The peculiar philosopher John Derbyshire once wrote :
Practically all conspiracy theories are false … You will likely get through life with your mind’s serenity undisturbed if you dismiss without investigation every conspiracy theory that comes to your attention. I do so reflexively.
Sound though wasted advice. The mildly educated and unwise believe in conspiracy theories the way earthworms believe the universe is mud. This is true even in industrialized countries, while in more superstitious regions they’re reluctant to believe in anything but conspiracy theories.
The reality is that conspiracies are rarely tried and usually caught. This is true despite an endemic desire to commit conspiracies. I will assume that Adam Smith’s judgment,
“People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public”
contains enough truth to rule out widespread innocence as an explanation for the lack of conspiracies.
To see the real reason, one must understand the central tension of a ringleader. If you increase the number of conspirators for greater effectiveness, you also increase the chance of failure. Moreover, effectiveness increases slowly as you add conspirators but the chance of failure increases rapidly.
This can be formulated in a model. Let n be the number of conspirators and let p= probability that a single conspirator will not cause failure, either through disloyalty or incompetence. Then
Where A is a proportionality constant. “Effectiveness” is a nebulous concept because I haven’t specified the conspiracy. You can think of it as some measure of success appropriate to a particular conspiracy. The simplest case is to assume Effectiveness is proportional to the number of conspirators, but one can imagine alternatives.
So for a typical example, A=1/10 and p=.75. These give a Chance of Success (for Effectiveness=1) of 6%. If the conspirators are in a Prisoner’s Dilemna situation where it’s advantagous to turn on the others, then p=.1 and the Chance of Success is , which nicely explains why conspiracies rarely work.
Furthermore thinking of crimes or terrorist acts as conspiracies broadly defined one can use this model to compare competing explanations for acts that did occur. Take for example the Sept 11 attack. One theory is that the attack was perpetrated and hidden by the US government and the other is that the attack was committed by group of mostly Saudi Al Qaida members.
Case 1: The attack was orchestrated they US government.
What p and n should be used for this case? Estimates will vary, but my experience has been that government employees are loyal to the American people, not psychotic, and not very competent. I put the frequency of such people who would be willing and able to kill thousands of Americans in cold blood to be not more than 1 in 1,000,000. I also estimate it would take about n=1000 people, who already held key positions and would have to be recruited, to pull it off and cover it up. This gives a Chance of Success = or zero for all practical purposes. (in fact, there wouldn’t be enough conspirators in the whole US)
If you’re less charitable toward government employees, and believe they are staggeringly more competent than evidence suggest, you might put the numbers at 1 in 100,000 and n=100. This still gives a Chance of Success = or zero again for all practical purposes. Note that the percentage of psychopaths who can kill without conscience in the general population is not more than 1%, so this surely is a upper bound for p. Even at p=.01 and n=10 the Chance of Success is 1 in 100 Billion Billion.
Case 2: It was Al Qaida
Here we know n was at least 20 and a typical value for p would max out at about .9 for al Qaida. Using these the Chance of Success is 12% which I submit squares pretty well with reality. Most such attacks do fail and there were several failures for the Sept 11 attack in particular.
Having seen this explanation though, one can imagine situations where conspiracies, crimes or terrorists acts are likely to succeed and hence tried. I don’t want to give anybody ideas, so no details, but for those whose job it is to counter conspiracies: either the conspirators have to make p close to 1 or they have to generate large effects for small n.