Statistical Obama

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.


  1. Anon2 (History)

    Have you thought about what the Iranian tree might look like?

    How about the Israeli tree — would it differ from the American tree?

    Or the Russian tree?

    Each diplomatic team has their own objective(s) to optimize in negotiation.

  2. Cyrus (History)

    Could someone explain what business the founder of a child’s toy company has in international affairs? Or a casino mogul?

    • Anon2 (History)

      “Could someone explain what business the founder of a child’s toy company has in international affairs? Or a casino mogul?”

      Pay to play. It is an aspect of most political economies unfortunately. In the old Soviet Union they were called politburo members. Now they are called oligarchs. In the United States it has been going on since the days of Rockefeller, or probably Washington and Jefferson. The Toy King gets to share the podium with the President of the United States. Or sleep in the Lincoln Bedroom.

      In the old days, the genetic offspring of the most ruthless warrior was crowned King and he got to make “international affairs”. Now it is the most profitable business person.

  3. j_kies (History)

    I cry ‘foul’; while statistics can be applied to model human interactions the underpinning basis of such statistics approaches must simulate the system being modeled for hope of validity or predictive application.

    Bayes law and similar approaches are based on ‘large populations and normal distributions’ (frequently Gaussian). I see two fundamental problems – 1) problem formulation – the trial population and test population appear singular and 2) observation of end states – other than a rising mushroom cloud (failure condition) how does the absence of obvious failure equate to success?

    Recall the classic danger of statistics for estimation; with one foot in ice and the other foot in boiling water – on average your comfortable.

    • Magpie (History)

      Mmmm. I guess the problem I have with this particular analysis (as much as I’ve enjoyed these posts) is exemplified by the problem of defining a failure state. Failure for who? And here the problem becomes very difficult because there are a lot more than two actors here.

      I think the production of a bomb represents a state of failure *for Iran*, almost as much as the US. But then it represents a “decent second place” for the KSA – who will then have tremendous freedom of action. So, in horrible pig-latin-esque half-remembered game theory, for the states of Incapable; Capable (but no bomb); and Bomb – where “capable” means the ability to make nuclear weapons in a reasonably short amount of time, some of the actors might assign values like this:

      I: 0; C: 5; B: 2

      US (and the rest of the P5+1, more or less. “Less” being Putin):
      I: 5; C: 2; B: 0

      I: 5; C: 0; B: 2

      I: 5; C: 0; B: 3

      Nobody’s 5-value is set at “having a bomb” – though KSA comes close, and both KSA and Israel would prefer that state to the “capable” state.

      And for Iran, the preferred option is to stay in a state of “capable” – a state of intentional ambiguity, har har, but more tenuous than other such ambiguous states – but they’d still prefer a B to an I. That gives them a tremendous amount of power in the situation, because they know they can force the situation to what is for the P5+1 the worst case, but for them is a painful, but acceptable, alternative to failure.

      No-one, including Iran, really wants Iran to have a bomb. But Iran would prefer that to losing the capability to get one – so if forced to decide, the answer is obvious. Equally obvious is the P5+1’s way out: the C state isn’t perfect, but it’s still better than B. Having failed to force I, and with the failure-state of B as Iran’s eventual alternative to continued pressure, realism asserts itself.

      The actors distressed by this are those for whom the likely C outcome is the worst one. They see the opportunity to force B, or they’ve convinced themselves that I is still an option. Or both.

      If the KSA or Israel find a way to force B despite the resistance of the P5+1 and Iran… what then?

      ‘Course, their win/loss matrix for overt action against Iran would look VERY scary, so…

    • Anon2 (History)

      “Bayes law and similar approaches are based on ‘large populations and normal distributions’ (frequently Gaussian)”


      Bayes’ Theorem is based upon then probability of a binary event. Nothing normal about it.

    • Jonah Speaks (History)

      j_kies, All models are a simplification of reality. The best models are neither too simple to be useful nor too complex for computation. It is usually not necessary to model a whole system in all its complexity to get useful results.

      Given the sample of one (final outcome not yet observed), Harry’s model should be seen as an aid to decision making, not as a scientific test. An estimated probability of 52.2% or 47.2% can’t be seriously distinguished based on one observation of bomb or no bomb. However, it should be possible to check the quality of reasoning in other respects.

      Anon2, Bayes’ theorem can be applied to any probability distribution, both simple and complex, including both normal and binary.

      Magpie, Not sure why you think both Israel and Kingdom of Saudi Arabia (KSA) prefer that Iran have a bomb to merely having capability? I would think their preferences would be similar to those of U.S. and P-5. Iran having an actual bomb means risk of Middle Eastern nuclear war; virtual bomb is much safer for everyone concerned. I hope you are right about Iran not wanting an actual bomb. I see the virtual bomb as Iran’s probable goal, but not a sure thing.

    • Magpie (History)

      KSA and Israel presumably value freedom of action.

