Monday, March 06, 2006

Making Decisions About Bombing Iran's Nuke Facilities

Decision theory says the US should destroy the Mullahs' nuke facilities once they are more 2% confident that the Mullahs are building weapons. Since that level is already comfortably exceeded, it's just a matter of time.

The situation is similar to deciding whether to shoot a suspected suicide bomber on the London Underground - you may kill an innocent illegal immigrant, or - if you don't shoot & the guy really is a bomber, let him kill 13 people. You have to choose a level of certainty that reflects the costs of shooting an innocent against the deaths of 13 others.

In the case of the Mullahs, there are two possibilities.

1. The Mullahs are not building nukes

This isn't impossible - their bloodthirsty rhetoric may be like that of the Brit Muslim toon-protesters - empty threats, since if the latter did slaughter their hosts, they'd end up back in Pakistan without welfare. Also, Muslim dictatorships have low levels of military and technical competence.

2. The Mullahs are building nukes

However the dictatorships of the USSR and China - with the help of espionage - did build nukes. Plus the weapon design and uranium manufacturing technology (and some plant) has been provided to the Mullahs by Pakistan, so it's not hard. And nukes provide the only practical way of wiping Israel off the map.

So now let's look at the costs of destroying the two key plants, whether or not they're actually being used to build nukes. We'll just count deaths, not total casualties, since the two are closely correlated.

The US will probably use the Trident II D5 equipped with a 3-ton kinetic warhead. The Trident has a range of 4,000 nautical miles and an accuracy measured in meters. A more detailed analysis of the ballistics shows that each Trident warhead would be about 23 times more destructive than the bunker-busters used by the RAF in WW2 to destroy German fortifications, quite adequate for the job.

Cost of striking

The kinetic warhead is highly selective - it burrows into the underground fortification and does its destruction there. So, even if the Mullahs locate kindergartens above the plants, the kids will be largely untouched. The people operating the plant would mostly die - however the plants will be fairly automated, and my estimate is 100 casualties/weapon. On this assumption, a strike by 5 missiles on each of the 2 plants would kill about 1,000 people.

Cost of not striking

Conversely, if the plants are not attacked, and the Mullahs do use them to build nuclear weapons, then the cost would be the probability that they'd use them times the deaths that use would cause.

It's possible that a show of force that threatened the Mullahs personally would be an adequate deterrent - perhaps a megaton-range Israeli airburst over the Negev. But the Mullahs belong to a religion that celebrates death, so let's assign a probability of 50% to their using their nukes.

Then assume that they'd use 2 Hiroshima and Nagasaki sized weapons against Israel. In that case the Israelis would suffer the same dead as the Japanese - between 100,000 and 200,000 - say 150,000.

Now we can use Bayesian analysis to compute the probability estimate (P) of the Mullahs actually building a bomb above which it would cause least deaths to strike them:

- if they're not building a bomb (probability 1-P) and we do strike them, the probabilistic cost in innocent lives is (1-P)*1,000;

- if they are building the bomb and we do not strike them, the probabilistic cost in innocent lives is P*0.5*150,000.

The value of P that balances the two alternatives is just 1.3%, and even leaving a respectable margin of error we get 2%. So, if we think that there's just one chance in fifty that the Mullahs are building nukes, we should destroy their plants, since on balance that saves innocent lives.

Of course there are many other costs. Any strike - justified or not - will inflame Muslim nations, probably to cut off oil exports. But that will cause their customers to diversify away from imported oil, so the Muslims end up poor. Hence any boycott will likely be short-lived.

Conversely, an attack on Israel could be much more costly than estimated here. If Israel retaliates, the dead could run into tens of millions, with the local states and much of the EU heavily damaged by contamination.

The bottom line is that at a 1.3% probability, the only thing holding up the strike is deploying the weapons and arranging to minimize collateral economic and political damage. But - if the US behaves as a rational player - the attacks will come.