That is a good link, Ambitwistor. The last paragraph refers to an interesting psychological hypothesis, which I'd like to expand on in an example related to the "Look Into the Dark" post. Let's rephrase EY's proposition to give it more of a social "plot".
"You're a smuggler in a strange foreign land, where they only allow exports of goods in certain combinations of quantities, so as to keep their domestic lobby groups happy. [Yes, it's a convulated example, but governments can be convoluted.] Trouble is, everyone knows the rule except you and your gang of smugglers, and if you ask, you become a suspect. Furthermore, you don't actually know what you're smuggling, since your fence always seals them in the standard export containers, which are numbered ordinally "First", "Second", and "Third".
Since you're an amoral smuggler boss, in charge of a lot of obedient "mule" underlings, you can send as many people through customs as you want and no matter how many get arrested, you won't be a suspect. Also, you have an infinite number of empty export containers with the usual "First", "Second" or "Third" labels. If your mule gets arrested with an empty container, he'll be released immediately. So basically, you can test the rule all you want, since you'll witness any arrest that happens.
Just as you and your team of criminals arrives at the customs checkpoint, a man goes into customs with 2 "First" boxes, 4 "Second" boxes, and 6 "Third" boxes. You can start making a tidy profit as soon you determine what the rule is. What is your next move?"
Granted, it is a convoluted example and I'm worried that in its current form it would just confuse too many test subjects. Perhaps someone would think of a more straightforward equivalent. The point, though, is to make the test sound less like the sort of rule we are familiar with from math class. As several posters have alluded, usually a rule in math class is much stricter and requires some arithmetic. A bureaucratic rule, convoluted though it may be, will often be mathematically simpler. E.g., "The extremely powerful pineapple lobby has pushed through a law requiring that no other fruit (papaya or mango) be exported in greater numbers than pineapples. Exports from the politically weak mango industry must not exceed papaya exports. Pineapples are labelled Third; papayas labelled Second; mangos labelled First."
My hypothesis is that people will come up with this rule faster than they would when faced with the phrasing from the original post. (Of course, the "domestic lobby groups happy" phrasing is sort of a giveaway ... maybe it should be replaced with a more neutral explanation, or none at all.)
That is a good link, Ambitwistor. The last paragraph refers to an interesting psychological hypothesis, which I'd like to expand on in an example related to the "Look Into the Dark" post. Let's rephrase EY's proposition to give it more of a social "plot".
"You're a smuggler in a strange foreign land, where they only allow exports of goods in certain combinations of quantities, so as to keep their domestic lobby groups happy. [Yes, it's a convulated example, but governments can be convoluted.] Trouble is, everyone knows the rule except you and your gang of smugglers, and if you ask, you become a suspect. Furthermore, you don't actually know what you're smuggling, since your fence always seals them in the standard export containers, which are numbered ordinally "First", "Second", and "Third".
Since you're an amoral smuggler boss, in charge of a lot of obedient "mule" underlings, you can send as many people through customs as you want and no matter how many get arrested, you won't be a suspect. Also, you have an infinite number of empty export containers with the usual "First", "Second" or "Third" labels. If your mule gets arrested with an empty container, he'll be released immediately. So basically, you can test the rule all you want, since you'll witness any arrest that happens.
Just as you and your team of criminals arrives at the customs checkpoint, a man goes into customs with 2 "First" boxes, 4 "Second" boxes, and 6 "Third" boxes. You can start making a tidy profit as soon you determine what the rule is. What is your next move?"
Granted, it is a convoluted example and I'm worried that in its current form it would just confuse too many test subjects. Perhaps someone would think of a more straightforward equivalent. The point, though, is to make the test sound less like the sort of rule we are familiar with from math class. As several posters have alluded, usually a rule in math class is much stricter and requires some arithmetic. A bureaucratic rule, convoluted though it may be, will often be mathematically simpler. E.g., "The extremely powerful pineapple lobby has pushed through a law requiring that no other fruit (papaya or mango) be exported in greater numbers than pineapples. Exports from the politically weak mango industry must not exceed papaya exports. Pineapples are labelled Third; papayas labelled Second; mangos labelled First."
My hypothesis is that people will come up with this rule faster than they would when faced with the phrasing from the original post. (Of course, the "domestic lobby groups happy" phrasing is sort of a giveaway ... maybe it should be replaced with a more neutral explanation, or none at all.)