When using SSA (which I think the authors do implicitly), you can exclude worlds which contain no observer "like you", but there's no anthropic update to the relative probabilities of the worlds that contain at least one observer "like you". When using SIA, the probability of each worlds gets updates in proportion to the number of observers.
Consider a variant of "god's coin toss". God has a device that outputs A, B, or C with equal probability. When seeing A, god creates 0 humans, when seeing B god creates 1 human, and when seeing C god creates 2 humans. You're one of the humans created this way and don't know how many other humans have been created. What should be your probability distribution over {A, B, C}? According to SSA, B and C should have probability 1/2 each, while according to SIA, B has probability 1/3 and C has probability 2/3.
The fact that SSA has a discontinuity between zero and any positive number of observers is one of the standard arguments against SSA, see e.g. argument 4 against SSA here:
When using SSA (which I think the authors do implicitly), you can exclude worlds which contain no observer "like you", but there's no anthropic update to the relative probabilities of the worlds that contain at least one observer "like you". When using SIA, the probability of each worlds gets updates in proportion to the number of observers.
Consider a variant of "god's coin toss". God has a device that outputs A, B, or C with equal probability. When seeing A, god creates 0 humans, when seeing B god creates 1 human, and when seeing C god creates 2 humans. You're one of the humans created this way and don't know how many other humans have been created. What should be your probability distribution over {A, B, C}? According to SSA, B and C should have probability 1/2 each, while according to SIA, B has probability 1/3 and C has probability 2/3.
The fact that SSA has a discontinuity between zero and any positive number of observers is one of the standard arguments against SSA, see e.g. argument 4 against SSA here:
https://meteuphoric.com/anthropic-principles/