.5 * 0.21 (=0.0525), because the number of weapons used (and thus the number of deaths, if we stick with your assumption of linearity) would go down by 79%, to 21%, rather than going down by 21%. (Again, it’s very possible I’m misunderstanding the maths here.)
Also, wouldn’t it actually be that a Russian counterforce strike in general (not a Russian counterforce second strike) would cause 19.75%* fewer deaths in expectation, given that the second strike may involve fewer nuclear weapons? Put another way, would it actually be that a Russian counterforce second strike would cause 39.5% (two times 19.75%) fewer deaths in expectation than a Russian counterforce first strike? I ask this because the first multiplication by 0.5, to represent a 50% chance of the US striking first, seems to account for you taking the half of the possible worlds in which Russia strikes second, and thus to not to be needed if you’re discussing a Russian second strike anyway. This seems relevant because, if both that and the above are the case, then in the model of the total number of deaths expected from both side’s weapons in an exchange should be adjusted to reduce the deaths from Russian weapons by 19.75%. (As opposed to just reducing it by 9.875%, which you’d do if the 19.75% represented the reduction in weapons used conditional on Russia striking second, rather than in general.)
Apologies if I haven’t explained that very clearly or I’m misunderstanding your reasoning.
*Or ~5%, if my calculations to get 19.75% are mistaken.
Thanks for this series—it’s very interesting so far.
There’s a good chance I’m just misunderstanding this, but shouldn’t that be 19.75% fewer deaths in expectation? 0.5 * 0.5 * 0.79 (=0.1975), rather than 0.5 * 0.5 * 0.21 (=0.0525), because the number of weapons used (and thus the number of deaths, if we stick with your assumption of linearity) would go down by 79%, to 21%, rather than going down by 21%. (Again, it’s very possible I’m misunderstanding the maths here.)
Also, wouldn’t it actually be that a Russian counterforce strike in general (not a Russian counterforce second strike) would cause 19.75%* fewer deaths in expectation, given that the second strike may involve fewer nuclear weapons? Put another way, would it actually be that a Russian counterforce second strike would cause 39.5% (two times 19.75%) fewer deaths in expectation than a Russian counterforce first strike? I ask this because the first multiplication by 0.5, to represent a 50% chance of the US striking first, seems to account for you taking the half of the possible worlds in which Russia strikes second, and thus to not to be needed if you’re discussing a Russian second strike anyway. This seems relevant because, if both that and the above are the case, then in the model of the total number of deaths expected from both side’s weapons in an exchange should be adjusted to reduce the deaths from Russian weapons by 19.75%. (As opposed to just reducing it by 9.875%, which you’d do if the 19.75% represented the reduction in weapons used conditional on Russia striking second, rather than in general.)
Apologies if I haven’t explained that very clearly or I’m misunderstanding your reasoning.
*Or ~5%, if my calculations to get 19.75% are mistaken.