Our President yesterday at the Brookings Institution shared the podium with Haim Saban, the founder of Power Rangers bringing my short 17 year old life full circle.  (In a storage bin somewhere, I still have my hundreds of Power Rangers action figures, with their Megazords and all.)

During the Q&A [link], the President stated: “If you asked me what is the likelihood that we are able to arrive at the end state I was just describing earlier I wouldn’t say it was more than 50/50″. The backup to the end state was informative:

But precisely because we don’t trust the nature of the Iranian regime I think that we have to be more realistic and ask ourselves what puts us in a strong position to assure ourselves that Iran’s not having a nuclear weapon and that we are protected.  What is required to accomplish that and how does that compared to other options that we might take.  And it is my strong belief that we can envision a[n] end state that gives us an assurance that even if they have some modest enrichment capability it is so constrained and the inspections are so intrusive that they as a practical matter do not have breakout capacity.  Theoretically, they might still have some, but frankly theoretically they will always have some because as I said the technology here is available to any good physics student at pretty much any university around the world. And they have already gone through the cycle to the point where the knowledge we are not going to be able to eliminate. But what we can do is eliminate the incentive for them to want to do this.  And with respect to what happens if this breaks down I won’t go into details. I will say, that if we cannot get the kind of comprehensive end state that satisfies us and the world community and the P5+1, then the pressure that we’ve been applying on them and the options that I made clear I can avail myself of, including the military option, is one that we would consider and prepare for. (ACW unofficial transcription of the Brookings website mp3.)

Initially, 50% seems like a number that one can throw out, regardless of any statistical analysis, and support due to “back of the napkin logic” after Iran’s previous.  However, 50% actually represents a calculated probability, created via the Bayesian method that I proposed in Statistical Diplomacy during October on Arms Control Wonk.  This probability is extremely defensible, and demonstrates rigorous critical thought from the White House.  Perhaps his analyst read ACW?

First, the term failure must be defined.  It would be reasonable to assume that failure means Iranian production of a nuclear weapon.  It does not necessarily mean Iran reaching breakout capability.  Only an actual warhead would constitute negotiation failure (which is not to say that negotiations could not break down otherwise, as we saw this fall during the marathon of talks between the Islamic Republic and the P5+1).  However, the most likely proof of failure would be Iranian production of a weapon.  Therefore, we can equate failure and Iran’s production of a weapon, regardless of the additional probabilities of various events, such as Iranian breakout, or Iranian refusal to give up the Arak reactor.

Now, after settling that issue, we can move on to the statistical side of the argument.  My method that I first discussed in Statistical Diplomacy states that Bayesian analysis can yield conditional probabilities on a variety of negotiation events.  By laying out each event in sequential order in an “event tree,” with nodes of yes or no for each occurrence, one can easily apply Bayesian analysis to the probabilities each event is assigned.  One of the simplest calculations that one can make with the event tree is the final probability of a certain occurrence.  The only calculations required are the discovery of the product of each node in a certain branch of the event tree.  Once each branch probability is calculated, one can sum the final probabilities of each event occurring.  Logically, the final event in the Iranian negotiations tree is the Iran obtaining a nuclear weapon.  Thus, by summing and multiplying the required probabilities, one can create a rough estimate of the chance Iran will produce a weapon.

Here is the part where Obama’s estimate of 50% begins to make sense.  Initially, I assigned probabilities to each node in the event tree before the negotiations, and before the Geneva deal, when I wrote the first paper.  These probabilities were laid out in the abridged version of Statistical Diplomacy that I published in October.  Using those estimates, I calculated that Iran had a 52.2% chance of producing a nuclear weapon.  Following the November 23rd deal, I modified several probabilities in my tree. (I have submitted a version of the paper with those probabilities, and an analysis, to the Bulletin of the Atomic Scientists “Voices of Tomorrow” column.)  In that version of the paper, I calculated that Iran has a 47.2% chance of producing a nuclear weapon.  Obama’s 50% is “close enough for government work”.

Of course, the probabilities in my tree are subjective as are the President’s.  However, the fact that this Bayesian method explicitly results in Obama’s 50% estimate indicates that the White House’s assessment can be reasonably backed up by calculation.  Further, the fact that the Obama himself recognizes that the Iranian true intentions and the negotiated results can only be estimated with probability indicates that our President and ACW do not differ too greatly in opinion.