Observational selection effects and probability

This thesis develops a theory of how to reason when our evidence has been subjected to observational selection effects. It has applications in cosmology, evolutionary biology, thermodynamics and the problem of time's arrow, game theoretic problems with imperfect recall, the philosophical evaluation of the many-worlds and many-minds interpretations of quantum mechanics and David Lewis' modal realism, and even for traffic planning. After refuting several popular doctrines about the implications of cosmological fine-tuning, we present an informal model of the observational selection effects involved. Next, we evaluate attempts that have been made to codify the correct way of reasoning about such effects - in the form of so-called "anthropic principles" - and find them wanting. A new principle is proposed to replace them, the Self-Sampling Assumption (SSA). A series of thought experiments are presented showing that SSA should be used in a wide range of contexts. We also show that SSA gives better methodological guidance than rival principles in a number of scientific fields. We then explain how SSA can lead to the infamous Doomsday argument. Identifying what additional assumptions are required to derive this consequence, we suggest alternative conclusions. We refute several objections against the Doomsday argument and show that SSA does not give rise to paradoxical "observer-relative chances" as has been alleged. However, we discover new consequences of SSA that are more counterintuitive than the Doomsday argument. Using these results, we construct a version of SSA that avoids the paradoxes and does not lead to the Doomsday argument but caters to legitimate methodological needs. This modified principle is used as the basis for the first mathematically explicit theory of reasoning under observational selection effects. This observation theory resolves the range of conundrums associated with anthropic reasoning and provides a general framework for evaluating theories about the large-scale structure of the world and the distribution of observers within it.

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