The Mysteries of Self-Locating Belief and Anthropic Reasoning

Abstract

§1. HOW BIG IS THE SMALLEST FISH IN THE POND? YOU TAKE YOUR WIDE-MESHED fishing net and catch one hundred fish, every one of which is greater than six inches long. Does this evidence support the hypothesis that no fish in the pond is much less than six inches long? Not if your wide-meshed net can’t actually catch smaller fish. The limitations of your data collection process affect the inferences you can draw from the data. In the case of the fish-size-estimation problem, a selection effect—the net’s being able to sample only the big fish—invalidates any attempt to extrapolate from the catch to the population remaining in the water. Had your net had a finer mesh, allowing it to sample randomly from all the fish, then finding a hundred fish all greater than a foot long would have been good evidence that few if any fish remaining were much smaller. In the fish net example, a selection effect is introduced by the fact that the instrument you used to collect data sampled from only a subset of the target population. Analogously, there are selection effects that arise not from the limitations of the measuring device but from the fact that all observations require the existence of an appropriately positioned observer. These are known as observation selection effects. The study of observation selection effects is a relatively new discipline. In my recent book Anthropic Bias, I have attempted to develop the first mathematically explicit theory of observation selection effects. In this article, I will attempt to convey a flavor of some of the mysteries that such a theory must resolve. The theory of observation selection effects may have implications for a number of fields in both philosophy and science. One example is evolutionary biology, where observation selection effects must be taken into ac