I myself suffer from a morbid sense of despair, and even now, decades after I worked with von Neumann, I still find myself questioning our central tenet: Is there really a rational course of action in every situation? Johnny proved it mathematically beyond a doubt, but only for two players with diametrically opposing goals. So there may be a vital flaw in our reasoning that any keen observer will immediately become aware of; namely, that the minimax theorem that underlies our entire framework presupposes perfectly rational and logical agents, agents who are interested only in winning, agents who pose a perfect understanding of the rules and a total recall of all their past moves, agents who also have a flawless awareness of the possible ramifications of their own actions, and of their opponents’ actions, at every single step of the game. The only person I ever met who was exactly like that was Johnny von Neumann. Normal people are not like that at all. Yes, they lie, they cheat, deceive, connive, and conspire, but they also cooperate, they can sacrifice themselves for others, or simply make decisions on a whim. Men and women follow their guts. They heed hunches and make careless mistakes. Life is so much more than a game. Its full wealth and complexity cannot be captured by equations, no matter how beautiful or perfectly balanced. And human beings are not the perfect poker players that we envisioned. They can be highly irrational, driven and swayed by their emotions, subject to all kinds of contradictions. And while this sparks off all the ungovernable chaos that we see all around us, it is also a mercy, a strange angel that protects us from the mad dreams of reason.
Labatut, Benjamin. The MANIAC. Penguin Random House, 2023. p. 144-5. (italics in original)
Reading Kahneman’s Thinking Fast and Slow recently, at several points I was struck by what seemed like the unjustified assumption that people are competent at mental arithmetic. Specifically, that you can give a person a list of probabilities and payouts and then find it legitimately surprising that they can’t or don’t pick the best one. For people constantly immersed in calculation this may be puzzling, but I also have personal experience of highly intelligent and knowledgeable people struggling at (or being unwilling to even try) calculating what a certain percentage of a number is, like for a tip. Studies on the numerical literacy of the general public reveal a worrisome inability to properly gauge millions against billions.
When mathematicians, logicians, and game theorists forget that much of the population cannot or will not calculate, they miss the obvious cause of deviations from their predictions and theories.
