Anthropic reasoning and the Doomsday Argument: how do observation-selection effects constrain rational inference, and does the Self-Sampling Assumption refined with observer-moments solve the puzzles?

Nick Bostrom, answered from the texts and cited to the page.

The position in brief

The Self-Sampling Assumption (SSA) says that one should reason as if randomly selected from the set of all actual observers in one's reference class. SSA must be refined with observer-moments to handle the problems that motivated Ken Olum's defense of the Self-Indication Assumption (SIA). With this refinement, the Doomsday Argument is non-trivial but does not deliver the strong conclusion the early literature claimed; the Sleeping Beauty puzzle admits a hybrid solution that respects both halfer and thirder intuitions in their proper domains. Anthropic shadow — the way observation-selection biases mask the rate of past catastrophes from our records — is the practically most important application: we should not infer the safety of catastrophic events from our presence as observers, since the inference is contaminated by the selection that being able to make the inference imposes.12345

Sources

  1. That you should have such a low birth rank is less surprising, and more probable, if the total number of humans that will ever have existed is, say, 00 billion rather than, say, 200 trillion.
    The Doomsday Argument and the Self-Indication Assumption - Reply to Olum, pp. 2–3
  2. What is counterintuitive about SIA is not that we would have to accept that the universe is infinite - we might have independent reasons for that - but the grounds on which we should allegedly accept this, and the unreasonable level confidence that we would have in the conjecture. But if not SIA, then what?
    Observation Selection Effects, Measures, and Infinite Spacetimes, p. 9
  3. However, it is difficult to find a principle that satisfies all constraints that an observation selection theory ought to satisfy - a principle that both serves legitimate scientific needs and at the same time is probabilistically coherent and paradox-free. Here we lack the space to elaborate on the multitude of such theory constraints.
    Cosmological Constant and the Final Anthropic Hypothesis, p. 6
  4. Here we use the idea that the essential difference between T1 and T2 is that the fraction of observers who would be making observations in agreement with E' is enormously greater on T1 than on T2.
    Anthropic Bias, pp. 74–75
  5. How these areas of vagueness are resolved has serious consequences for what empirical predictions one gets when applying SSA to real empirical situations. Yet for present purposes we can sidestep these issues by introducing some simplifying assumptions. These will not change the fundamental principles involved but will on the contrary make it easier for us to focus on them.
    The Doomsday Argument, Adam and Eve, UN++, and Quantum Joe, pp. 4–6

Where the argument is made

  • Anthropic Bias: Observation Selection Effects in Science and Philosophy (Routledge, 2002)
  • "Self-Locating Belief in Big Worlds" (Journal of Philosophy, 2002)
  • "The Mysteries of Self-Locating Belief and Anthropic Reasoning" (Harvard Review of Philosophy, 2003)
  • "Observation Selection Effects, Measures, and Infinite Spacetimes" (Cambridge UP, 2007)
  • "The Doomsday Argument and the Self-Indication Assumption: Reply to Olum" with Ćirković (Philosophical Quarterly, 2003)
  • "The Doomsday Argument, Adam and Eve, UN++, and Quantum Joe" (Synthese, 2001)
  • "Sleeping Beauty and Self-Location: A Hybrid Model" (Synthese, 2007)
  • "Beyond the Doomsday Argument: Reply to Sowers" (c. 2002)
  • "Anthropic Shadow" with Ćirković & Sandberg (Risk Analysis, 2010)
  • "Cosmological Constant and the Final Anthropic Hypothesis" with Ćirković (Astrophysics and Space Science, 2000)

How the argument was received

Anthropic Bias (2002) is the canonical book-length treatment. The framework has remained the standard reference for two decades. Olum's SIA defense is the most-cited rival framework. Cosmological applications have grown in importance with the multiverse literature (Tegmark, Vilenkin, Susskind).