Large conspiracies quickly unfold

Everyone knows the story of Edward Snowden and the secret PRISM project on mass surveillance by the NSA, which Snowden told the world. If you believe mathematics from the University of Oxford, then it was not an accident, but a pattern. According to probability theory, the more people involved in a conspiracy, the faster someone will let it out. Dr. David Robert Grimes calculated exactly how long the average conspiracy period would last in secret, depending on the number of people involved.

Dr. Grimes’s calculations were published on January 26th in PLOS ONE magazine.

The key parameter in the formula is the probability that a particular participant in the conspiracy will cause information leakage. To calculate this parameter, the scientist used the well-known parameters of three already opened conspiracies: the PRISM project mentioned above (30,000 participants in the conspiracy, disclosure period is 6 years), the study of syphilis in Tuskigi (6,700 people, 25 years), and incorrect scientific methods used in the FBI 500 people, 6 years old).

Characteristics of the open conspiracies are given in the table.
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Based on the data, Grimes estimated the probability of a conspiracy being uncovered by one specific person at four per million.

Thus, it is possible to calculate the lifetime of other conspiracies, if they really existed. For example, the mathematician took four popular conspiracy theories: 1) the Americans did not fly to the moon; 2) global warming does not exist; 3) a conspiracy of doctors around vaccines, which are actually harmful; 4) withholding cancer drugs by pharmaceutical companies.

For example, the dramatization of the flight to the moon would have required a conspiracy of 411,000 people: so many employees worked at NASA in 1965.

The number of participants in other potential conspiracies is given in the table.



With so many conspirators, the secret could not be hidden for long. For example, a lunar conspiracy would exist for 3 years and 8 months before one of the participants revealed it. The graphs show the probability of disclosing every conspiracy in each time interval.



For a climatic plot, the blue solid line corresponds to if all the scientific organizations were involved in the plot, and the red dotted line - only climatologists. Accordingly, in the plot with vaccines, the blue line corresponds to the involvement of health authorities and pharmaceutical companies, and the red dotted line corresponds only to health authorities.

As you can see, in all cases, conspiracies are revealed after several years with one hundred percent probability.

Dr. Grimes calculated what the maximum number of conspirators should be in order for the conspiracy to keep in secret for a longer time.

5 years - no more than 2521 people
10 years - no more than 1000 people
100 years - no more than 125 people

A large number of conspirators also have a chance to keep a secret. To do this, they need to die at a relatively high speed: then their number will decrease with each passing year, as will the likelihood of disclosing a secret. The graph shows the likelihood of disclosing a conspiracy with a constant number of 5,000 conspirators (blue line); dying of natural causes in accordance with the Gompertz function and provided that all the conspirators were originally 40 years old (red dotted); with an exponential reduction in the number of conspirators by half every 10 years (orange dotted).



In the latter case, the probability of disclosure does not exceed 12% (maximum after 14 years).

Dr. Grimes hopes that his work will help in the fight against the anti-scientific views of those who believe in various conspiracy theories.