This book explores how to reason when you suspect that your evidence is biased by observation selection effects. An explanation of what observation selection effects are has to await chapter 1. Suffice it to say here that the topic is intellectually fun, difficult, and important. We will be discussing many interesting applications: philosophical thought experiments and paradoxes aside, we will use our results to address several juicy bits of contemporary science: 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?) and a lot more - the sort of stuff that intellectually active people like to think about...

Summary of the difficulties that a theory of observation selection effects faces and a sketch of a solution.

White argues, taking up and refining an earlier idea of Ian Hacking's, that the anthropic explanation that seeks to explain why we see a fine-tuned universe by postulating a the existence of a multiverse fails because we must look at the most specific version of the evidence we have, and that is not just that "Some universe is fine-tuned." but that "This universe is fine-tuned." - this latter fact not being one that is made any more probable by the existence of lots of other universes according to White.

Abstract: Anthropic reasoning often begins with the premise that we should expect to find ourselves typical among all intelligent observers. However, in the infinite universe predicted by inflation, there are some civilizations which have spread across their galaxies and contain huge numbers of individuals. Unless the proportion of such large civilizations is unreasonably tiny, most observers belong to them. Thus anthropic reasoning predicts that we should find ourselves in such a large civilization, while in fact we do not. There must be an important flaw in our understanding of the structure of the universe and the range of development of civilizations, or in the process of anthropic reasoning.

Addresses the reference-class problem (or measure problem) in information-theoretic terms. Abstract: Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical? There is a widespread belief that this question is inherently vague, and that there are various possible choices for the types of reference objects which should be counted in. Here we argue that the ``ideal'' reference class (for the purpose of making predictions) can be defined unambiguously in a rather precise way, as the set of all observers with identical information content. When the observers in a given class perform an experiment, the class branches into subclasses who learn different information from the outcome of that experiment. The probabilities for the different outcomes are defined as the relative numbers of observers in each subclass. For practical purposes, wider reference classes can be used, where we trace over all information which is uncorrelated to the outcome of the experiment, or whose correlation with it is beyond our current understanding. We argue that, once we have gathered all practically available evidence, the optimal strategy for making predictions is to consider ourselves typical in any reference class we belong to, unless we have evidence to the contrary. In the latter case, the class must be correspondingly narrowed.

Argues that the Measure problem has not been solved.

Discussion of various types of anthropic principle.

Abstract: John Leslie presents a thought experiment to show that chances are sometimes observer-relative in a paradoxical way. The pivotal assumption in his argument - a version of the weak anthropic principle - is the same as the one used to get the disturbing Doomsday argument off the ground. I show that Leslie’s thought experiment trades on the sense/reference ambiguity and is fallacious. I then describe a related case where chances are observer-relative in an interesting way. But not in a paradoxical way. The result can be generalized: At least for a very wide range of cases, the weak anthropic principle does not give rise to paradoxical observer-relative chances. This finding could be taken to give new indirect support to the doomsday argument.

Abstract: Barrow and Tipler's attempt to stave off the inference to divine design by appealing to the Weak Anthropic Principle is demonstrably logically fallacious unless one conjoins to it the metaphysical hypothesis of a World Ensemble. But there is no reason for such a postulate. Their misgivings about the alternative of divine design are shown to be of little significance.

A response to the above paper by Craig.