I write about Margot, Othello, Sherlock Holmes and Mr. Market. But probabilities, beliefs, evidence and trust have much wider significance.

Here is US Secretary of State John Kerry on the Ghouta attacks:

Let’s put Kerry’s speech in our framework.

Hypothesis: The attacks were carried out by the Syrian army.

To evaluate the hypothesis, Kerry draws a list of several pieces of evidence, and for each one he says: We know. But knowing the evidence is not enough. In 9/11 we knew that two planes hit the Twin Towers. Othello knew that his handkerchief was in Cassio’s lodgings. Inspector Hubbard knew that Tony opened the door. The point is not just to know the evidence: we need to evaluate it, i.e. define TPR: the probability of the evidence, in case the hypothesis is true; and FPR: the probability of the evidence, in case the hypothesis is false.

Let’s take one of the items on the list – let’s call it E1:

E1: “We know that a senior regime official, who knew about the attack, confirmed that chemical weapons were used by the regime, reviewed the impact, and actually was afraid that they would be discovered.”

What is the probability of E1, in case the Syrian army conducted the attacks? The sensible answer is: very likely. Let’s say TPR1=95%.

What is the probability of E1, in case the Syrian did not conduct the attacks? The sensible answer is zero: FPR1=0%.

Result: E1 is a Smoking Gun – conclusive evidence, incompatible with the hypothesis being false. As such, it would be sufficient by itself to prove the hypothesis, irrespective of all other evidence, provided that it is trusted. In this respect, Kerry implies: if the US government says it, you should trust it. But the reality is different:

Russian President Vladimir Putin called the idea that the Syrian regime would use chemical weapons “absolute nonsense” and said “run-of-the-mill interceptions of some conversations that don’t prove anything” can’t justify military action against a sovereign state.

“Claims that they have evidence, but it’s secret and they can’t make it available to anyone and can’t withstand any criticism—it’s just disrespect to their partners,” Mr. Putin said. He said “if there is evidence, it should be presented, and if it’s not presented, that means there is none.”

Of course, as we know, evidence is cumulative: PO=LR1∙LR2∙…∙LRN∙BO. Even if FPR is not zero, the product of N large Likelihood Ratios converges to the truth. As Kerry rightly says:

In all of these things that we know – all of them – the American intelligence community has high confidence. This is common sense. This is evidence. These are facts. (at 8:00).

But the point is that, especially after the 2003 fiasco, as long as there is no trusted Smoking Gun, Posterior Odds will remain exposed to contrary evidence, with the resulting tug of war ultimately dominated by Prior Odds. As Peter Osborne wrote in the Telegraph just before the UK Parliament vote (italics are mine):

Mr Cameron first of all needs to show us that we have solid evidence, capable of standing up in a court of law, that proves his claim that the Assad regime has used chemical weapons on a large scale against its own people. On the face of things, it looks highly unlikely that Assad would have carried out such an action – let alone within three days of international inspectors arriving in Syria.

Consider this: the only beneficiaries from the atrocity were the rebels, previously losing the war, who now have Britain and America ready to intervene on their side. While there seems to be little doubt that chemical weapons were used, there is doubt about who deployed them. It is important to remember that Assad has been accused of using poison gas against civilians before. But on that occasion, Carla del Ponte, a UN commissioner on Syria, concluded that the rebels, not Assad, were probably responsible.

The rush to judgment by Britain and the US looks premature, especially in view of the record of our intelligence agencies in providing misleading and fabricated evidence as a justification for war before 2003. (This time it is said that they have been convinced by intercept evidence, but this too can prove seriously misleading.)

What are the Prior Odds that the Syrian army orchestrated the attack? High, if you view Bashar al-Assad as a ruthless master of deception; zero, if you are Bashar al-Assad (again, my italics):

The statements by the American administration, the West and other countries were made with disdain and blatant disrespect of their own public opinion; there isn’t a body in the world, let alone a superpower, that makes an accusation and then goes about collecting evidence to prove its point. The American administration made the accusation on Wednesday and two days later announced that they would start to collect the evidence – what evidence is it going to gather from afar?!

They claim that the area in question is under the control of the “rebels” and that the Syrian Army used chemical weapons. In fact, the area is in contiguity with the Syrian Army positions, so how is it possible that any country would use chemical weapons, or any weapons of mass destruction, in an area where its own forces are located; this is preposterous! These accusations are completely politicized and come on the back of the advances made by the Syrian Army against the terrorists.

As for the UN Commission, we were the first to request a UN investigation when terrorists launched rockets that carried toxic gas in the outskirts of Aleppo. Several months before the attack, American and Western statements were already preparing public opinion of the potential use of chemical weapons by the Syrian government. This raised our suspicion that they were aware of the terrorists’ intentions to use these weapons in order to blame the Syrian government. After liaising with Russia, we decided to request a commission to investigate the incident. Whereas we requested an investigation based on the facts on the ground, not on rumors or allegations; the US, France and the UK have tried to exploit the incident to investigate allegations rather than happenings.

During the last few weeks, we have worked with the Commission and set the guidelines for cooperation. First of these, is that our national sovereignty is a red line and as such the Commission will directly liaise with us during the process. Second, the issue is not only how the investigation will be conducted but also how the results will be interpreted. We are all aware that instead of being interpreted in an objective manner, these results could easily be interpreted according to the requirements and agendas of certain major countries. Certainly, we expect Russia to block any interpretation that aims to serve American and western policies. What is most important is that we differentiate between western accusations that are based on allegations and hearsay and our request for an investigation based on concrete evidence and facts.

Only an incontrovertible Smoking Gun will be able to break the impasse. At that point, Russia itself would need to change its tack:

“With regard to the possible use of any weapons of mass destruction, including chemical weapons, our position is consistent,” Mr. Putin said. “We are categorically against them and condemn them, and accordingly, if their use is proved, we will participate in the development of measures to counteract such occurrences.”

leaving President Assad in the same awkward position as Richard Pryor‘s cheating husband who, after his wife finds him in bed with another woman, attempts a last defiant denial:

Are you gonna believe me or your lying eyes?

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