Teacakes, Trains, Taxicabs and Toxins: a Bayesian Account of Predicting the Future the Copernican Anthropic Principle

This paper explores how people make predictions about the future. Statistical approaches to predicting the future are discussed, focussing on the method for predicting the future suggested by J. R. Gott (1993). A generalized Bayesian form of Gott's method is presented, and a speciic psychological model suggested. Three experiments show that the predictions people make about the future are consistent with a Bayesian approach. Despite the diiculty of predicting the future, people happily do it every day. We are conndent about being able to predict the durations of events, how much time we will need to get home after work, and how long it will take to nish the shopping. In many cases we have a great deal of information guiding our judgments. However , sometimes we have to make predictions based upon much less evidence. When faced with new situations our decisions about how much longer we can expect events to last are based on whatever evidence is available. When the only information we possess concerns how long a particular event has lasted until now, predicting the future becomes a task of induction. In this paper we explore the question of how people predict the future when told only about the past. We examine a simple statistical method of predicting the future, and consider how such a method could be made suuciently exible to be useful in everyday situations. The resulting Bayesian model makes strong predictions about the eeects of providing further information, the symmetry of this form of reasoning, and how it should be aaected by prior knowledge. We test these predictions empirically. A simple solution to the problem of predicting the future was recently proposed by the cosmologist J. Richard Gott III (1993). Gott's method is founded upon what he calls the \Copernican anthropic principle", which holds that ... the location of your birth in space and time in the Universe is priveleged (or special) only to the extent implied by the fact that you are an intelligent observer, that your location among intelligent observers is not special but rather picked at random (1993, p. 316) Gott extends this principle to reasoning about our position in time { given no evidence to the contrary, we should not assume that we are in a \special" place in time. This means that the time at which an observer encounters a phenomenon should be randomly located in the total duration …