Statistical Diplomacy: A Bayesian Inference Tool for the P5+1+Iran Negotiations

Life can be modeled as a tree of future events with branches that will be realized with different probabilities.  Each branch can be thought of as forked paths in the forest.  Each branch in the past or the future relates to other branches.

Bayesian inference offers a method to relate the conditional probability of a certain branch to the probabilities of other branches.  This can be a useful tool in improving the odds of achieving a desired result.  I have applied such a tool to the Iranian nuclear negotiating portfolio, looking at the situation from the perspective of the P5+1 negotiation team (a tree created from Iran’s perspective would have different nodes and primary goals).  It is simple in concept, yet surprising in results.  This tool, which I have modeled in Excel spreadsheet form, can help to realize the implications of various decisions on the ultimate outcome: an Iran with or without “the Bomb.”

Bayes in a Bombshell

Let us suppose there is a nation-state that might be developing weapons-capable technology (meaning technology with both weapons and civil applications).  None of these decisions or results are known (ex-ante) at the present time, but both can be estimated via probabilistic techniques (the initial percentage estimates would come from said nation-state’s past actions, and public statements and written works made by national leaders).

Figure 1 – Example: Weapons-Capable Technology and Weapons Outcomes

The branching node at the left represents the total probability of nation-state’s development of weapons capable technology.  The nodes in the middle are conditional on the branch they lie on.  Thus, the upper-branch probabilities (weapons or no weapons) are conditional on leftmost node (weapons-capable technology development or not).  The outcome nodes on the right can be calculated by multiplying the probabilities of the paths through the branches to the left.  Thus, the probability of developing the technology and creating a weapon is 50% * 75% or 37.5%.  I refer to reader to the excellent Wikipedia article for a more detailed explanation (with a more lighthearted example).

An interesting result is that by estimating the probabilities at the nodes, one can estimate the probability that the nation-state will obtain weapons by summing up the end nodes (the rightmost nodes) that result in weapon creation, via production or external purchase (37.5% + 5% = 42.5%).

The Bayesian trick is that the tree’s branching nodes can be reversed as shown below, putting the “weapons” question first:

Figure 2 – Example: Reversing the Nodes to Get Useful Results

Each tree is consistent with the other.

From the analysis we can infer a useful result: that the probability of the nation-state using the weapons-capable technology to develop weapons is 88.2% (calculated from the probability of developing the technology AND weapons divided by the total probability of a weapon as calculated above, or 37.5% / 42.5%).

The formula and notation for this would be:

P(Tech|Weapons) = P(Tech & Weapons)/P(Weapons)

where

P(Weapons) is read “the probability of weapons”;

P(Tech|Weapons) is read “the probability of the tech conditional on the probability of weapons”;

and

P(Tech & Weapons) is read “the probability of the tech AND the weapons.”

Another important conclusion is that by calculating a variety of component tree probabilities, we can use algebra or a spreadsheet to derive additional consistent probabilities.

Finally, even if our probability estimates are not perfect, using reasonable best guesses can improve the likelihood of obtaining the desired results.  In this case, it is clear that we can lower the probability of a weapons outcome by convincing the nation-state to take the “no” branch for the weapons-capable technology.  The technique lets the negotiating team quantify their estimates of improvement by achieving certain branches; and thus prioritize their negotiating strategy.

How to Use the Technique for Iranian Nuclear Negotiations 

The situation in the Iranian negotiations can be characterized in a more detailed tree.  I have extended the tree to the following decision nodes. The current version of the tree has been modeled for the P5+1’s negotiating team.  Their apparent objective is to minimize the probability that Iran obtains nuclear weapons. The tree nodes are

Table 1 – Model Tree Nodes

Branch probabilities were estimated from President Hassan Rouhani’s published works, former actions, assessments written by other authors in the diplomatic and arms control fields, and other assessments on Iranian nuclear goals.  Probabilities are assumed to be within about 5 to 10% of the true value.  The assumed probabilities are detailed in the spreadsheet, which is available upon request as detailed at the bottom of this article.  I also have written a more detailed 20-page academic journal style paper (that I hope to have published, hint to journal editors) and which I can provide on request to interested parties.

