= 27d567bc2d48d9f40e9ccc20ea370b15)
ciphergoth comments on [Paper] On the 'Simulation Argument' and Selective Scepticism - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (56)
(Updated)
I think your interpretation of "if I don't live in a simulation, then a fraction x of all humans lives in a simulation" as P(SIM or A) is wrong; it makes more sense to interpret it as P(A|¬SIM). This actually makes the proof simpler: for any A, B, we have that P(A) ≤ P(A|B)/P(B|A) by Bayes theorem, so if we accept that P(¬SIM|A) = (1-x), then we have P(¬SIM) ≤ (1-x)/P(A|¬SIM).
Huh?
The paper talks about P(SIM | ¬SIM → A), which is equal to P(SIM | SIM ∨ A) because ¬SIM → A is logically equivalent to SIM ∨ A. I wrote the P(SIM | ¬SIM → A) from the paper in words as P(I live in a simulation | if I don't live in a simulation, then a fraction x of all humans lives in a simulation) and stated explicitly that the if-then was a logical implication. I didn't talk about P(SIM or A) anywhere.
Mark Eichenlaub and Patrick LaVictoire point out on Facebook that if we let p=P(A|B) and q=P(B|A), there's a bound P(A) <= p/(p+q-pq), which is smaller than p/q.