Forgive me if I’m misunderstanding, but doesn’t the fallacy you bring up apply specifically to continuous functions only? For step-wise functions, a significantly small change in input will not correspond to a significantly small change in output.
Assuming the unit is a 100 burger box (100BB), then my purchase of a burger only affects their ordering choices if I bring the total burger sales over some threshold. I’m guesstimating, but I’d guess it’s around 1⁄3 of a box, or 33 burgers in a 100BB. So if I’m the 33rd additional customer, it might affect their decision to buy an extra box; but if I’m one of the first 32, it probably won’t. This puts a very large probability on the fact that my action will not have an effect.
Is my reasoning here flawed? I’ve gone over it again in my head as I wrote this comment, and it still seems to apply to me, even after reading your above comment. But perhaps I’m missing something?
This puts a very large probability on the fact that my action will not have an effect.
However, the complementary probability is the probability of a correspondingly large effect. The smallness of the probability and the largeness of the effect exactly cancel, giving an expected effect of 1 burger bought from the distributor for every burger bought by you.
The fact that the effect is nigh invisible due to the high level of stochastic noise does not mean it is not there.
To eat meat without it having been killed for your benefit, you should raid supermarket waste bins for the time-expired stuff they throw out.
When I first thought about this, I was fairly confident of my belief; after reading your first comment, I rethought my position but still felt reasonably confident; yet after reading this comment, you’ve completely changed my position on the issue. I had completely neglected to take into account the largeness of the effect.
You’re absolutely correct, and I retract my previous statements to the contrary. Thank you for pointing out my error. (c:
Forgive me if I’m misunderstanding, but doesn’t the fallacy you bring up apply specifically to continuous functions only? For step-wise functions, a significantly small change in input will not correspond to a significantly small change in output.
Assuming the unit is a 100 burger box (100BB), then my purchase of a burger only affects their ordering choices if I bring the total burger sales over some threshold. I’m guesstimating, but I’d guess it’s around 1⁄3 of a box, or 33 burgers in a 100BB. So if I’m the 33rd additional customer, it might affect their decision to buy an extra box; but if I’m one of the first 32, it probably won’t. This puts a very large probability on the fact that my action will not have an effect.
Is my reasoning here flawed? I’ve gone over it again in my head as I wrote this comment, and it still seems to apply to me, even after reading your above comment. But perhaps I’m missing something?
However, the complementary probability is the probability of a correspondingly large effect. The smallness of the probability and the largeness of the effect exactly cancel, giving an expected effect of 1 burger bought from the distributor for every burger bought by you.
The fact that the effect is nigh invisible due to the high level of stochastic noise does not mean it is not there.
To eat meat without it having been killed for your benefit, you should raid supermarket waste bins for the time-expired stuff they throw out.
When I first thought about this, I was fairly confident of my belief; after reading your first comment, I rethought my position but still felt reasonably confident; yet after reading this comment, you’ve completely changed my position on the issue. I had completely neglected to take into account the largeness of the effect.
You’re absolutely correct, and I retract my previous statements to the contrary. Thank you for pointing out my error. (c: