The maths behind why large scale conspiracies eventually fail

Following on from a 9/11 truther discussion ( ? ) in another forum , I thought it is timely to repost this research. It pertains to many grand conspiracy theories you see posted here .

From the second posted link:

I hope that by showing how eye-wateringly unlikely some alleged conspiracies are, some people will reconsider their anti-science beliefs.

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0147905
Abstract

mce-anchor
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. Conversely, historical examples of exposed conspiracies do exist and it may be difficult for people to differentiate between reasonable and dubious assertions. In this work, we establish a simple mathematical model for conspiracies involving multiple actors with time, which yields failure probability for any given conspiracy. Parameters for the model are estimated from literature examples of known scandals, and the factors influencing conspiracy success and failure are explored. The model is also used to estimate the likelihood of claims from some commonly-held conspiratorial beliefs; these are namely that the moon-landings were faked, climate-change is a hoax, vaccination is dangerous and that a cure for cancer is being suppressed by vested interests. Simulations of these claims predict that intrinsic failure would be imminent even with the most generous estimates for the secret-keeping ability of active participants—the results of this model suggest that large conspiracies (≥1000 agents) quickly become untenable and prone to failure. The theory presented here might be useful in counteracting the potentially deleterious consequences of bogus and anti-science narratives, and examining the hypothetical conditions under which sustainable conspiracy might be possible.


For Easier Reading :
https://phys.org/news/2016-01-equation-large-scale-conspiracies-quickly-reveal.html
Equation shows that large-scale conspiracies would quickly reveal themselves

'It is common to dismiss conspiracy theories and their proponents out of hand but I wanted to take the opposite approach, to see how these conspiracies might be possible. To do that, I looked at the vital requirement for a viable conspiracy - secrecy.'
Dr Grimes initially created an equation to express the probability of a conspiracy being either deliberately uncovered by a whistle-blower or inadvertently revealed by a bungler. This factors in the number of conspirators, the length of time, and even the effects of conspirators dying, whether of old age or more nefarious means, for those conspiracies that do not require active maintenance.
However, the equation required a realistic estimation of the chances of any one individual revealing a conspiracy. Three genuine conspiracies were used to provide this - including the NSA Prism project revealed by Edward Snowden.
In each case, the number of conspirators and the time before the conspiracy was revealed were over-estimated to ensure that the odds of a leak happening were a 'best case scenario' for the conspirators - around a four in one million chance of deliberate or accidental exposure.
Dr Grimes then looked at four alleged plots, estimating the maximum number of people required to be in on the conspiracy, in order to see how viable these conspiracies could be. These include: the theory that the US moon landings were a hoax (411,000 people); that Climate Change is a fraud (405,000 people); that unsafe vaccinations are being covered up (22,000 people assuming that only the World Health Organisation and the US Centers for Disease Control are conspirators and that others involved in advocating, producing, distributing and using vaccines are dupes. 736,000 people if, as would be more likely, pharmaceutical companies were included); that the cure for Cancer is being supressed by the world's leading pharmaceutical firms (714,000 people).
Using the equation, Dr Grimes calculated that hoax moon landings would have been revealed in 3 years 8 months, a climate change fraud in 3 years 9 months, a vaccination conspiracy in 3 years 2 months, and a suppressed Cancer cure in 3 years 3 months. In simple terms, any one of the four conspiracies would have been exposed long before now.
He then looked at the maximum number of people who could take part in an intrigue in order to maintain it. For a plot to last five years, the maximum was 2521 people. To keep a scheme operating undetected for more than a decade, fewer than 1000 people can be involved. A century-long deception should ideally include fewer than 125 collaborators. Even a straightforward cover-up of a single event, requiring no more complex machinations than everyone keeping their mouth shut, is likely to be blown if more than 650 people are accomplices.
Dr Grimes said: 'Not everyone who believes in a conspiracy is unreasonable or unthinking. I hope that by showing how eye-wateringly unlikely some alleged conspiracies are, some people will reconsider their anti-science beliefs.