I have intentionally been listening to, and reading comments from, ordinary Russians regarding their view of the “special operation” being conducted by their military into Ukraine. The similarities of their arguments to positions being amplified daily in right-wing American media are troubling. The similar threads I pull out are:
- Paranoia
- Conspiracy-thinking, and
- Reinforcement by religious leaders
Of these, #1 may have some merit. When you are physically threatening other people and suppressing their human rights, there will naturally be push-back and yes, “there ARE people out to get you” because of your own actions. However, most of the time people really don’t give a second thought to you and just want to be left alone. I have recently posted about #3, but it is time to re-visit conspiracy thinking with some very simple math.
Here is the short version: Grand conspiracies are nearly mathematically impossible to sustain, and likely never existed in the first place. Small conspiracies, on the other hand, can work for a time, but only with a very small number of loyal, usually related, conspirators.
Many small conspiracies can work for a time
Small conspiracies frequently pull off their con, at least in the short run. A “campaign contribution” from a powerful or foreign source creates a “wink and a nod” implied contract with a politician that may or may not be legally adjudged a “bribe,” but it has the same conspiratorial effect. Only two people, and maybe a staffer or two, may know of the “deal.”
Organized crime families, because of the tight genetic and voluntary relationships among the participants, can also pull off successful conspiracies for a time. That is, until they fall when they get too big or too bold. Similarly, any closely-held family business enterprise with sufficient loyalty from employed children and paid-off accountants can pull off lucrative-but-shady “small conspiracy” deals or tax shenanigans, especially in business areas such as, say, real estate.
The math of small conspiracies is simple. It is said that omertà, the Mafia code of silence, works only as long as it the trusted insiders don’t exceed the number of fingers on one hand. Or if one of those fingers is a Joe Valachi or a Michael Cohen.
Grand conspiracies and the math of secrets
Grand conspiracies, on the other hand, demand that hundreds or even thousands of individuals “keep the secret” of their nefarious actions. And right there is the math that demonstrates how virtually all allegations of grand conspiracy are fantasy.
The Apollo moon landing, the subject of persistent conspiracy theories for decades, involved many thousands of workers at Cape Canaveral in Florida, the Johnson Space Center in Texas, and employed by sub-contractors across the United States. Every single one would need to “keep the secret” of their part in a very complex ruse, and the technology required to fake that space flight in 1969 was likely harder than actually going to the Moon itself.
The same goes more recently for allegations that millions of votes were “stolen” in the 2020 U.S. presidential election. America has one of the most de-centralized election systems in the world, with numerous technologies and “real audit” points (and not amateurish “Arizona-style” audits), managed by thousands of local elections managers of all political stripes. Well-designed mail-in ballot systems in most states have multiple points of audit control, not to mention customized ballots often for most individual voting districts with their own local candidates on the same ballots. Machine voting also has multiple internal self-auditing points known to thousands of election administrators (but not to amateurs who get their news from conspiracy-mongering sites). Data cross tabulations across races will show anomalies for further investigation very quickly. And voter impersonation fraud, the target of numerous new complex and vote-suppressing ID systems, has always been proven to be a problem only with a small handful of nuts in every election.
And it is not just the math of thousands of people who need to keep secrets. Weak links in any conspiracy or fraud case almost always come down to a broken relationship between just two parties in the “secret sharing.” A “falling out” or financial disagreement with another party often causes a conspirator to come forward or quickly fold to an investigator. Here is some more math: If you have just ten people sharing a secret, you have 362,880 separate “trust against the lie” one-on-one relationships that need to be kept intact (nine factorial, or 9 times 8 times 7, etc.).
That “one-hand” five-fingered omertà set of trust relationships noted earlier, by the way, has 24 relationships among the parties (4 times 3 times 2 times 1; the fifth finger’s relationships are covered by the other four). One “Don” at the top of an organized crime conspiracy can perhaps manage 24 one-on-one relationships. But add just one more finger and you are up to 120 relationships, and it gets mathematically out of hand from there.
Grand conspiracy obsession is a form of magical thinking, that human brain condition where cause-effect, math, and science go out the window. Huge swaths of the American and Russian populations are infected with magical thinking. Professional magicians, by the way, don’t really believe in magic. They just know how to con people.
Election overthrow in the middle
Richard Nixon’s Watergate started as a small conspiracy that edged past the “one hand omertà” rule and got bigger, leading inevitably to its failure. A few weak links in the omertà chain included White House Counsel John Dean, a tangentially-involved aide who knew about the taping of conversations, one conspirator’s wife, and a disgruntled FBI official. Note that Richard Nixon escaped criminal consequences while most of his close associates in the Watergate “Small-C” conspiracy did prison time.
History may repeat itself as the attempt by Donald Trump and his insiders to overturn the 2020 election is a similar example of a “Small-C” conspiracy from the outset that passed that “one hand omertà” rule, as we see the threads unravel, one by one. If the Democrats hold power long enough, I predict a “Nixonian” outcome here, where many in Trump’s closest circle will face significant legal and professional consequences for their actions in the 2020 election. But likely not the ex-President himself. Financial consequences from at least one of Trump’s many small family conspiracy real estate frauds are probabilistically more likely to get him first. But I would love to be proven wrong.
Related posts:
Pingback: Pedagogy is difficult – especially math – When God Plays Dice