Causality and the Doomsday Argument

Using the Autodialer thought experiment, we show that the Self-Sampling Assumption (SSA) is too general, and propose a revision to the assumption that limits its applicability to causally-independent observers. Under the revised assumption, the Doomsday Argument fails, and the paradoxes associated with the standard SSA are dispelled. We also consider the effects of the revised sampling assumption on tests of cosmological theories. There we find that, while we must restrict our attention to universes containing at least one observer, the total number of observers predicted in each universe is irrelevant to the confirmation of a theory. The Doomsday Argument (Bostrom 1997, 2002; Leslie 1989, 1996) concludes that the prior probability we assign to the short-term extinction of humanity is greatly magnified by our observation that we exist at the present time in human history. Before we discuss the Doomsday Argument itself, it is instructive to examine one of the thought experiments that is held up as its analogue. The following experiment, Cubicles, is a minor variation of the original Incubator described by Bostrom (2002). Cubicles One hundred cubicles are numbered 1 to 100. A coin is flipped to determine how many people will be placed in the cubicles. If the result is heads, one person is placed in all 100 cubicles. If the result is tails, only the first 10 cubicles are occupied. Each person who enters a cubicle is led in blindfolded so they cannot tell which cubicle they are placed in, nor can they tell how many other people have been placed in cubicles. Initially, you find yourself in a cubicle, but you do not know which one. You are asked to estimate the probability that the coin toss was tails. You have no additional information, so you answer 50%. Next, you learn that you are in cubicle #5. What is the posterior probability that the coin flip was tails? The revised probability of the coin flip having been tails can be computed using Bayes' theorem: p(tails|#5) = p(#5|tails) p(tails) / (p(#5|tails) p(tails) + p(#5|heads) p(heads)) (1) = 10% 50% / (10% 50% + 1% 50%) = 10 / 11 = 91% This calculation is a natural outcome of the fact that occupancy in cubicle #5 is ten times more likely if the coin flip was tails rather than heads. To get to the Doomsday Argument, one must argue that the Cubicles scenario is analogous to the question of how many humans will ever be born. Suppose we assign every human individual a unique birth rank. Adam and Eve would be numbered one and two, respectively, and contemporary humans would have birth ranks in the 60 billion range (to date, about 60 billion humans have ever lived). To construct the Doomsday Argument, we suppose that a finite number of humans will ever live, and theorize that humanity will either