Suppose I have an N-sided die, where N could be 10, 100, 1000, etc. I roll the die and get a 1. What is your probability distribution over N?
The solar system is pretty ordinary (not a high roll).
What if you wake up in a room with amensia to watch a video of yourself playing russian roulette with a gun (or perfectly random death machine) that has exactly a 1 in N chance of not killing you. You know only with certainty that you survived this random 1 in N process. What is your posterior probability distribution over N?
So N=10 is 100x more likely than N=1000, assuming a uniform prior on N.
Maybe this is just the argument for SIA vs SSA—but I never understood the complexity of that framing when I last skimmed it—this is just bayes theorem 101.
Solomonoff/Bayes tells us to always prefer the simplest model that explains our existence, and any history with a highly improbable chance of survival is penalized exactly in proportion to the improbability of survival. There is absolutely nothing wierd whatsover about ‘observational selection effects’. And bayes perfectly postdicts the confirmed Copernican mediocrity principle.
Suppose I have an N-sided die, where N could be 10, 100, 1000, etc. I roll the die and get a 1. What is your probability distribution over N?
The solar system is pretty ordinary (not a high roll).
What if you wake up in a room with amensia to watch a video of yourself playing russian roulette with a gun (or perfectly random death machine) that has exactly a 1 in N chance of not killing you. You know only with certainty that you survived this random 1 in N process. What is your posterior probability distribution over N?
Simple application of relative bayes:
p(N=1000|rand(N)=1)≈p(rand(N)=1|N=1000)p(N=1000)=(1/1000)p(N=1000)
p(N=10|rand(N)=1)≈p(rand(N)=1|N=10)p(N=10)=(1/10)p(N=10)
So N=10 is 100x more likely than N=1000, assuming a uniform prior on N.
Maybe this is just the argument for SIA vs SSA—but I never understood the complexity of that framing when I last skimmed it—this is just bayes theorem 101.
Solomonoff/Bayes tells us to always prefer the simplest model that explains our existence, and any history with a highly improbable chance of survival is penalized exactly in proportion to the improbability of survival. There is absolutely nothing wierd whatsover about ‘observational selection effects’. And bayes perfectly postdicts the confirmed Copernican mediocrity principle.