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No, it's not incorrect. You are giving one example when that would be incorrect. To prove this is incorrect, you would need to offer a large number of examples
by brabel 5y ago
No, it's not incorrect. You are giving one example when that would be incorrect. To prove this is incorrect, you would need to offer a large number of examples similar to what you did, but with a uniform distribution of population distributions (because we're claiming complete ignorance on how populations should be distributed - so each scenario is as likely). Once you do that, do you still believe the statement to be incorrect?
Hint: write code that tries all distributions wihin a certain range, then check the probabilities of a person within any of those scenarios being correct.
- user-the-name 5y agoNo, I would not. We have zero knowledge of the distributions involved, and we can not get that information, so we are not allowed to make any assumption about it. However, this statement does make a huge assumption about it, and thus, it is invalid.
- brabel 5y agoWhat huge assumption? That we know nothing of the distribution, hence we must assume each distribution is as likely? You seem to fail to grasp what it means to not make assumptions.
- user-the-name 5y agoIt makes the huge assumption that these things follow a distribution where their claims are true. As we do not know the distribution, you can not make that assumption.
- fergussimpson 5y agoNot so - the result holds for all feasible distributions.
- user-the-name 5y agoI just gave one where it doesn't hold.
- fergussimpson 5y agoAh I see, apologies, I understand your concern. If we define 'big' and 'small' as being above or below the average (mean) value, then you're quite right that it breaks down for many cases, like the one you gave. But if we define 'big' and 'small' relative to the middle (median) value of the distribution, then it becomes a robust result. Hope that helps!
- user-the-name 5y agoBut if you do that, it becomes a truism, and I do not think it actually gives you any useful information any longer.
- fergussimpson 5y agoJust so we're clear, you no longer consider this to be a fallacy if by 'high' we use the median as a reference point? "I am more likely to have been born in a high population country than a low population country" And you don't think that's useful?