Figure 3 – Nuclear Negotiation Tree Model

The tree is show above in miniature in Figure 3.  Please click on this link for the high-resolution pdf.  Each probability estimate is shown for the yes (up) and no (down) nodes.  Note that italics are used throughout to denote node decisions as shown in the second row.

Users can enter and use their own probability estimates.  Certainly, others can provide better estimates than I.

Analysis Results as Applied to Negotiation and Discussion

As the objective is to minimize the probability of Iran’s acquiring nuclear weapons, the most useful results are how various branch decisions that can be affected by negotiation change that probability. The absolute accuracy is only as good as the (somewhat subjective) input estimates, but even if the assessments are +/- 10% or more, the relative changes in probability are extremely useful.  I present results to 0.1% in the calculation for clarity to the reader following the calculations.

Table 2 – Analysis: Key Results

Key Negotiating Take-Away 1: The Effect of the Medical Isotope Program

For the past several years, Iran has insisted that 20% enriched uranium is necessary to fuel the Teheran Research Reactor, which in turn produces medical isotopes for internal diagnostic and nuclear medicine purposes.  What would the estimated effect be of such a medical isotope program (abbreviated “Medical Isotopes” or “Iso” on the spreadsheet) on the probability of Iran obtaining nuclear weapons (abbreviated as “Bomb“)?

First, for comparison, the base case Bomb probability estimate must be calculated. Multiplying all the conditional probability estimates in the tree will yield the right-hand node paths probability estimates.  Then summing only those where Bomb results reveals this probability.  Thus, the base case Bomb for comparison purposes, sums to 52.2%; i.e. there is a 52.2% chance (+/- the analysis error) that Iran will obtain a nuclear weapon.

Now, if only paths are considered where Iran has a Medical Isotopes program the Bomb probability is increased to 61.9%, i.e. almost 10%.  However, if the Medical Isotopes program is eliminated, the Bomb probability falls by about half, to 29.7%.

Therefore, successfully negotiating with Iran to eliminate the 20% enriched uranium Medical Isotopes path lowers the risk of the Bomb outcome significantly.  This should be one of the P5+1’s primary negotiating objectives.

Applying Bayes’ Theorem to reverse the calculation, as shown in the second tree example, reveals the probability that IF Iran creates the Bomb, it has a Medical Isotopes program.  This is a very high 82.9%. Thus if Iran creates a Bomb, a Medical Isotopes program is highly associated, possibly as cover.

Overall, analyzing this aspect of the tree yields two important findings.  First, if Iran has a medical isotope program, its probability of obtaining a nuclear weapon increases by 9.7%, to 61.9%.  Second, if Iran does create a nuclear weapon, there is an 82.9% chance that it has a medical isotope program, and possibly used as cover to enrich uranium to a higher level.  This strongly indicates to P5+1 negotiators that they should make preventing Iran from keeping a full medical isotope program a high priority, as the isotope program’s existence greatly increases the likelihood of a nuclear-armed Iran.

Key Take-Away 2: The Effect of Fuel Cycle (3.5% enriched Uranium)

It appears to the Wonktern that the Iran commercial power fuel cycle (the “Fuel Cycle”) is already a foregone conclusion in any negotiated settlement.  Nevertheless, what is the effect of eliminating the Fuel Cycle as compared to maintaining it?

Again, from the base case estimate of a 52.2% probability of Iran producing a Bomb if we only consider the paths of maintaining the Fuel Cycle, the probability of the Bomb is increased to 60.2%.  However, if the Fuel Cycle is eliminated, the probability of Iran’s obtaining the Bomb is estimated by the model to be reduced to 24.6%.  In the model’s estimation, it is only marginally better to eliminate the Fuel Cycle than to simply eliminate Medical Isotopes.  This marginal benefit and massively increased negotiating difficulty indicates that the P5+1 should focus on the more realistic goal of eliminating Iran’s medical isotope program.

