Past Longevity as Evidence for the Future

Abstract

Gott (1993) has used the ‘Copernican principle’ to derive a probability distribution for the total longevity of any phenomenon, based solely on the phenomenon's past longevity. Leslie (1996) and others have used an apparently similar probabilistic argument, the ‘Doomsday Argument’, to claim that conventional predictions of longevity must be adjusted, based on Bayes's Theorem, in favor of shorter longevities. Here I show that Gott's arguments are flawed and contradictory, but that one of his conclusions is plausible and mathematically equivalent to Laplace's famous—and notorious—‘rule of succession’. On the other hand, the Doomsday Argument, though it appears consistent with some common-sense grains of truth, is fallacious; the argument's key error is to conflate future longevity and total longevity. Applying the work of Hill (1968) and Coolen (1998, 2006) in the field of nonparametric predictive inference, I propose an alternative argument for quantifying how past longevity of a phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity.