The self-indication assumption (SIA)¹, a philosophical principle defined by Nick Bostrom², one of the two major schools of anthropic probability (the other being the self-sampling assumption (SSA)), states that:

SIA: All other things equal, an observer should reason as if they are randomly selected from the set of all possible observers.

Note that "randomly selected" is weighted by the probability of the observers existing: under SIA you are still unlikely to be an unlikely observer, unless there are a lot of them.

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 three possible observers (1st observer on heads, 1st on tails, 2nd on tails), each existing with probability 0.5, so SIA assigns 1/3 probability to each. Alternately, this could be interpreted as saying there are two possible observer (1st observer, 2nd observer on tails), the first existing with probability one and the second existing with probability 1/2, so SIA assigns 2/3 to being the first observer and 1/3 to being the second - which is the same as the first interpretation.

This is why SIA gives an answer of 1/3 probability of heads in the Sleeping Beauty problem.

Notice that unlike SSA, SIA is not dependent on the choice of reference class, as long as the reference class is large enough to contain all subjectively indistinguishable observers. If the reference class is large, SIA will make it more likely, but this is compensated by the much reduced probability that the agent will be that particular agent in the larger reference class.

Although this anthropic principle was originally designed as a rebuttal to the Doomsday argument (by Dennis Dieks in 1992) it has general applications in the philosophy of anthropic reasoning, and Ken Olum has suggested it is important to the analysis of quantum cosmology.

Ken Olum has written in defense of the SIA³. Nick Bostrom and Milan Cirkovic have critiqued this defense.⁴

Nick Bostrom originally used the term SIA in a slightly different way. What is here referred to as SIA, he referred to as the combined SSA+SIA↩
Nick Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy (New York: Routledge, 2002).↩
Ken Olum, The Doomsday Argument and the Number of Possible Observers, Philosophical Quarterly (2002), Vol. 52, No. 207, pp. 164-184↩
Nick Bostrom and Milan Cirkovic, The doomsday argument and the self-indication assumption: reply to Olum, Philosophical Quarterly, (2003), Vol. 53, No. 210, pp. 83-91↩