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This is an extreme generalization of the confirmation bias and the cognitive bias, involving not only mind-set, memory and methodology, but the whole way in which one sees oneself as an entity investigating an environment.
The original statement of the problems related to anthropic bias is due to Eugene Wigner's 1960 paper, The Unreasonable Effectiveness of Mathematics in the Physical Sciences. He noted that being a human on one planet was not a bias that could be easily overcome, and noted the necessity of considering the point of view of other, less "anthropic", species.
A more rigorous statement of these problems is that of George Lakoff and Rafael E. Núñez in their book Where Mathematics Comes From, 2000. According to them, Euler's Identity itself expresses an anthropic bias, that embedded in human cognition, and investigatable only via cognitive science — which relies on empirical methods. This necessarily leaves some uncertainty which, according to Lakoff, can't be overcome even in theory. Thus, anthropic bias is due to cognitive bias, and investigating it leads to yet another cognitive bias.
Bostrom thinks otherwise and suggests a way out using what amounts to quasi-empirical methods. In his book Anthropic Bias: observation selection effects in science and philosophy, 2002, Bostrom explores the implications of these for "polling, cosmology (how many universes are there?), evolution theory (how improbable was the evolution of intelligent life on our planet?), the problem of time's arrow (can it be given a thermodynamic explanation?), game theoretic problems with imperfect recall (how to model them?), traffic analysis (why is the "next lane" faster?)."
One conclusion is that the so-called anthropic principle or rather the many competing concepts that claim that name, are confused. He further claims that "existing methodology does not permit any observational consequences to be derived from contemporary cosmological theories, in spite of the fact that these theories quite plainly can be and are being tested empirically by astronomers. What is needed to bridge this methodological gap is a more adequate formulation of how observation selection effects are to be taken into account."
The Self-Sampling Assumption he proposes is "that you should think of yourself as if you were a random observer from a suitable reference class." Refining this idea by applying to more down-to-earth problems suggests that the Assumption applies "to “observer-moments” rather than just observers. This increases our analytical firepower. A second step is to relativize the reference class. The result is a general framework for modeling anthropic reasoning, which is given a formal expression in an equation, the Observation Equation, that specifies how to take into account evidence that as an indexical component or that has been subjected to an observation selection effect." This he then applies rigorously to the arguments to show that they achieve the same results, and illustrates with the Sleeping Beauty problem and the related Absent-Minded Driver and Absent-Minded Passenger problems."
He acknowledges a limit to the approach, as an "element of subjectivity that may reside in the choice of a prior credence function for indexical propositions. We compare it with the more widely recognized aspect of subjectivity infesting the non-indexical component of one’s credence function, and we suggest that the issue throws light on how to rank various applications of anthropic reasoning according to how scientifically rigorous they are."
This he proposes as a way to overhaul the whole philosophy of science from first principles, rather as Lakoff and Nunez seek to overthrow the whole prior philosophy of mathematics. It is not at all clear that he can do so.
See also: algebra of doing
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