Right. The idea is: “What are the odds that China invading Taiwan derails chip production conditional on a world where we were otherwise going to successfully scale chip production.”
I would not have guessed that! So in slightly more formal terms:
CHIPS = There are enough chips for TAGI by 2043
WAR = There is a war that catastrophically derails chip production by 2043
P(x) = subjective probability of x
ObjP(x) = objective probability of x
P(CHIPS and WAR) = 0% (by definition)
Then as I understand your method, it goes something like:
Estimate P(CHIPS given not WAR) = 46%
This means that in 46% of worlds, ObjP(CHIPS given not WAR) = 100%. Call these worlds CHIPPY worlds. In all other worlds ObjP(CHIPS given not WAR) = 0%.
Estimate P(not WAR given CHIPPY) = 70%.
The only option for CHIPS is “not WAR and CHIPPY”.
Calculate P(not WAR and CHIPPY) = 70% x 46% = 32.2%.
Therefore P(CHIPS) = 32.2%.
(probabilities may differ, this is just illustrative)
However, I don’t think the world is deterministic enough for step 2 to work—the objective probability could be 50% or some other value.
Right. The idea is: “What are the odds that China invading Taiwan derails chip production conditional on a world where we were otherwise going to successfully scale chip production.”
I would not have guessed that! So in slightly more formal terms:
CHIPS = There are enough chips for TAGI by 2043
WAR = There is a war that catastrophically derails chip production by 2043
P(x) = subjective probability of x
ObjP(x) = objective probability of x
P(CHIPS and WAR) = 0% (by definition)
Then as I understand your method, it goes something like:
Estimate P(CHIPS given not WAR) = 46%
This means that in 46% of worlds, ObjP(CHIPS given not WAR) = 100%. Call these worlds CHIPPY worlds. In all other worlds ObjP(CHIPS given not WAR) = 0%.
Estimate P(not WAR given CHIPPY) = 70%.
The only option for CHIPS is “not WAR and CHIPPY”.
Calculate P(not WAR and CHIPPY) = 70% x 46% = 32.2%.
Therefore P(CHIPS) = 32.2%.
(probabilities may differ, this is just illustrative)
However, I don’t think the world is deterministic enough for step 2 to work—the objective probability could be 50% or some other value.
Bingo