Link to the full article that I found about this study on BBC Science
A conspiracy theory is very unlikely to be true because, sooner or later, one of the conspirators will blow its cover, a study suggests.
The research examines how long alleged conspiracies could "survive" before being revealed - deliberately or unwittingly - to the public at large.
Dr David Grimes, from Oxford University, devised an equation to express this, and then applied it to four famous collusions.
The work appears in Plos One journal.
The Journal article at PLOS.org for a more detailed analysis.Using a handful of assumptions, combined with mathematical deduction, Dr Grimes produced a general, but incomplete, formula.
Specifically, he was missing a good estimate for the intrinsic probability of a conspiracy failing. To determine this, Dr Grimes analysed data from three genuine collusions.
The first was the surveillance program conducted by the US National Security Agency (NSA), known as PRISM. This programme involved, at most, 36,000 people and was famously revealed by Edward Snowden after about six years.The second was the Tuskegee syphilis experiment, in which the cure for syphilis (penicillin) was purposefully withheld from African-American patients.
The experiment may have involved up to 6,700 people, and Dr Peter Buxtun blew the whistle after about 25 years.
The third was an FBI scandal in which it was revealed by Dr Frederic Whitehurst that the agency's forensic analysis was unscientific and misleading, resulting in the imprisonment and execution of innocent people.
Dr Grimes estimates that a maximum of 500 people could have been involved and that it took about six years for the scandal to be exposed.
The equation he created represents a "best case scenario" for conspirators - that is, it optimistically assumes that conspirators are good at keeping secrets and that there are no external investigations at play.