I ran across this page that is an outline for a lecture given by a professor of statistics at Berkeley. The title of his talk is “The top ten things that math probability says about the real world”, but he just glosses over six of them and spends the majority of his lecture discussing the last four. Still, all of the points are valid and important, in fact a lot of his lecture covers subjects that are pet peeves of mine. But the one that never ceases to amaze me is is the title of my post: people are predictably irrational in actions involving uncertainty.
Take for example the opening scene in Rosencrantz and Guildenstern Are Dead, where they are flipping the coin. Rosencratz (or is it Guildenstern?) gets heads something like 92 times in a row. Now assuming a fair coin, the odds of that are laughably improbable: \(2^{-92}=2.019\times 10^{-28}\) . You’d have a millions of times better chance of winning the lottery than achieving this feat. In fact, given a lottery that has a one in one billion chance of winning, you’d have a better chance of winning said lottery 3 times in a row then you would of getting 92 heads in a row on a fair coin.
Proof: \(\left(1\times 10^{-9}\right)^3=1\times 10^{-27}>2.019\times 10^{-28}\).
But that’s not what’s important here. The issue in question is what people will predict the next coin flip to be. If they see the large number of successive identical coin flips, and you then ask them what the probability of the next flip also being heads is, they will usually give one of two answers: 1) It is most likely to be heads, because the coin is obviously ‘on a roll’ of heads. 2) It is most likely to be tails, because it’s had so many heads in a row that there is a ‘negative balance’ of tails that needs to be met. This is despite any and all assurances that the coin is perfectly fair. So the real answer is of course, 0.5 probability of heads, and 0.5 probability of tails. This is always true, no matter what the previous record of instances may be. The thing that many people fail to realize is this:
In any simple game of pure chance, every turn/round/instance is completely independent of previous turns, and and every single turn has the exact same probability every time. This is how casinos make the majority of their money.
So why are most people so predictably irrational in such situations? Obviously I’m not a psychologist (or other such similar profession, but see this slide from the end of the lecture), but I think it has to do with the fact that as humans, we almost never have to make judgments in situations where the outcome is truly random. Such situations have only arisen quite recently in human history with the advent of gambling. And even then there is only a subset of gambling games that are purely random (like craps or roulette, assuming they are truly fair) while many have a combination of chance and skill (card games fall into this category) and some are flat out not fair (slot machines).
In most everything that we deal with in daily life, even when there are events that seem random when we we observe them, they are almost never random. For example, take my daily bus commute. Even though the bus has a regularly scheduled time to arrive, from my perspective it appears random within a time frame of +/- 10 minutes. Also how long it take to arrive at school or home also appears to be random, with a total time of anywhere from 15 to 45 minutes, depending on traffic. But in reality, both when the bus comes and how long it takes to arrive at my destination are not random at all. The problem is that the number of variables that go into determining these two times are so vast and unpredictable that the end result may as well seem to be random when it isn’t.
Back to my former point though, I think we as humans tend to find pattern and correlation in many things (even when they don’t exist) because finding correlations and patterns is extremely useful. Such thought processes have fueled man’s scientific progress, and help humans navigate the dangerous minefield of social interaction. It has its downsides though. People losing lots of money in gambling is obvious, but also things like finding pictures of Mary or Jesus in just about anything, or the existence of most every pseudoscience out there (numerology, cryptozoology, paranormal phenomena, etc.).
In my undergrad days, I was a political science major. Yes, I know, one of the very squishy sciences. (Basically, if you have to declare it a science, it probably isn’t.) I did a lot of research into heuristics and other mental shortcuts that people use, and I always thought it was interesting. Attaching meaning to random acts is apparently useful for humans. It helps them organize things in their mind, and a lot of people are more comfortable with the thought that there is some pattern in life than the proposition that everything really happens randomly. This sort of approach has surprisingly large effects in voting, polling, public trends, etc. I guess I like those topics because it’s interesting to see how people act, even though they don’t realize why they act that way.
I’m reminded of Humean skepticism, which had philosophers in a bind until Kant came along (whose ideas, in turn, created the state of civil war in philosophy that split analytic philosophy from its dissenters). In one perhaps overly simplified version my professor liked to use, “You have no reason to infer from the fact the last 100 people who walked in front of a bus were run over that the same will happen to you.” Hume’s actual argument behind this was a little more subtle and, if I remember correctly, depended upon an equivocation that Kant pointed out. As you say, though, and Hume himself admitted, as humans we find ourselves constantly doing well when we make these sorts of judgements that lie at the foundation of all inductive reasoning, even when they seem to contradict with the more solid ground of the realm of the deductive.
I haven’t studied much philosophy so I hadn’t known that the same concept had been debated in that field, but it doesn’t surprise me. There’s probably a lot that’s been said about it in philosophy of science, which I have a much easier time understanding than more mainstream philosophy.
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