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Anthropic Bias
Anthropic Bias: Observation Selection Effects in Science and Philosophy (2002) is a book by philosopher Nick Bostrom. Bostrom investigates how to reason when one suspects that evidence is biased by "observation selection effects", in other words, when the evidence presented has been pre-filtered by the condition that there was some appropriately positioned observer to "receive" the evidence. 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.
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, while on tails it will create two, then we have two possible worlds, the first with one observer, the second with two. These worlds are equally 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 × 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.
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 may imply the doomsday argument depending on the choice of reference class.
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Anthropic Bias
Anthropic Bias: Observation Selection Effects in Science and Philosophy (2002) is a book by philosopher Nick Bostrom. Bostrom investigates how to reason when one suspects that evidence is biased by "observation selection effects", in other words, when the evidence presented has been pre-filtered by the condition that there was some appropriately positioned observer to "receive" the evidence. 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.
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, while on tails it will create two, then we have two possible worlds, the first with one observer, the second with two. These worlds are equally 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 × 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.
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 may imply the doomsday argument depending on the choice of reference class.