Y’see, this sort of thing is why I distrust the betting model for extreme probabilities like this.
I mean, I would take that bet as well, but I’m pretty sure that my estimate under normal circumstances is closer to jimrandomh’s… it’s just that the offer itself is so outrageous that the circumstances stop being normal. I think my reasoning would be more along the lines of “what the hell, I’m willing to throw away ten cents just to get to tell this story,” or possibly even “I no longer have any idea what’s going on, but losing ten cents is no big deal and I’m curious to see what happens next.”
Put another way: I very much doubt that my willingness to take that bet is the result of an EV calculation using my real prior probability of a randomly selected pen falling to the ground; therefore, I am disinclined to treat that willingness as significant evidence of that prior.
Would you take the offer if it was only $10? I wouldn’t (I get to tell the story either way), which suggests my decision really does depend upon my prior.
Another interefering factor is the fact that my utility function is nowhere near monotonic in dollars, especially for large amount. I’d take a certainty of $1 million over a 5% chance of $1 billion, which suggests that $50 billion is worth a lot less than a trillion times as much as 5 cents to me, so my prior must be some way below 99.9999999999%
Bear in mind overconfidence bias, its very easy to get trigger happy with 9s, and forget that even 99.9% is very impressive in a world with as many unknowns and interfering factors as ours.
If it were Warren Buffet? Probably. “Warren Buffet offered me $50 billion if my pen falls to the ceiling” is a much cooler story than “Warren Buffet offered me $10 if my pen falls to the ceiling,” but the latter is still easily worth ten cents.
OTOH, “Some guy on the Internet offered me $10 if my pen falls to the ceiling” is not so cool a story. I probably would turn that down.
Agreed that utility is radically nonmonotonic in dollars.
Agreed that it’s easy to get overconfident with 9s. It’s also easy to anchor on the integers.
All that said: roughly how many objects have you seen or otherwise had compelling experience of having been dropped in your lifetime, would you estimate? How many of those have fallen to the ground, and how many have floated to the ceiling? What happens to those numbers if we eliminating ones more theoretically likely to float than pens (e.g., helium balloons)?
At a guess, I’d say I’ve personally seen on the order of five thousand non-helium-balloon-like objects dropped in my life, and they’ve all fallen down. So just starting from there, I’d estimate a > 99.9998 chance that the next one will, too.
If I start additionally factoring in the additional evidentiary value of theoretical considerations, and the absence of other people’s reports of such objects floating, and of stories people tell involving objects falling to the ground… man, the evidence starts to add up.
(We’ve established what I am, now we’re haggling over the price...)
All that said: roughly how many objects have you seen or otherwise had compelling experience of having been dropped in your lifetime, would you estimate? How many of those have fallen to the ground, and how many have floated to the ceiling? What happens to those numbers if we eliminating ones more theoretically likely to float than pens (e.g., helium balloons)?
At a guess, I’d say I’ve personally seen on the order of five thousand non-helium-balloon-like objects dropped in my life, and they’ve all fallen down. So just starting from there, I’d estimate a > 99.9998 chance that the next one will, too.
This a good point, 99.9% probably is too low, although I’d be a little worried to go as high as 99.9998%. I’m not sure how you got that figure anyway, if you’ve seen five-thousand that means Laplace’s law suggests about 99.98% doesn’t it? I’ve probably seen a similar number (maybe a bit less), and I can remember one that failed to fall downward (although it was in very high winds so perhaps I should have been able to predict it).
The other evidence probably doesn’t count for a Bayes factor of as much as 100:1, since by that point a good part of the remaining probability mass is concentrated in hypotheses like “pens always fall downwards except under this one specific rare circumstance” and “I am completely insane”.
I distrust the betting model for extreme probabilities like this.
Can any of us really comprehend that much money? Frankly, I bet even Warren Buffet would have trouble; he has said after he gives away 99% of his wealth, he and his family will have all the money they will ever need. Does 100 times as much money as you’ll ever need really feel different from 10x or 1000x?
