The Alitos’ Monty Hall Problem
If she didn’t think the upside-down flag was a symbol of Trump’s insurrection, why did she fly it?
WHAT DO MARTHA-ANN ALITO AND MONTY HALL have in common? Quite a bit, as it turns out. And therein hangs a tale about credulity and a mathematician named Thomas Bayes.
Here’s the background: The news broke recently that Justice Samuel Alito’s house flew an upside-down American flag for several days in January 2021, immediately after the January 6th assault on the Capitol. This was at a time when Justice Alito and the Supreme Court were considering several legal challenges to the election results by then-President Trump (all eventually unsuccessful). The upside-down flag (typically flown as a sign of maritime distress) was considered by some of President Trump’s supporters to be a symbol of their movement and their attempt to keep President Trump in power. Many were flown at the Capitol as it was stormed.
Naturally, when the public became aware that a Justice of the Supreme Court had flown a pro-insurrectionist flag, it caused some consternation as it suggested the possibility of bias on the Justice’s part, if not adherence to the insurrectionist's cause. Justice Alito explained the event, however, by saying that the flag was flown by his wife, Martha-Ann Alito, and that he was unaware of her actions.
There is much that one can say in response to this incident, but the response that caught my eye has its apparent origin with Professor David Bernstein of George Mason University, who speculated that in flying the flag upside down, Martha-Ann Alito may not have known that she was displaying an insurrectionist symbol. He professes not to have been aware of its symbolism himself until the recent controversy and suggests that a Google search reveals few contemporaneous instances of this symbology in January 2021. Others, including Megan McCardle and Tim Carney, have joined in, saying they personally had no idea until recently that the upside-down flag was a symbol of “Stop the Steal” and echoing this defense: “We don’t know what Mrs. Alito meant. How do we know she intended this as an insurrectionist symbol?”
All of which raises the question: If Martha-Ann Alito didn’t intend the flag as a symbol of the Trumpian attempt to forestall Biden’s inauguration, then what exactly did she intend it to mean? Was it a sign of personal distress? Was it an accident? Was it a call for greater civility?
One can never know another’s mind completely, but anyone familiar with Monty Hall and the classic game “Let’s Make a Deal” can make an educated guess. Seriously.
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FOR THOSE UNFAMILIAR with the premise of the game: A contestant is confronted with three concealed choices, one of which is a winning choice (e.g., a car) and the other two of which are losing choices (e.g., a donkey). The contestant randomly chooses one of the possibilities—“I’ll take door number one, Monty.” At that point, Monty Hall, who knows where the good prize is hidden, opens one of the two unchosen doors to reveal a donkey and asks the contestant if he wants to change his choice. Most do not, but the mathematically correct answer is that you should change.
This is an example of Bayes Theorem in action. Named after Thomas Bayes, an eighteenth-century mathematician and philosopher, the theorem is based on the realization that the probability of an event occurring can be calculated based on one’s prior knowledge of conditions that might be related to the event. In a vacuum of information, we might, for example, predict a person’s life expectancy based on the average for all Americans alive today. But if we add in other known factors—the person’s age, gender, etc.—our statistical model changes. In short, Bayes Theorem is the idea that probabilities change the more information you have and that you should take new information into account and reassess your probabilities based on that information.
That’s what is happening to Monty Hall’s contestant. The guest now has more information—that one specific door did not have and never had the car behind it. That new information changes the odds substantially. And if you work it out, his best result is to change his choice and pick the other door. It’s not a guaranteed win, but changing increases his odds substantially.
Here’s another example: Some time ago I had a neighbor who was a quiet, slightly nerdy sort. In the vacuum of information about him beyond our everyday interactions, I’d never have thought of him as a criminal. But one day the FBI raided his house. And that one piece of information changed the probabilities—given his nerdy nature plus the fact of an FBI investigation, I was pretty confident in supposing he was under suspicion for some sort of computer-related criminal act. It turned out that was the case. New information changed the probabilities.
SO, IT IS ENTIRELY POSSIBLE in a vacuum of any other information to suppose that Martha-Ann Alito, like her contemporary defenders, was ignorant of the “Stop the Steal” symbolism of the upside-down flag. Even though there had been, as the New York Times reports, “a flood of social media posts exhorting Trump supporters to flip over their flags or purchase new ones to display upside down,” there is no reason without more information to suppose that she was familiar with that social media meme.
But we do have more information: the added context of what happened before she flew the flag. It is said (by no less an authority than Justice Alito) that the flag was flown in response to an insulting sign (reading “F--- Trump”) posted by one of their neighbors. Justice Alito also said that a neighbor put up a sign personally blaming Martha-Ann Alito for the events of January 6th.
These additional facts put the upside-down flag in a different light. As a general matter, perhaps we might have thought that Martha-Ann Alito did not know its meaning. But when the flag is flown in direct response to anti-Trump attacks and specifically linked to January 6th, the probabilities shift significantly. It strains credulity to suppose that she did not know she was using a pro-Trump symbol when she was responding to an anti-Trump assault—indeed, given the additional facts we now have, we are more likely to think that she almost certainly chose the symbol precisely because she did know its meaning and wanted to invoke it in response. Knowing the context changes the probability.
It is generous of Martha-Ann Alito’s defenders to posit that she might have been ignorant of what she was saying. But like Monty Hall’s contestant, in light of the additional facts provided by the context of her actions, they would be wise to change their choice.
Correction, May 21, 2024, 12:51 p.m.: Justice Samuel Alito’s wife’s first name has been corrected.
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