The Amelioration of Uncertainty

Why Conspiracy Theories are Bunk

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 equation, 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 = equation 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 =equation 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.

September 16, 2011
  • October 3, 2011Chet

    Except that in practice they work all the time. The Tuskeegee Syphilis experiment went for 40 years in complete secrecy, despite the involvement of 600 involuntary subjects, researchers at 20 American universities across the country, and as many as 200 medical professionals.

    Project MK-ULTRA is one of those things that even just knowing about it makes you a “conspiracy theorist”, but it actually did happen that the CIA killed a guy during experiments involving psychotropic drugs.

    I’m not saying that every conspiracy theory is true. Most of them are not. But it should be on the basis of the evidence on which we believe or dismiss them, not simply because they’re theories about conspiracies. After all, a complete and sweeping rejection of anything that could be described as a “conspiracy theory” gives a pretty effective cover to actual conspiracies.

  • October 3, 2011Chet

    Also I think you overestimate the number of people who have to be in on the conspiracy in order to take part in the conspiracy. Institutional secrecy and standard operating procedures make it possible to tell a low-level grunt “I was never here” without having to tell him why your presence has to remain a state secret. That’s a conspiracy that now involves at least two people, but only one of them is able to betray the conspiracy in any meaningful way.

  • October 3, 2011Heron

    However, they can be tremendously successful when they do. Consider the Tet Offensive; a massive assault all across a heavily militarized country carried out by a widely popular insurgency that came as a complete surprise because no one talked about it through the months of planning it took to stage it. Also consider the various Iraqi insurgency groups, many of which maintained operational secrecy for years.

    I think your formula works well for general “theoretical” conspiracies, but concerning real-world examples, I believe it leaves out certain contingent factors, like the nature of the conspiracy, the social conditions in which the conspiracy takes place, and the care taken in choosing conspirators.

  • October 3, 2011Joseph

    No real argument from me. If a man dismisses all conspiracies as phantoms, it would likely greatly improve the correlation between his beliefs and reality, while guaranteeing the correlation is imperfect.

    Actually, the insight was inspired by real world experience (three years in Iraq doing Intelligence work). The selectivity of co-conspirators has to be very good. In practice, conspirators have to go to enormous lengths to get p close to 1, because even high values of p lead to a surprisingly large chance of failure. On the other hand, it has been observed throughout history, that unskilled conspirators will enlarge their numbers for the comradery, even though it almost guarantees long term failure.

  • December 23, 2011Antonio

    Very interesting read. I have mixed feelings about it. I cannot comment more because you are right, you have not defined “conspiracy” precisely.
    However, I wish to propose to you another scenario for your model.

    Case 1: US government really did believe that Saddam had Mass Destruction Weapons and wanted to use them.

    Case 2: US government conspirated to bring Saddam down and occupy Iraq using MDW as a pretext.

    I’m wondering if since all conspiracy theories are false I have to think a gang guided by idiocy but promoting intelligence work (please forgive me for the calembour).

  • December 27, 2011Joseph


    No conspiracy I’m unafraid to say. The intelligence community got it wrong most likely through bureaucratic incompetence rather than an honest analytical mistake. Then the President mistakenly decided to use it as his main casus belli even though he had others (all those UN resolutions for example). Finally, everyone including both political parties as well the key international allies believed it because, well Saddam had already used WMD on his own people, and well, Saddam was acting pretty guilty of something.

    Similar things could be said for the conspiracy theory that President Roosevelt knew about the attack on Pearl Harbor and allowed it to happen, or that President Johnson had the Gulf of Tonkin incident staged as a pretext to escalating the Vietnam War.

    There were genuine mistakes involved in the Iraq WMD claims, the attack on Pearl Harbor, and the Gulf of Tonkin incident. They are exactly the sorts of mistakes though that are extraordinarily common and don’t require a conspiracy theory to explain. To pull off any of these conspiracies on the other hand, would have required probability values for p extremely close to 1 because of the large number of people involved. Realistic values for p would be much closer to 0. So if any such conspiracy had of been tried, we’d have overwhelming evidence for it.

    The place to look for conspiracies is when n is small or special circumstance allow for values of p close to 1. A couple of examples from finance will illustrate the point.