The betting heuristic is useful because our intuitive sense for money has a much larger dynamic range than our intuitive sense of probability—it’s easier to conceptualize “a subway ticket against a nice house” than “million to one odds”, but “0.05 subway tickets against 25000 nice houses” doesn’t really fit the way we think.
Y’see, this sort of thing is why I distrust the betting model for extreme probabilities like this.
I mean, I would take that bet as well, but I’m pretty sure that my estimate under normal circumstances is closer to jimrandomh’s… it’s just that the offer itself is so outrageous that the circumstances stop being normal. I think my reasoning would be more along the lines of “what the hell, I’m willing to throw away ten cents just to get to tell this story,” or possibly even “I no longer have any idea what’s going on, but losing ten cents is no big deal and I’m curious to see what happens next.”
Put another way: I very much doubt that my willingness to take that bet is the result of an EV calculation using my real prior probability of a randomly selected pen falling to the ground; therefore, I am disinclined to treat that willingness as significant evidence of that prior.
Would you take the offer if it was only $10? I wouldn’t (I get to tell the story either way), which suggests my decision really does depend upon my prior.
Another interefering factor is the fact that my utility function is nowhere near monotonic in dollars, especially for large amount. I’d take a certainty of $1 million over a 5% chance of $1 billion, which suggests that $50 billion is worth a lot less than a trillion times as much as 5 cents to me, so my prior must be some way below 99.9999999999%
Bear in mind overconfidence bias, its very easy to get trigger happy with 9s, and forget that even 99.9% is very impressive in a world with as many unknowns and interfering factors as ours.
If it were Warren Buffet? Probably. “Warren Buffet offered me $50 billion if my pen falls to the ceiling” is a much cooler story than “Warren Buffet offered me $10 if my pen falls to the ceiling,” but the latter is still easily worth ten cents.
OTOH, “Some guy on the Internet offered me $10 if my pen falls to the ceiling” is not so cool a story. I probably would turn that down.
Agreed that utility is radically nonmonotonic in dollars.
Agreed that it’s easy to get overconfident with 9s. It’s also easy to anchor on the integers.
All that said: roughly how many objects have you seen or otherwise had compelling experience of having been dropped in your lifetime, would you estimate? How many of those have fallen to the ground, and how many have floated to the ceiling? What happens to those numbers if we eliminating ones more theoretically likely to float than pens (e.g., helium balloons)?
At a guess, I’d say I’ve personally seen on the order of five thousand non-helium-balloon-like objects dropped in my life, and they’ve all fallen down. So just starting from there, I’d estimate a > 99.9998 chance that the next one will, too.
If I start additionally factoring in the additional evidentiary value of theoretical considerations, and the absence of other people’s reports of such objects floating, and of stories people tell involving objects falling to the ground… man, the evidence starts to add up.
(We’ve established what I am, now we’re haggling over the price...)
This a good point, 99.9% probably is too low, although I’d be a little worried to go as high as 99.9998%. I’m not sure how you got that figure anyway, if you’ve seen five-thousand that means Laplace’s law suggests about 99.98% doesn’t it? I’ve probably seen a similar number (maybe a bit less), and I can remember one that failed to fall downward (although it was in very high winds so perhaps I should have been able to predict it).
The other evidence probably doesn’t count for a Bayes factor of as much as 100:1, since by that point a good part of the remaining probability mass is concentrated in hypotheses like “pens always fall downwards except under this one specific rare circumstance” and “I am completely insane”.
I got that figure stupidly (1-1/5000), and I am chagrined. hides under desk
Ah, the old decimal turns into a percentage error. You reduce all of us to gibbering heaps.
Can any of us really comprehend that much money? Frankly, I bet even Warren Buffet would have trouble; he has said after he gives away 99% of his wealth, he and his family will have all the money they will ever need. Does 100 times as much money as you’ll ever need really feel different from 10x or 1000x?
The betting heuristic is useful because our intuitive sense for money has a much larger dynamic range than our intuitive sense of probability—it’s easier to conceptualize “a subway ticket against a nice house” than “million to one odds”, but “0.05 subway tickets against 25000 nice houses” doesn’t really fit the way we think.