Can mathematics help solve conspiracy theory debates?

There is a mathematical way to tell if conspiracy theories are true, says Oxford University researcher David Robert Grimes. 

“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 told the Guardian. “My results suggest that any conspiracy with over a few hundred people rapidly collapses, and big science conspiracies would not be sustainable.” 

Grimes applied his equation to four “anti-science narratives” in particular: that NASA faked the 1969 moon landing, that human-caused climate change isn’t real, that pharmaceutical companies are hiding the cure to cancer, and that vaccines are unsafe for children.

The mathematical model gives the probability of success for each of these conspiracy theories by calculating the number of conspirators involved, the length of time and the possibility of a conspirator leaking the truth. 

According to his calculations, the moon landing and climate change conspiracies would require about 400,000 secret-keepers each, the unsafe vaccination conspiracy would involve 22,000 people, and the cancer cure conspiracy would involve over 710,000 people.

And using his equation, Grimes suggests all four of these conspiracies – if they were true - would be revealed between three to four years after their inception. 

So for a conspiracy theory to succeed, few people need to be involved. For a planned hoax to last a decade undetected, fewer than 1,000 people can be involved. And for a planned hoax to last a century, fewer than 125 collaborators can be involved. 

“The theory presented here might be useful in countering the potentially deleterious consequences of bogus and anti-science narratives, and examining the hypothetical conditions under which sustainable conspiracy might be possible,” Grimes explains in his paper, published Tuesday in the journal PLOS ONE. 

But Grimes doesn’t think his new model will end conspiracies once and for all. 

“The grim reality is that there appears to be a cohort so ideologically invested in a belief that for whom no reasoning will shift, their convictions impervious to the intrusions of reality,” Grimes says in his paper.

In other words, conspiracies will always exist, regardless of a math equation proving they are wrong. Some individuals remain confident in their conspiracy beliefs, regardless of outside data.  

But Grimes hopes his mathematical equation can appeal to rational people considering a conspiracy. 

“While I think it’s difficult to impossible to sway those with a conviction,” he tells BBC, “I would hope this paper is useful to those more in the middle ground who might wonder whether scientists could perpetuate a hoax or not.”