Want to model minds? Need to model stupidity

A recent post dealt with a puzzle involving perfect deductive intellects, beings who could, instantly, deduce every possible implication of their current state of knowledge. Obviously, it's not something that can be achieved with physical computers nor brains. Indeed, there's at least one whole art form concerning itself with the control of how people allocate their cognitive resources. So it's not too insightful to suggest that any model of a human mind -or any mind- needs to account for that mind's limitations.

The problem is not just one of limited resources. In particular, in some regards the human mind is patently weird, as a few other puzzles show.

I've mentioned the Monty Hall problem. Here it is, in a version best suited to the simple, yet counter-intuitive, solutions provided for it.

You are participating in a game show and are about to be shown three closed doors. You know that behind one of them there is a car, or some other prize you desire. Behind the other two doors, you know there are goats or some other joke, undesirable prizes. Alas, you don't know which door is which, but you know that, before the show started, someone made a random choice as to where to hide the car, and that all doors were an equally likely choice.

You will be asked to pick a door.

At that point, the game show host, who you know is aware of the prizes behind each door, will choose one of the other two doors and open it. You also know that the host will only choose a door with a goat. If there are two doors with a goat that he could choose, he chooses randomly among them.

Next, you'll be offered the chance to 'switch'- to change the door you picked from that which you first chose, to that which the host didn't open. Whatever door you select now, it will be opened and reveal the prize that you will take home.

Your knowledge of the game's rules, the behavior of the host and so on are accurate.

Now the question: is it better to switch, or not?

The game hasn't even started yet, and the question asks you whether you plan to switch after the host opens a door or not. 'Better' here means a choice that gives you a better chance of winning the desirable prize.

So what do you think is the answer? Ok, so what -did- you think was the right answer when you first heard of the problem?

Here's another somewhat similar problem.

Three cupboards have two drawers each, and in each drawer there is one coin, which may be gold or silver. You know that in one cupboard there are two gold coins, one in each drawer. In another, two silver, one in each cupboard. In the last, one drawer has a silver coin and the other a gold one.

You don't know which cupboard is which, nor do you know whether the top or bottom drawer has the golden coin in the 'mixed-coin' cupboard.

Someone else, who you trust to be truthful, opens a random drawer from a random cupboard (he doesn't tell you which drawer nor which cupboard) and says that the content of that drawer was a gold coin.

The question he asks then: what's the chance that, if I opened the other drawer from the same cupboard, I will reveal another gold coin?

Note, none of these are paradoxes of probability or anything. These are fairly easy, firmly decided problems. It's just that the answers aren't necessarily intuitive. It's very common in fact to get them wrong, and confidently argue for a wrong solution.

So it's become a bit of a meme that people are bad at judging probabilities. We tend to overestimate some odds, underplay others. We don't have an intuition of how likely it is that an unlikely event will happen if given enough opportunity. But the puzzles presented aren't even about that.

In fact, one need not go to probability for instances of the mind behaving oddly. Simple logic sometimes gets mangled:

You are shown three cards on a table: on one there's a '3', on one there's an '8', one is solid red, the last is solid blue. Which card or cards do you need to flip (and thus see the other side of) so that you can test the truth of 'if a card has an even number on one face, then it is blue on the other'?

Many/most people get this wrong. Funnily enough, if the problem had been worded as

The law is that someone is not allowed to drink an alcoholic beverage (of which beer is an example) until they are 18. You see four people, one is drinking beer, the second is drinking water (you can't tell the ages of these people just by looking at them), the third you know to be 45 but can't tell what he's drinking, the fourth you know to be 15 but can't tell what she's drinking. Which people do you need to check on (asking for ID/looking in their glass) to make sure the law is upheld?

most  people would get it right, and evolutionary psychology interprets this as an adaptation to living in groups resulting in skills that don't necessarily spread easily into more abstract uses.

So are these 'quirks' (stupidity is merely a provocative title, I apologize) bugs or features? Hypothetical intelligent machines may lack them, would those hypothetical machines lack something else because of this? My guess is no. It's possible to understand the solution to those probability puzzles and still remain a thinking human. I can even boast of performing the Wason selection task correctly regardless of whether it was abstract or not (though I must admit that the solution to Monty Hall initially boggled my mind; so logic yay, probability nay, I guess; counting my blessings).

Oh, incidentally, the answers to the various puzzles. Solutions left to the reader.

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++Monty Hall: always switch. Chances to win the prize are 2/3 in that case, as opposed to 1/3 if not switching.

++Three cupboards: 2/3 chance of the other drawer also containing a gold coin.
++Wason selection task, abstract: flip the '8' and the red card.
++Wason selection task, law enforcement: ask the first (the beer drinker) for ID and look into the glass of the 15-year old.