Key Take-Away 3: Compounding the Fuel Cycle and the Medical Isotope Program

If we consider the joint probability of the Fuel Cycle together with the Medical Isotope program (read: both or none), the effects on curtailing the acquisition of the Bomb are enhanced.  Conditional on both Fuel Cycle AND Medical Isotope programs the probability of the Bomb is 68.3%.  When both are eliminated, the Bomb probability falls to 23.2%.   Ignoring how one could have a medical isotope program without a fuel enrichment program, we see that eliminating the Fuel Cycle program in addition to the Medical Isotope program only decreases the probability by about 6%, compared to eliminating the Isotope program all together.  Both P5+1 and Iranian nuclear negotiators must decide at what point attempting to eliminate the Fuel Cycle, a point that Iran has stood hard on since Rouhani’s days as a negotiator, is not worth the risk of jeopardizing other negotiation gains.

Key Take-Away 4: Genuine Negotiations vs. Iran Subterfuge Strategy

For the P5+1 negotiators, there is no way to determine if Iran (by political implication both Rouhani and Khamenei) is genuine in its willingness to agree to a settlement (“Genuine“) without nuclear weapons.  For the P5+1 negotiators, this is just another unknown decision node with probabilities.  In the model, this has been subjectively assigned a 50/50 probability and is not conditional on other decisions (i.e. it is the left-most node).

For Iran, it knows whether it is being genuine or not; and by changing the decision to be genuine, it can greatly influence the probability of its acquiring nuclear weapons (the Bomb). If Iran is Genuine, the probability of its acquiring the Bomb is reduced to 33.1%.  If it is not Genuine, the probability increases to 71.3%.  Clearly, the P5+1 should look for telltale signs that Iran is following the non-Genuine path, and modify its strategy accordingly.

Conclusion

Overall, the total probability over all tree paths lead to Iran obtaining a nuclear weapon just over half the time.  Thus, western policymakers must use clues that Rouhani gives during negotiation to determine which path of the decision tree Rouhani is following.  Negotiators can use Bayesian inference with the aforementioned tree method to derive Bayesian conditional probabilities.  Once they determine the probabilities of each of Iran’s actions on separate branches of the tree, negotiators can tailor strategies to each situation that arises to increase the chances of the desired result.

Concerning overall strategy, it appears that the West should pursue a mix of policies that encourage Iran to not progress past a commercial power fuel cycle.  One of the West’s primary negotiating goals should be to secure the negotiated elimination of Iran’s medical isotope program.

To achieve this strategy goal, the West can openly offer relaxation of sanctions, as well as increased trade with Iran.  However, using the probability tree, P5+1 negotiators can statistically estimate whether a strategy of initially offering a full fuel cycle, a “stick and carrot” approach, or implicit, wink-and-nod style signals would encourage the optimal result — no Iranian nuclear weapons.  Western negotiators will determine what appears reasonable to exchange in return for an agreed Iranian fuel cycle. The most optimal outcome would be obtaining a mostly, if not totally, transparent peaceful civilian nuclear program with limited or no breakout capability.  Over time, increased economic contact between Iran and the West should chip away at the tensions between the nations and cultures, decreasing the chance of weaponization attempts.  On the subject of Iranian medical isotope program, the West should offer to create a multinational isotope production facility that could replace the TRR (in the manner described in greater detail in my academic larger paper).  Aside from the medical isotope program’s role in exposing Iran’s path on the decision tree, it could also serve to remedy similar problems with other nations that are nuclear weapons proliferation risks, but would still desire to have access to nuclear medicine.

The event tree will be a valuable tool to Western negotiators in dealing with President Rouhani.  If used correctly, negotiators can create strategies that have an extremely high chance of success, and resolve the diplomatic mess that is the current state of Iranian and Western relations.