Here’s an even more unappealing implication of SIA+EDT.
Set-up:
There’s a lottery where you can pay $10 for a 1% probability of winning $100.
You have the ability to cheaply create up to 1000 copies of yourself in whatever epistemic state you want.
All you care about is the amount of $ donated to a particular charity.
I think the optimal thing for an SIA+EDT agent to do is to commit to the following policy. (Let’s call it “buy and copy”.)
“buy and copy” = “I will pay for a lottery ticket. If I lose, I won’t create any copies of myself. If I win, I will donate the money to charity and then create 1000 copies of myself in the epistemic that I’m in right now. (Of evaluating whether to commit to this policy.)”
Let’s compare the above to the (IMO correct) policy of “don’t buy”, where you immediately donate $10 to the charity without buying a lottery ticket.
Since $91 > $10, SIA+EDT thinks the “buy and copy” strategy is better than the “don’t buy” strategy.
IMO, this is a pretty decisive argument against these versions of SIA+EDT. (Though maybe they could be tweaked in some way to improve the situation.)
(Writing this out partly as a reference for my future self, since I find myself referring to this every now and then, and partly as a response to this post.)
Here’s an even more unappealing implication of SIA+EDT.
Set-up:
There’s a lottery where you can pay $10 for a 1% probability of winning $100.
You have the ability to cheaply create up to 1000 copies of yourself in whatever epistemic state you want.
All you care about is the amount of $ donated to a particular charity.
I think the optimal thing for an SIA+EDT agent to do is to commit to the following policy. (Let’s call it “buy and copy”.)
Let’s compare the above to the (IMO correct) policy of “don’t buy”, where you immediately donate $10 to the charity without buying a lottery ticket.
E(donated_dollars | “don’t buy”, observations) = $10
E(donated_dollars | “buy and copy”, observations =
= $100 * p_SIA(lottery_win | “buy and copy”, observations)
= $100 * E( #copies_with_my_observations | lottery_win, “buy and copy” ) * p(lottery_win | “buy and copy”) / E( #copies_with_my_observations | “buy and copy” )
Where: E( #copies_with_my_observations | “buy and copy” ) =
= E( #copies_with_my_observations | lottery_win, “buy and copy” ) * p(lottery_win | “buy and copy”)
+ E( #copies_with_my_observations | lottery_loss, “buy and copy” ) * p(lottery_loss | “buy and copy”)
Let’s plug in the numbers:
E( #copies_with_my_observations | lottery_win, “buy and copy” ) = 1001
E( #copies_with_my_observations | lottery_loss, “buy and copy” ) = 1
p(lottery_win | “buy and copy”) = 0.01
p(lottery_loss | “buy and copy”) = 0.99
So: E(donated_dollars | “buy and copy”, observations) = $100 * (1001 * 0.01 / [1001 * 0.01 + 1 * 0.99]) = $100 * (10.01 / 11) = $91.
Since $91 > $10, SIA+EDT thinks the “buy and copy” strategy is better than the “don’t buy” strategy.
IMO, this is a pretty decisive argument against these versions of SIA+EDT. (Though maybe they could be tweaked in some way to improve the situation.)
(Writing this out partly as a reference for my future self, since I find myself referring to this every now and then, and partly as a response to this post.)