Consider a scenario in which there are three rooms. In each room there is an independent 1/1000 chance of an agent being created. There is thus a 1/109 probability of there being an agent in every room, a (3*999)/109 probability of there being two agents, and a (3*9992)/109 probability of there being one.
Given that you are one of these agents, the SIA and SSA probabilities of there being n agents are:
Number of agents
SIA
SSA
0
0
0
1
(1*3*9992)/(3*1+2*3*999+1*3*9992)
(3*9992)/(1+3*999+3*9992)
2
(2*3*999)/(3*1+2*3*999+1*3*9992)
(3*999)/(1+3*999+3*9992)
3
(3*1)/(3*1+2*3*999+1*3*9992)
(1)/(1+3*999+3*9992)
The expected numbers of agents is (1(3*9992) + 2(2*3*999) + 3(3*1))/(3*1+2*3*999+1*3*9992) = 1.002 for SIA, and (1(3*9992) + 2(3*999) + 3(1))/(1+3*999+3*9992) ≈ 1.001 for SSA. The high unlikelihood of life means that, given that we are alive, both SIA and SSA probabilities get dominated by worlds with very few agents.
This of course only applies to agents who existence is independent (for instance, separate galactic civilizations). If you're alive, chance are that your parents were also alive at some point too.
Basically SIA and SSA are seen as very different. But some problems that we would feel instinctively should illustrate their differences - situations with varying numbers of agents like above - do not.
One obvious point is that if this is correct then in our universe one can probably safely reason with SIA and SSA and get similar results. This means that if there's something that goes wrong with applying anthropic reasoning in some contexts it probably isn't lack of precision in the anthropic principles being applied.
Consider a scenario in which there are three rooms. In each room there is an independent 1/1000 chance of an agent being created. There is thus a 1/109 probability of there being an agent in every room, a (3*999)/109 probability of there being two agents, and a (3*9992)/109 probability of there being one.
Given that you are one of these agents, the SIA and SSA probabilities of there being n agents are:
The expected numbers of agents is (1(3*9992) + 2(2*3*999) + 3(3*1))/(3*1+2*3*999+1*3*9992) = 1.002 for SIA, and (1(3*9992) + 2(3*999) + 3(1))/(1+3*999+3*9992) ≈ 1.001 for SSA. The high unlikelihood of life means that, given that we are alive, both SIA and SSA probabilities get dominated by worlds with very few agents.
This of course only applies to agents who existence is independent (for instance, separate galactic civilizations). If you're alive, chance are that your parents were also alive at some point too.