49% of people are iidiots
Conversation
It would be interesting to run this poll in different languages 🤔
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Interesting that many treat it as a standardized “logic puzzle” — as a logic puzzle it is ill-posed since no distribution is implied unlike with coin, dice, or cards. But iid as an explicit modeling assumption is not usually taught in basic stats afaik… usually advanced material
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This is a fermi estimation type problem. You have to make assumptions about seasons, streaks, sizes of pressure systems, set of places that average 122 days etc. I’d say >1/3 has best abductive reasoning, but that’s aesthetic judgment. You’d have to look at the data harder.
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There is no definitive right answer here. But interestingly there is an almost certainly wrong answer: the one a bad textbook or teacher would suggest. It would be a shocking coincidence if the answer from careful modeling and empirical data were actually close to 1/3.
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Interestingly the ~1 answer is not easy to dismiss as obviously wrong despite seeming outlierish. 122 days of rain is a lot. Suggests monsoon type pattern where it rains daily for months. I wouldn’t be surprised if the answer were >0.9 if restricted to South Asia for eg.
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Oh for those unfamiliar with the acronym, iid = independent and identically distributed. Like a sequence of fair coin tosses or dice rolls. In modeling natural phenomena, unlike games, you normally specify and defend iid assumptions explicitly because it’s not default reasonable
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tldr: you live in a world you know a lot about. Refusing to make reasonable assumptions to turn an underdetermined question into a somewhat one guessable with some confidence is… unreasonable.
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This isn’t even about Bayesian vs Fisherian religious wars or “rationality.”
It’s just about giving yourself permission to model things using what you know.
Weird that schooling kinda beats folk modeling out of you and ingrains a What Would Test Setter Expect attitude instead
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Interestingly if you think of overnight rain, streaks of 2 days become extremely likely. A better version of this question would account for that (“it just stopped raining, what are the chances next 24h are dry?”)
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There might even be a length-of-Norway-coast type situation here where the stats depend on the temporal resolution 🤔
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In school “insufficient data” is a clever answer. In everyday life it’s learned helplessness. Most questions require you to make enough assumptions to get somewhere. There are no points for staying stuck. There’s not always a right answer but there’s almost always a good guess.
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If this approach bothers you, try snow rather than rain. Snow is more obviously and strongly seasonal.
Even more obvious: You’re at an indeterminate location where Christmas music plays in public X days a year. You heard Christmas music today, will you hear it tomorrow?
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Another example. You’re in a random city on earth where there’s traffic delays ~4 of 24 hours. There are reports of traffic delay right now. What are the chances there will still be traffic delays in 20 minutes?
Think rush hours, streets being empty at night…
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Unknown information is rarely fully unknown. True zero-mean white noise is rare. Directional tendencies can be reasonably/justifiably guessed from anecdotal/qualitative information. We do such guessing all the time except when “test taking” reflexes are triggered, and it works.
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Oh yeah… there’s a school of “worse than test taker” reasoning that would argue the answer is 50-50 “because it either rains or it does not”
I don’t think this is stupidity. It’s a sort of semantic confusion where probability = number of distinguishable outcomes/states.
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We seem to exist in a culture where questions with even slightly formal contours are so strongly associated with bureaucrat test setters, we think they’re only meaningful if they’re 100% completely specified with a correct answer known to asker, otherwise the question is “wrong”
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To be fair, the multiple choice poll is an extremely strong cue. We are primed to that being either a pure opinion poll or a “fully determined right answer” situation. We rarely encounter the most common kind of question — reasoned guesswork — in poll form.
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Btw “indeterminate location where it rains ~122 days in a year” is strong scoping. Deserts are out, as are places like equatorial rainforests where it rains almost every day (so >300). Whether you’re count snow as rain is interpretation. I didn’t intend that but it’s justifiable
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I’d word the poll in a less trolly way if I were actually looking for the wisdom of crowds estimate. I’d ask people explicitly to make seasonality etc assumptions and use less loaded options. I think polls work great for that. A lot of my polls are sincere WoC polls.
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Replying to @vgr
And do u think such polls are likely the most useful in terms of generating wisdom from crowds? "This is an ambiguous question, but give it your best shot" type of wisdom helps us the most in decision making?
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More footnoting… “iidiot” (2 i’s) was a stats joke, not a serious dis. As in people assuming iid. I don’t think people who answered 1/3 are dumb. They’ve just gotten too good at test taking.
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This is reasonable approach. I do believe if you averaged over all locations that have say 110-130 days of rain, you’d get further away north of the iid expectation. But hey if anyone runs the full global analysis and shows it’s nearly iid, I’ll be surprised and contrite 😆
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Replying to @vgr
You're being too harsh. I ran some analysis, in many places chance of rain tomorrow is only slightly higher than average given it rained today (in many its lower!), the effect is strongest in dry places (much less than 122 days of rain). So "a bit more than 1/3" is a good answer.
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Interestingly, Taleb, who did a lot to deprogram test-taker mindset, used a contrived “coin that comes up heads 10 times in a row” in a Fat-Tony context to argue you should expect a rigged coin. It’s really hard to shift anchors away from coins/dice/cards to natural phenomena
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We experience weather patterns every day both locally and from news/friends/travel in other places. But I’ve never actually tossed a coin 10 times in a row, and I’ve never seen a trick 2-headed coin. I just know they exist and conmen/creative teachers/magicians might have them.
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Overall point I’m making is even when there is no obvious or easily discoverable right answer there is a right *approach* — throw in what you can readily assume or find out with a minute of googling/reflection. You don’t need to do a nuanced phd to beat “test prep” thinking
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Test-prep thinking I suspect is rarely right in the real world in a stronger way than a stopped clock is right twice a day.
There are exceptions. Textbook linear programming is the right approach unreasonably often even in the real world for eg.
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This is yet another rantvertisement 🤣
In the Discord we run a weekly "fermi gym" to practice assumptions+estimation skills. Last week's problem was "estimate number of stars in galaxy." This week's is "estimate length of DNA in a cell"
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