      As Iran’s regional rivals they’ve both worked to undermine Iran’s stability, and probably have a long view of encouraging any internal divisions to eventually effect regime change, or at least a significant weakening of Iran’s position.

      If Iran has a bomb, or the ability to rush one if things are starting to look precarious, then a destabilised Iran has potentially catastrophic consequences. Those two parties (and others) will be forced to curb that particularly promising approach to reducing Iran’s influence. Without a bomb, or the ability to rush one, it’s quite realistically possible that Iran’s internal factions, given enough support, could eventually topple the ruling regime. As long as they have one, though, or could make one if things get bad enough, then a serious destabilisation effort and/or effectual support for internal dissenters in the future is too risky to pursue.

      However: if Iran has an actual bomb, KSA probably has some justification for pursuing its own program, and could probably do so with less consequence than it otherwise might. Israel could justify greater conventional military opposition, even if by proxy. Both nations will be free to more agressively pursue other options in curbing Iranian power – encourage greater sanctions, argue for more limited third party engagement with Iran, etc.

      A virtual bomb has all the disadvantages of a potential one, with none of the benefits that an enemy of Iran could hope to gain.

      …and that’s exactly the reason Iran itself will almost certainly be content with a virtual bomb themselves. Why give their opponents’ a whip to beat them with?

    • Jonah Speaks (History)

      Magpie, Yes, freedom of action is valuable, and may offset (to some extent) increased risk of death. However, I am not sure how Iran having an actual bomb increases its enemies’ freedom of action.

      Suppose I wish to bother Iran, or sponsor regime overthrow. If Iran has a virtual bomb, I must worry that Iran may choose to acquire an actual bomb. If Iran has an actual bomb, I must worry that Iran may choose to bomb me. The second worry is more palpable than the first worry, and should constrain my freedom of action more than the first worry.

      As you suggest, if Iran had an actual bomb, it would be easier to organize trade sanctions and maybe motivate conventional attacks on Iran. Would this additional punishment of Iran adequately compensate Israel and Saudi Arabia for Iran’s possession of an actual bomb? I don’t see this, so I think neither country prefers that Iran have an actual bomb.

    • Magpie (History)

      Under what circumstances would Iran launch (or allow to be launched) an Iranian nuke? The exact same circumstances that would have lead into a nuke being rapidly developed. Sprinting then deploying a nuke has the exact same result as simply deploying a nuke, and the two outcomes have so close to the same triggers as makes no difference.

      If you contemplate destabilisation efforts that will take a decade or more to come to fruition, and the end result includes a fair chance of a nuclear strike against your country, it is of no consolation that you will make them go through the inconvenience of acquiring the bomb as an intermediate step. You will know that your decision to initiate (or continue) such an effort is too risky, and you will not make that decision – exactly as if they had a nuke today.

      There will be no sudden surprises in Iran’s political scene. The build-up to an overthrow won’t happen overnight.

      So the chances of death-by-nuke are no different whether Iran has an actual or virtual nuke – especially as those chances are close to zero, as the situation going forward necessitates that Iran’s stability be ensured, rather than attacked. But regardless: if Iran is sprint-capable, and my country bizarrely ignores the situation (we won’t), and supplies support and weapons to an insurgency (we won’t), the virtual weapon will become real, and the end result will be precisely the same as if Iran had built one today.

      Serious destabilisation is off the table either way. The only difference (for a local actor) is in freedom of action outside of that.

      The ultimate failure point is an unstable Iran with a nuke. Whether you start with them merely capable of rushing one, or whether you start at them actually developing one, the end point is identical, and the path to reach that end point is identical. The fact is, it is in everyone’s interests to avoid that endpoint. So, given that we are avoiding it, given that we must treat Iran exactly as if it had a weapon – at least with respect to regime change and internal stability – which of the two situations offers local actors the most freedom of action?

    • Magpie (History)

      Of course, a theory isn’t much use unless it predicts future outcomes.

      So if this is approximately true, then Israel (publically) and KSA (more quietly) will continue to antagonise Iran to the best of their abilities. It’s unlikely that they have the power, but if they can push or otherwise convince Iran to develop an actual weapon, then it is of benefit to them (as long as long-term stability of Iran isn’t actually threatened by those efforts, and the likely cost of those efforts is not great).

      And what are those two countries doing now? Are they supportive of a peaceful resolution? What can we expect to see from them in future?

      If Israel ever thinks it can get away with an air-strike, do you think they will? Indeed, is the possibility that their antagonism might force a nuke on Iran a factor in the P5+1’s own diplomacy?

      Is the present deal aimed as much at curbing Israel’s future actions as it is Iran’s? Was it Bibi’s red line that meant the pressure had to be taken *off*?

    • Jonah Speaks (History)

      Magpie, It is good to test hypotheses. Focusing on Israel’s preferences, the hypotheses that must be distinguished are whether Israel prefers that Iran have an actual bomb, or prefers that Iran not have an actual bomb. If we take Netanyahu at his word, Israel does not prefer that Iran have a bomb.

