http://en.wikipedia.org/wiki/Self-Indication_Assumption says there are now two different versions of the SIA :-(
The definitions given on http://en.wikipedia.org/wiki/Self-Indication_Assumption and http://en.wikipedia.org/wiki/Self-Sampling_Assumption seem as though they refer to the same thing - under many "multiverse" cosmologies. IIRC, these two terms once referred to two different ideas.
In multiverses or many worlds, SSA and (new) SIA are the same thing.
SIA used to be: "universes with more observers are more likely". This has no intuitive reason to be true, and seems gratuitous. The new SIA is the old SIA plus SSA, which is "reason as if you were drawn at random from the space of all possible observers". This has a lot more intuitive appeal, and implies the old SIA.
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.