Anthropic Bias

Anthropic Bias: Observation Selection Effects in Science and Philosophy (2002) is a book by philosopher Nick Bostrom. It investigates how to reason when one suspects that evidence is biased by "observation selection effects"—when the evidence has been pre-filtered by the condition that some observer was appropriately positioned to "receive" it. This conundrum is sometimes called the "anthropic principle", "self-locating belief", or "indexical information".

The book first discusses the fine-tuned universe hypothesis and its possible explanations, notably considering the possibility of a multiverse. Bostrom argues against the self-indication assumption (SIA), a term he uses to characterize some existing views, and introduces the self-sampling assumption (SSA). He later refines SSA into the strong self-sampling assumption (SSSA), which uses observer-moments instead of observers to address certain paradoxes in anthropic reasoning.

Self-sampling assumption

The self-sampling assumption (SSA) states that:

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 and on tails will create two, then we have two possible worlds, one with one observer and one with two. These worlds are equally probable, so 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 × 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.