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Why the Internet’s biggest conspiracy theories don’t make mathematical sense

Karman Willmer, left, and Shelby Messenger protest against SB277, a measure requiring California school children to get vaccinated, on, June 9, 2015, in Sacramento. (Rich Pedroncelli/AP)

If NASA really faked the moon landing in 1969, about 411,000 people would have worked together to keep that information from the public, and the whole thing would have been exposed about four years later, according to an Oxford researcher who has found a mathematical way to examine the viability of conspiracy theories.

David Robert Grimes is a physicist and cancer researcher, but he also writes science pieces for the Irish Times and the Guardian. As a science writer, he’s used to being contacted by people who adhere to science-based conspiracy theories, which generally involve accusing the scientific community at large of colluding on fake data for nefarious purposes, Oxford University said in a release about Grimes’s new paper, published in PLOS this week.

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To help demonstrate the viability (or lack thereof) of several well-known conspiracy theories, Grimes wrote an equation to show just how hard it would be to keep large-scale conspiracies — if they were true — a secret.

“For a conspiracy of even a few thousand actors, intrinsic failure would arise within decades. For hundreds of thousands, such failure would be assured within less than half a decade,” Grimes concluded. In other words: bad news for a lot of the Internet’s most persistent conspiracies.

For instance, more than 440,000 people would have to be working together to fool the public if climate change deniers are correct. Grimes’s equation calculated that such a conspiracy would have been exposed — either by an internal whistleblower or, accidentally — three years and nine months after it began.

“The results of this model suggest that large conspiracies (≥1,000 agents) quickly become untenable and prone to failure,” Grimes said.

How? The equation considers several factors, including the number of conspirators required over time to keep any given wrongdoing a secret, whether said conspiracy simply requires silence on the part of the people involved or active maintenance, and the rate at which those involved would die out over time, either because of natural causes or because of, uh, deliberate targeting.

The probability of exposure used in the equation comes from a handful of conspiracies that turned out to be true in real life: the U.S. mass surveillance tactics that were made public by whistleblower Edward Snowden; the Tuskegee syphilis experiment, where researchers unethically refused to give penicillin to African American men who were part of a syphilis study; and the FBI forensics scandal. Information about those conspiracies were interpreted to create a ” ‘best-case’ scenario for the conspirators,” for the sake of the equation, he said.

Grimes then used the equation to indicate the viability of four major conspiracy theories: climate change denial, anti-vaccination movements, the NASA moon hoax, and the cancer cure conspiracy — or the belief that a cure for cancer is being withheld from the public.

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The full paper has a detailed rundown of how different interpretations of the size of the alleged conspiracy might affect the probability of exposure. For instance, the number of people involved in covering up a vaccination plot could either be about 22,000, or more than 700,000, depending on whether you believe pharmaceutical companies are colluding with the CDC and the World Health Organization, as many anti-vaccination believers do, or whether the companies were simply duped into furthering the conspirators’ interests.

As you can see from the chart below, the inclusion of pharmaceutical companies in the vaccine makes a huge difference in the probable time to exposure. The same goes for whether the climate change coverup conspiracy involves only active climate research scientists, or whether it, as is more commonly alleged, includes all the scientific bodies endorsing the scientific consensus on the existence and cause of climate change:

These numbers represent the maximum time to imminent failure and are based on conservative assessments of the size of the alleged plots, even for the more widespread scenarios. They also don’t take into account any possible external exposures of a conspiracy, which would only increase the likelihood of a conspiracy going public.

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Recent research has shown that models like Grimes’s, however clever they are, probably won’t do very much to sway the minds of those who are invested in these conspiracy beliefs. The Intersect’s Caitlin Dewey put it this way while discussing hoax news sites in her final installment of the “What was Fake on the Internet” series:

Institutional distrust is so high right now, and cognitive bias so strong always, that the people who fall for hoax news stories are frequently only interested in consuming information that conforms with their views — even when it’s demonstrably fake.

Grimes, too, knows that “it is highly unlikely” that his equation would change the viewpoint of most conspiracy believers. But he ended his study on a mildly optimistic thought anyway: “For the less invested,” he wrote, “such an intervention might indeed prove useful.”

“‘Not everyone who believes in a conspiracy is unreasonable or unthinking,” Grimes added in a statement accompanying his study. “I hope that by showing how eye-wateringly unlikely some alleged conspiracies are, some people will reconsider their anti-science beliefs.”

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