      Netanyahu is a hard liner. Because he is a hard liner, he overestimates the efficacy of threats, force, and coercion, and underestimates the efficacy of discussion, negotiation, and compromise. He may genuinely believe that bombing Iran would be effective in delaying or preventing Iran’s nuclear weapons program, though he may realize he lacks adequate firepower. Whether he bombs Iran or not, this does not tell us whether he prefers that Iran have an actual bomb.

      Right now, Netanyahu is simply talking about bombing Iran, not actually bombing Iran. He may believe that his threats put pressure on Iran to make more concessions, and put pressure on the P-5 to make fewer concessions. From his perspective, it is rational to make threats, even if he would never carry them out. Again, this does not tell us whether he prefers that Iran have an actual bomb.

      Switching topics, I do not believe the bomb is particularly useful to prevent regime change from within. For example, see Soviet collapse in 1991, or removal of Mubarik in Pakistan. Possession of the bomb does not make contemporary regimes feel secure either, see purges in North Korea, and repression in Russia and China. As always, such regimes find it useful to blame their troubles on foreigners, but the bomb is of no use in suppressing dissent or preventing coups.

  4. Mark Gubrud (History)

    If a question is defined as having a binary-valued answer (outcome), then P=0.5 represents zero information.

    With a bit more thought, one could probably describe a kind of central limit theorem in which a large Bayesian tree containing many terms of nearly complete uncertainty will converge (if done properly) to zero information.

    Also, we can say with certainty that there is no information in anybody’s model of negotiations with Iran which lends meaning to any distinction between 47.2% and 50%.

    So, will the current engagement with Iran yield success in the sense of avoiding an Iranian nuke and Mideast nuclear arms race. The intellectually rigorous answer is “I don’t know.”

    However, optimism being something of a virtue, my answer is “Yeah, probably.”

    • Jonah Speaks (History)

      “With a bit more thought, one could probably describe a kind of central limit theorem in which a large Bayesian tree containing many terms of nearly complete uncertainty will converge (if done properly) to zero information.”

      I think such a game tree with uninformative variables would be irrelevant. Harry put six variables in his model, each of which he thought would provide relevant information. If a proposed variable contained nil information, parsimony would dictate not including that variable in his model.

      Hypothetically, one could have a model with 100 variables, each of which has only 1% impact on the outcome of interest. If 80 point up, that yields a significantly different probability prediction than if 80 point down. This provides a counter-example to the hypothesis of zero information in the limit.

  5. Ara Barsamian (History)

    I think many ACW commentators are missing the point (as are the Western “powers”), and the Bayesian statistical model reflects that.

    How about the scenario where Iran ALREADY BOUGHT 3 four kT nukes from North Korea, say, for 5 billions/each in cash or gold or…Or maybe 10 billions? 20 billions? Pick a number!

    And if the “negotiations” fail, what about Iran doing a test demo with one of the three nukes? What would Israel do, since US would simply just send more “messages”? I hate to think of the potential deflagration in the Middle East through lack of vision and statemanship..

    • kme (History)

      Is that Tom Clancy’s lost manuscript?

    • Anon2 (History)

      “How about the scenario where Iran ALREADY BOUGHT 3 four kT nukes from North Korea”

      Does anyone have any idea how large a NK “weapon” is, i.e. is it the size of a shipping container?

      A shipping container weapon is more a terrorist device than a deterrent weapon as there is no practical way to deliver it.

      Finally, does anyone here have any estimates on the number of NK nuclear weapons and on their degree of actual weaponization.

    • Magpie (History)

      Look, it’s reasonable to conclude that Iran and NK are cooperating in weapons development. Quite apart from the evidence (of which there is some), there’s also the powerful point of “why wouldn’t they?” And I wouldn’t put it beyond all the realms of possibility that either the last test in NK, or the next one, was or will be testing an Iranian design. Unlikely, but possible.

      But why on earth would Iran buy and ship over an NK device? It’d be cheaper and easier and stupendously less risky for Iran to put together an HEU device – and it’s probably too risky to do even that.

      *Maybe* if they somehow get epically rolled on the negotiations – after someone doses the negotiating team’s water with LSD, and then replaces the Supreme Leader with a credible clone – and Iran suddenly finds itself without cascades, or any of the many people there who now know how to make more (on account of maybe they got Raptured), MAYBE, after all of that, they might be tempted to buy an NK nuke. And then if they somehow manage to smuggle it home to Iran without anyone noticing it, and manage to keep it hidden long enough to set up a “test”, and make it tremble some seismometers, then everyone is going to run the numbers and conclude that either they just used all the HEU they could feasibly have extracted from their domestic processing, and don’t have any more, or they bought an NK nuke and set it off to look scary, and they probably don’t have any more, or if they do, the things probably barely work even under perfect test conditions.

      This is a sub-optimal use of resources.