But at what difficulty does it become rational to approximate, or do a meta-analysis?
It depends on how much resources you choose to, or can afford to, devote to the question.
Say I have only a few seconds to ponder the product 538 time 347, and give a probability assignment for its being larger than 150,000; for its being larger than 190,000; and for its being larger than 240,000.
My abilities are such that in a limited time, I can reach definite conclusions about the two extreme values but not about the third; I’d have to be content with “ooh, about fifty-fifty”. Given more time (or a calculator!) I can reach certainty.
If we’re talking about bounded rationality rather than pure reason, the definition “identical states of knowledge” needs to be extended to “identical states of knowledge and comparable expenditure of resources”.
Alternatively you need to revise your definition of “irrational” to admit degrees. Someone who can compute the exact number faster than I can is perhaps more rational than I am, but my 1:1 probability for the middle number does not make me “irrational” in an absolute sense, compared to someone with a calculator.
I wouldn’t call our friend “irrational”, though it may be appropriate to call them lazy.
In fact, the discomfort some people feel at hearing the words “irrational” or “rational” bandied about can perhaps be linked to the failure of some rationalists to attend to the distinction between bounded rationality and pure reason...
ETA:
the more stupid the person, the more difficult it would be to claim that they were, in fact, irrational.
So ? You already have a label “stupid” which is descriptive of an upper bound on the resources applied by the agent in question to the investigation at hand. What additional purpose would the label “irrational” serve ?
It depends on how much resources you choose to, or can afford to, devote to the question.
Say I have only a few seconds to ponder the product 538 time 347, and give a probability assignment for its being larger than 150,000; for its being larger than 190,000; and for its being larger than 240,000.
My abilities are such that in a limited time, I can reach definite conclusions about the two extreme values but not about the third; I’d have to be content with “ooh, about fifty-fifty”. Given more time (or a calculator!) I can reach certainty.
If we’re talking about bounded rationality rather than pure reason, the definition “identical states of knowledge” needs to be extended to “identical states of knowledge and comparable expenditure of resources”.
Alternatively you need to revise your definition of “irrational” to admit degrees. Someone who can compute the exact number faster than I can is perhaps more rational than I am, but my 1:1 probability for the middle number does not make me “irrational” in an absolute sense, compared to someone with a calculator.
I wouldn’t call our friend “irrational”, though it may be appropriate to call them lazy.
In fact, the discomfort some people feel at hearing the words “irrational” or “rational” bandied about can perhaps be linked to the failure of some rationalists to attend to the distinction between bounded rationality and pure reason...
ETA:
So ? You already have a label “stupid” which is descriptive of an upper bound on the resources applied by the agent in question to the investigation at hand. What additional purpose would the label “irrational” serve ?