The self-sampling assumption (SSA), one of the two major schools of anthropic probability¹ (the other being the self-indication assumption (SIA)), states that:

SSA: All other things equal, an observer should reason as if they are randomly selected from the set of all actually existent observers (past, present and future) in their reference class.

For instance, if there is a coin flip that on heads will create one observer, while on tails they will create two, then we have two possible worlds, the first with one observer, the second with two. These worlds are equi-probable, hence the SSA probability of being the first (and only) observer in the heads world is 1/2, that of being the first observer in the tails world is 1/2 x 1/2 = 1/4, and the probability of being the second observer in the tails world is also 1/4.

This is why SSA gives an answer of 1/2 probability of heads in the Sleeping Beauty problem.

Notice that unlike SIA, SSA is dependent on the choice of reference class. If the agents in the above example were in the same reference class as a trillion other observers, then the probability of being in the heads world, upon the agent being told they are in the sleeping beauty problem, is ≈ 1/3, similar to SIA.

SSA implies the doomsday argument if the number of total observers in one's reference class is finite.

References

Nick Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy (New York: Routledge, 2002).↩