| Summary: | A number of problems in physics, mathematics, and philosophy involve observers in given situations which lead to debates about whether observer-specific information should affect the probability for some outcome or hypothesis. Our purpose is not to advocate for such observer selection effects but rather to show that any such effects depend greatly on the assumptions made. We focus on the debate about the existence of a “doomsday effect”—whether observer index information should cause one to favor possibilities with fewer observers, which has been argued to have implications for models of cosmology. Our central goal is to reconcile the apparent inconsistencies in the literature by introducing a formalism to lay bare assumptions made and address a key issue that has not been clearly articulated in such problems: whether the observer is selected by picking from or being in a set of worlds. In the former there generally are observer selection effects, and in the latter there generally are not. This leads us to differentiate what we call inclusive from exclusive selection and how they relate to the concept of a multiverse. Then we relax the assumption that all observers are equally typical and consider the problem of Boltzmann brains, showing that typicality can play a role in solving the problem. We then stress the need for scale-invariant questions, which causes us to analyze J. Richard Gott's approach to the problem. This all allows us to analyze the doomsday and universal doomsday arguments. We find that there is no doomsday effect, absent a set of assumptions we find somewhat unreasonable. Then we use our formalism to resolve a debate in the philosophy community called the “Sleeping Beauty problem.” Finally, we conclude with a heuristic summary, free from equations, and point to possible future directions of this line of research.
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