Jan 28 2016

Math vs Conspiracies

A recent paper in PLOS One explores the mathematical probability of a grand conspiracy being revealed from within. The paper, of course, does not disprove any particular conspiracy theory, but it does make a compelling argument by putting into rigorous form a frequent argument against grand conspiracies, that they are too big not to fail.

As an aside, I love reading dry technical papers that are well-written. There is a certain efficiency and clarifying poetry to a precise technical discussion. It feels like it must be true because it sounds so objective and factual. A well crafted technical paper can slice through confusion and ambiguity like a scalpel.

For example, the author of this paper, David Robert Grimes, writes about conspiracies.

Conspiratorial ideation is the tendency of individuals to believe that events and power relations are secretly manipulated by certain clandestine groups and organisations. Many of these ostensibly explanatory conjectures are non-falsifiable, lacking in evidence or demonstrably false, yet public acceptance remains high. Efforts to convince the general public of the validity of medical and scientific findings can be hampered by such narratives, which can create the impression of doubt or disagreement in areas where the science is well established.

See what I mean – this is a conceptually dense statement, which has a poetry all to itself.

Grand Conspiracies

Whenever I write about conspiracies I frequently get questions challenging my apparent dismissal of the notion of conspiracies, complete with historical examples of actual conspiracies. So to clarify up front what we are discussion here, it is the so-called “grand conspiracy.”

Actual conspiracies of course exist. Whenever two or more people get together and agree to commit an illegal or nefarious act, there is a conspiracy. When we interviewed Gerald Posner on this topic, he called such conspiracies, “kitchen conspiracies,” because they could be perpetrated by a few people sitting in someone’s kitchen.

There is a continuum, of course, and no sharp line between a regular conspiracy and a grand conspiracy. Rather, the larger a claimed conspiracy gets, the more unlikely it becomes as it takes on more and more features of a grand conspiracy. Those features are what are important, because they define the pathological process that creates and supports grand conspiracies.

To quickly review, grand conspiracies are problematic because they are structured in such a way that they are unfalsifiable. Any evidence against the conspiracy was planted or is part of a false-flag operation. The lack of evidence for the conspiracy is explained away as being covered up by the conspiracy itself.

When conspiracies get very large, involving large numbers of people across multiple institutions and many years or even decades of time, this raises many questions about the plausibility and logistics of orchestrating and maintaining such a conspiracy. Those questions are typically answered in two ways, by giving more power and cleverness to the people perpetrating the alleged conspiracy, and by widening and deepening the conspiracy in order to give them the power and reach they need to pull it off.

If 911 were an inside job of the Bush administration, why hasn’t a plucky reporter exposed the whole thing? Because the press are in on the conspiracy. Why didn’t the Democrats when they controlled congress or the White House launch an investigation and expose their political foes? Because both parties are secretly controlled by a shadow government. Why didn’t other countries expose the lies of the US? Because there is really a secret world government pulling all the strings.

That is exactly why there are conspiracy theories about the New World Order, the Illuminati, Reptilians, or the shadow world government – because grand conspiracies tend naturally in that direction in order to maintain the conspiracy.

I have often summarized the situation by saying that grand conspiracy theories tend to grow larger and more complex until they collapse under their own weight.

The Probability of Grand Conspiracies

This brings us to the current paper. Grimes set out to do a probability failure analysis of grand conspiracies. What is the probability that they will fail from within, meaning that someone who is in on the conspiracy either deliberately or accidentally exposes the conspiracy sufficiently that it fails. He did not consider extrinsic failure – being exposed from outside investigation.

Grimes used real historical conspiracies as his guide, namely the NSA spying scandal (exposed by Snowden), the Tuskegee syphilis experiments, and the FBI forensics scandal.

In order to make a mathematical model of grand conspiracy failure he had to plug in several factors. These include, how many people would need to be involved in the conspiracy, how does that number change over time, and how reliable is each individual on average? From the historical examples used, he came up with a range of reliability, and then used the most reliable end of the spectrum for his calculations, to come up with the most conservative estimate of failure probability.

How the number of conspirators change over time is an interesting variable. For some conspiracy theories, like the alien recover from a crashed saucer as Roswell, the people involved at the time would die off over the years, reducing the number of people who can expose the conspiracy and decreasing the probability that this would happen.

However, other conspiracies, such as covering up the “real” risks of vaccines, would have at the least a steady state of people involved.  This is because the conspiracy is not just covering up a single historical event, but ongoing scientific research and the analysis of data.

For his analysis he used four grand conspiracies: The moon landing hoax, that climate change is fake, vaccines, and the hidden cancer cure. For each he had to come up with some way of estimating the number of people necessarily involved in the conspiracy. I think he used conservative numbers, but others might argue that a small number of people could control the process. I disagree, especially whenever scientific data is involved. Any scientists with adequate training can look at the data and do their own analysis.

For the moon landing he used the peak total employment of NASA in 1964, which was 411,000 people. For the climate change hoax he used the membership of scientific organisations that have backed the notion of AGW, resulting in 405,000 people. For vaccine he used the employment of the CDC and WHO, 22,000. (He could have easily added the members of every pediatrics professional organization.) For the hidden cancer cure he used the employees of the major pharmaceutical companies, which is 714,000.

You can, of course, quibble about these numbers. I do think they are probably reasonable to an order of magnitude, which is all that matters for his analysis.

The result is that Grimes’ model predicts these grand conspiracies would intrinsically fail within about four years. Remember, he is using the most conservative estimates for individual reliability and dedication to the conspiracy. For average values, the conspiracies would fail much more quickly. Even if you think he is off by an order of magnitude, involving tens of thousands of people in a conspiracy still results in high probability of failure within a few years.

You can adjust the variables (reliability, number of people involved and the change in that number over time) to generate failure curves with his model. If you have several thousand highly reliable conspirators you still get a fairly high probability of failure within decades, with more rapid failure as the conspiracy grows or reliability decreases.


The conspiracy failure mathematical model developed by Grimes demonstrates rigorously what many grand conspiracy critics have been saying for a long time – grand conspiracies are not plausible. They are simply not sustainable.

Grand conspiracies can only exist in a fantasy world in which individuals can have preternatural competence, in which it is possible for a few people to secretly have tremendous reach and control, and in which these powerful and brilliant people also make ridiculously stupid mistakes that expose them to the enlightened few who can see through the conspiracy.

Author Dean Koonz summarized it this way:

“The sane understand that human beings are incapable of sustaining conspiracies on a grand scale, because some of our most defining qualities as a species are inattention to detail, a tendency to panic, and an inability to keep our mouths shut.”

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