    Financial risk managers know that the chance of embezzlement is dramatically higher if one person handles all aspects of the money. While investigators who look for stock market fraud find it suspicious when all the top positions in a company are held by family members, since family loyalty can pushed p much closer to 1 than normal.

  • December 30, 2011Antonio

    I don’t agree with you, even if really I don’t think to be a defender of consipracy theories. Simply, I think to have a feelings different than yours, living in a country which is experiencig US terrorism since a very long time.
    I cannot prove (even if I think so) that US intervention in Vietnam war did happen anyway, aside from Tonkin incident, as well as US intervention in WWII did happen anyway, aside from Pearl Harbour attack, but I am sure that many (if not all) historians agree with me thinking that WWII event did not depend on Gleiwitz incident (I’m wondering if in this latter case you are more inclined to conspiracy explanations). You speak about sorts of mistakes that are extraordinarily common, but you forgot the foundamental role of governments that could act to make such incidents more or less probable (and in all the cases I have cited they heavily did act so, as many historians recognize).
    Anyway. Statistically speaking, if a probability calculation hurts me, I can change parameters values, and eventually I can reject the model if I’m not satisfied. It’s not important for me if Colin Powell demostrated his idiocy or his conspiracy during his dramatic UN speech (indeed, my example was inspired just for its ridiculousness and absurdity). But my good sense tells me that even if he was an idiot it is hard to believe that all the guys behind him were idiots (please, don’t hide youself behing UN resolutions fig leaf; UN resolutions are US resolutions). Assuming for simplicity the same previous numbers, the choice according you is: conspiracy by 1000 US government criminals vs. no conspiracy of 20 idiots. Why not conspiracy by 20 government machiavellian subjects vs. no conspiracy of 1000 idiots? Obviously I have no knowledge of US power structure, but I think it is not honorable to think that 20 idiots can convince the government of the most powerful state in the world to cause a war costed hundreds of thousands of lives. Unless one considers factors that influence the probability of such mistakes and so, last analysis, determine events.

  • December 30, 2011Joseph


    I think I understand the difficulty you’re having with this. You believe the Iraq war hinged on the WMD issue and that if we’d had known the truth about the WMDs then we wouldn’t have invaded. This simply isn’t true.

    There was widespread support for the invasion in the US and it would have happened without the WMD claims. In fact, it would have happened without UN or allied support. The US was willing to go it alone. If the Iraq war had of ended in a few months, it would have been wildly popular. Even after 8 years of fighting and the truth coming out about the WMDs something like 40% of the US population still strongly supports the Iraq War.

    Once this point is seen it becomes much easier to see that the intelligence community simply made a mistake, albeit an avoidable one.

    Immediately after Sept 11, there were generally three views. There was the “anti-war” lobby who didn’t want any involvement in Iraq. There was a “realist” lobby that wanted us to oust Saddam and possibly other dictators in the Middle East, but without any attempt to occupy and create viable Democracies. They wanted the dictators removed purely for the benefit the US. Then there was “spreading democracy” lobby that wanted to fundamentally remake the Middle East so they’d move away from extremism.

    These positions were staked out very publicly within days of the Sept 11 attack and there was a massive public debate for more than a year in the US for them. None of this was hidden in any way. George Bush was very openly and publicly campaigning for the “spreading democracy” option. Again none of this was hidden or any type of conspiracy and it is simply bizarre to claim it was. It was a completely open and usually rancorous debate about how to make the Middle East less of a breeding ground for terrorism.

    When it came time to formally justify the casus belli in the UN, the Bush administration decided to emphasize the WMD issue. This was done for the benefit of our European Allies and not for the benefit of the US population which was already willing to invade. There was significant criticism of this emphasis at the time by the way. Not because people doubted the existence of the WMDs but because many felt we should have just used the existing UN resolutions or bypassed the UN altogether. Many believed we had catered to the European Allies too much already by delaying the invasion and thereby giving Saddam’s troops more time to prepare.

    Now you may think that the people who held these views and made these decisions were idiots and highly mistaken. You’re not alone and many smart people would agree with you. But mistakes are just mistakes not conspiracies.

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