Simplified Anthropic Doomsday

Stuart_Armstrong

Here is a simplified version of the Doomsday argument in Anthropic decision theory, to get easier intuitions.

Assume a single agent A exists, an average utilitarian, with utility linear in money. Their species survives with 50% probability; denote this event by S. If the species survives, there will be 100 people total; otherwise the average utilitarian is the only one of its kind. An independent coin lands heads with 50% probability; denote this event by H.

Agent A must price a coupon C_S that pays out €1 on S, and a coupon C_H that pays out €1 on H. The coupon C_S pays out only on S, thus the reward only exists in a world where there are a hundred people, thus if S happens, the coupon C_S is worth (€1)/100. Hence its expected worth is (€1)/200=(€2)/400.

But H is independent of S, so (H,S) and (H,¬S) both have probability 25%. In (H,S), there are a hundred people, so C_H is worth (€1)/100. In (H,¬S), there is one person, so C_H is worth (€1)/1=€1. Thus the expected value of C_H is (€1)/4+(€1)/400 = (€101)/400. This is more than 50 times the value of C_S.

Note that C_¬S, the coupon that pays out on doom, has an even higher expected value of (€1)/2=(€200)/400.

So, H and S have identical probability, but A assigns C_S and C_H different expected utilities, with a higher value to C_H, simply because S is correlated with survival and H is independent of it (and A assigns an ever higher value to C_¬S, which is anti-correlated with survival). This is a phrasing of the Doomsday Argument in ADT.

Here is a simplified version of the Doomsday argument in Anthropic decision theory, to get easier intuitions.

Note that C_¬S, the coupon that pays out on doom, has an even higher expected value of (€1)/2=(€200)/400.

in which I try to construct more clear example of ADT reasoning for a civilization which is at a risk of extinction, and which you said is, in fact, presumptious philosopher variant (I hope to create an example which is applicable to our world situation)

I do not think there is a sensible ADT DA that can be constructed for reasonable civilizations. In ADT, only weird utilities like average utilitarians have a DA.

SSA has a DA. ADT has a SSAish like agent, which is the average utilitarian. Therefore, ADT must have a DA. I constructed it. And it turns out the ADT DA via this has no real doom aspect to it; it has behaviour that looks like avoiding doom, but only for agents with strange preferences. ADT does not have a DA with teeth.