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I have never understood this type of argument. Even in my regular life, I am atypical in more than one one-in-a-million way. I was born in a tiny city, populat
by 317070 4y ago
I have never understood this type of argument. Even in my regular life, I am atypical in more than one one-in-a-million way.
I was born in a tiny city, population less than 1000. But following your line of reasoning, that is sufficient argument that the population of the world is less than 1 billion.
It is fine to say "we don't know". Events in which you are in a one-in-a-million situation will be rare, but unless you know the number of events in consideration, there are few conclusions you can draw. There are way more than a million events, even in trivial probability spaces. This style of trickery with probabilities irks me as a statistician.
- wcoenen 4y agoImagine you are kidnapped and knocked unconscious. Then you wake up in a prison cell by yourself. You are now wearing a prison uniform with a label that says "prisoner N", where N is some number. Would it really be "trickery with probabilities" to say that there is only a one-in-thousand chance that the total number of prisoners is more than 1000*N? And that the real number of total prisoners is probably much closer to N?
- 317070 4y agoYes to the first question! The distribution representing my beliefs in such a scenario would not have a finite variance. Given the question, are you aware of the Pareto distribution? Nassim Taleb has great work explaining fat-tail distributions. (I do have strong priors on various things, such as the size of the human population and the sizes of large prisons, which I ignore here as they break the metaphore)