Apr 5, 2024
It’s every blogger’s curse to return to the same arguments again and again. Matt Yglesias has to keep writing “maybe we should do popular things instead of unpopular ones”, Freddie de Boer has to keep writing “the way culture depicts mental illness is bad”, and for whatever reason, I keep getting in fights about whether you can have probabilities for non-repeating, hard-to-model events. For example:
What is the probability that Joe Biden will win the 2024 election?
What is the probability that people will land on Mars before 2050?
What is the probability that AI will destroy humanity this century?
The argument against: usually we use probability to represent an outcome from some well-behaved distribution. For example, if there are 400 white balls and 600 black balls in an urn, the probability of pulling out a white ball is 40%. If you pulled out 100 balls, close to 40 of them would be white. You can literally pull out the balls and do the experiment.
In contrast, saying “there’s a 45% probability people will land on Mars before 2050” seems to come out of nowhere. How do you know? If you were to say “the probability humans will land on Mars is exactly 45.11782%”, you would sound like a loon. But how is saying that it’s 45% any better? With balls in an urn, the probability might very well be 45.11782%, and you can prove it. But with humanity landing on Mars, aren’t you just making this number up?
Since people on social media have been talking about this again, let’s go over it one more depressing, fruitless time.
https://www.astralcodexten.com/p/in-continued-defense-of-non-frequentist