We Need a Conspiracy Probability Theorem

I remember a few years back when a friend at work would passionately support the idea that there was a conspiracy behind the events of September 11. Even though I thought he was off-his-rocker, we had a number of impassioned conversations about the subject. The flaw I saw in his logic was the number of people needed to pull off such a stunt. It seemed to me at the time and still does, that given the number of people needed to ‘cover up’ this event, it is highly unlikely. I mean, there was talk that workers came into the building and weakened the structure before the event and that the true planes were diverted to another airport, and that the people were alive and living in secrecy.

I wish someone would come up with a formula or theorem for calculating the probability of a given conspiracy theory that takes into account the number of people required to keep a ‘conspiracy’ secret and the probability that someone would leak the information.

One of the allures of a conspiracy is that the lack of evidence becomes evidence for a cover-up. The problem is the lack of evidence is not evidence for anything, let alone a cover-up. The issue here is a good example of a prior bias. In other words, conspiracy supporters come in predisposed to believe there is a conspiracy and see the lack of evidence as evidence for a cover-up. Those who tend to be more skeptical will, of course, come in with a bias of disbelief.

Some people will seemingly hold to the conspiracy no matter what evidence is presented to them. It may make sense to hold a position when there is no supporting evidence. However, there is no logical reason to hold a position when there is evidence to the contrary or the evidence to the contrary outweighs the evidence.

In the same way, the skeptic needs only have one piece of evidence that there is no good answer to in order to reject the conspiracy. As Greg Kokul once said, “Just because it is possible to be mistaken about something that seems obvious doesn’t mean it’s reasonable to think we are. This is the skeptic’s error.”

If a conspiracy is true; and I believe there must be some that are; then what evidence will help us determine the validity of such claims. I think one way is to look at the probability. One thing to consider is the number of people involved in the cover-up. As the number involved in the cover-up grows, the likelihood that they will be able to keep it under wraps decreases. Another thing to consider is the resources need to pull off the conspiracy. This is why you often hear that some group of ultra-rich people is calling the shots. In order for some of these conspiracies to be true, you would have to have considerable resources. Who else but an ultra-rich and elite group would have such resources?

Assuming we have someone or some organization with the required resources, we still need to have a motive. Why did they want Kennedy dead? Why do they want to cover up the UFO crash in Roswell? Why did they take down the World Trade Center? Even if someone had a motive, that does not mean they did it. Assuming they had a motive and opportunity (resources), it does not follow that they did whatever the conspiracy theory states. We still need some other type of evidence tying them to the act.

Assuming we can demonstrate the means, motive, and opportunity of a group of conspirators, can we show any other evidence of said conspiracy? We have to look at the conspiracy as a whole and try to determine the probability of such an event. At least, at this point, our belief, while not necessarily true, will at least be rational.

Bayesian Cognitive Science research is looking into questions like how much evidence to the contrary is needed for someone to move from their initial position to an opposing position. I think this research might have some promise on this front. Research has suggested that the brain may employ Bayesian inference, in other words the greater the number of pieces of evidence and the strength of those pieces of evidence leads to greater degrees of certainty. It seems it makes sense to go overboard on the evidence in order to convince the greatest number of people.

Of course, there is a human emotion that brings in the irrational aspect that might just throw the potential conspiracy probability theorem out the door.

Post scriptum

As a side note, after I fished writing this post, I received the latest issue of Philosophia Christi (Vol. 13 Num. 2) and one of the articles caught my eye. Right away, I had to read John W. Montgomery’s article, “How Much Evidence to Justify Religious Conversion? Some Thoughts on Burden and Standard of Proof vis-a-vis Christian Commitment.” Although my post is about the requirement commitment to believe in a conspiracy, John Montgomery’s comments on burden and standard of proof are insightful and appropriate to my point. I have taken a number of his points and consolidated them into my topic of belief in conspiracies.

1. Dr. Montgomery points out then the burden of proof is on the believer to show that their belief is true and not on the unbeliever that the belief is not true. In the same way, I think the burden is on the conspiracy theorist to show the conspiracy is true and not on the skeptic to show the conspiracy is not true.

2. “Proof depends on probability – not on absolute certainty or on mere possibility.”[1] There is a spectrum for the standard of proof from possible to absolute certainty. For a court of law, the standard of proof does not use absolute certainty or mere possibility because absolute proof is impossible to obtain and anything is possible in our Universe. Just because something is possible it does not mean that it is also compelling.

Probability, in a United States court of law, has three levels; moral certainty – beyond a reasonable doubt; clear, strong, and cogent; and preponderance of the evidence.

For the preponderance of the evidence, you need only show the evidence is more compelling than the evidence against it. For moral certainty, we need to have no other reasonable explanation.

For conspiracies, it is unwise to ask for absolute proof or to give credence to mere possibilities. Instead, we must determine if we are comfortable with evidence beyond a reasonable doubt or simply the preponderance of the evidence.

[1] Montgomery, John W. “How Much Evidence to Justify Religious Conversion?” Philosophia Christi Vol. 13 No. 2 (2011): 449-460