Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom

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Anthropic Bias
Observation Selection Effects in Science and Philosophy
Nick Bostrom


This book explores how to reason when you suspect that your evidence is biased by observation selection effects. An explanation of what observation selection effects are has to await chapter 1. Suffice it to say here that the topic is intellectually fun, difficult, and important. We will be discussing many interesting applications: philosophical thought experiments and paradoxes aside, we will use our results to address several juicy bits of contemporary science: cosmology (how many universes are there?), evolution theory (how improbable was the evolution of intelligent life on our planet?), the problem of time’s arrow (can it be given a thermodynamic explanation?), game theoretic problems with imperfect recall (how to model them?), traffic analysis (why is the “next lane” faster?) and a lot more – the sort of stuff that intellectually active people like to think about…


Preface 2


Acknowledgements 6


Observation selection effects 7

A brief history of anthropic reasoning 10

Synopsis of this book 12


Does fine-tuning need explaining? 17

No “Inverse Gambler’s Fallacy” 19

Roger White and Phil Dowe’s analysis 21

Surprising vs. unsurprising improbable events 25

Observation selection effects 34

Conclusions 40

CHAPTER 3: Anthropic Principles, the motley family 43

The anthropic principle as expressing an observation selection effect 43

Anthropic hodgepodge 46

Freak observers and why earlier formulations are inadequate 50

The Self-Sampling Assumption 55

CHAPTER 4: thought experiments supporting the SELF-SAMPLING ASSUMPTION 57

The Dungeon 57

Two thought experiments by John Leslie 60

Incubator 61

The reference class problem 65

chapter 5: The Self-Sampling Assumption in science 69

SSA in cosmology 69

SSA in thermodynamics 71

SSA in evolutionary biology 73

SSA in traffic analysis 77

SSA in quantum physics 78

Summary of the case for SSA 81


Introduction 83

Doomsday à la Gott 84

The incorrectness of Gott’s argument 86

Doomsday à la Leslie 88

The assumptions used in DA, and the Old evidence problem 90

Leslie on the problem with the reference class 97

Alternative conclusions of the Doomsday argument 100

CHAPTER 7: invalid objections against the DOOMSDAY ARGUMENT 102

Objection One (Korb and Oliver) 102

Objection Two (Korb and Oliver) 104

Objection Three (Korb and Oliver) 107

Objection Four (Korb and Oliver) 108

Objection Five (Korb and Oliver) 110

Couldn’t a Cro-Magnon man have used the Doomsday argument? (Various) 111

Aren’t we necessarily alive now? (Mark Greenberg) 111

Sliding reference of “soon” and “late”? (Mark Greenberg) 112

How could I have been a 16th century human? (Mark Greenberg) 112

Doesn’t your theory presuppose that the content of causally disconnected regions affects what happens here? (Ken Olum) 113

But we know so much more about ourselves than our birth ranks! (Various) 113

Safety in numbers? Why the Self-Indication Assumption should be rejected (several) 114


Leslie’s argument, and why it fails 118

Observer-relative chances: another go 121

Discussion 123

Conclusion 126

Appendix 127


The Adam & Eve experiments 131

Analysis of Lazy Adam: predictions and counterfactuals 133

The UN++ gedanken: reasons, abilities, and decision theory 139

Quantum Joe: SSA and the Principal Principle 142

Conclusion 144

Appendix: The Meta-Newcomb problem 146

CHAPTER 10: Observation theory: A methodology for anthropic reasoning 147

Building blocks, theory constraints and desiderata 147

Outline of the solution 149

SSSA: Taking account of indexical information of observer-moments 149

Reassessing Incubator 152

How the reference class may be observer-moment relative 155

Formalizing the theory: the Observation Equation 158

A quantum generalization of OE 160

Non-triviality of the reference class: why must be rejected 161

Final thought on the reference class problem 167

Chapter 11: Observation selection theory applied to cosmological fine-tuning 170

Chapter 12: The Sleeping-Beauty problem: modelling imperfect recall 178

The Sleeping Beauty Problem 178

The case of no outsiders 179

The case with outsiders 180

Synthesis 181

General summary: How the theory measures up against desiderata 182



This work has benefited from copious feedback generated by bits and pieces of it that have been published earlier. Over the years, I must have corresponded with several hundreds of people about these issues. In addition, I’ve received comments from conference audiences, journal referees, students, and authors of replies to parts of this research that have already been published. For all this, I am most grateful!

There is a website associated with the book,, where there is a preprint archive collecting relevant writings that are available online, an updated bibliography, primers on various topics, and other resources that will make it easier for a scholar or interested layperson to get up to speed with the latest research on observation selection effects.

Although I cannot name everybody who has helped me in some way with this manuscript, there are some persons who must be singled out for my special thanks: Paul Bartha, Darren Bradley, John Broome, Jeremy Butterfield, Erik Carlson, Douglas Chamberlain, Pierre Cruse, Wei Dai, J-P Delahaye, Jean-Michel Delhotel, Dennis Dieks, William Eckhardt, Ellery Eells, Adam Elga, Hal Finney, Paul Franceschi, Mark Greenberg, Robin Hanson, Daniel Hill, Christopher Hitchcock, Richard Jeffrey, Bill Jefferys, Vassiliki Kambourelli, Loren A. King, Kevin Korb, Eugene Kusmiak, Jacques Mallah, Neil Manson, Peter Milne, Bradley Monton, Floss Morgan, Jonathan Oliver, Ken Olum, Don N. Page, David Pearce, Elliott Sober, Richard Swinburne, Max Tegmark, Alexander Vilenkin, Saar Wilf, and Roger White. I am so grateful to all those friends, named and unnamed, without whose input this book could not have been written. (The faults that it contains, however, I was perfectly capable of producing all by myself!)

I want to especially thank John Leslie for his exceedingly helpful guidance, Colin Howson and Craig Callender for long assistance and advice, Nancy Cartwright for removing a seemingly insurmountable administrative obstacle, and Milan C. Ćirković for managing to keep up collaboration with me on a paper whilst bombs were falling all around him in Belgrade. Finally, I want to thank Robert Nozick for encouraging rapid publication.

I gratefully acknowledge a generous research grant from the John Templeton Foundation that helped fund large parts of the research. I’m thankful to Synthese, Mind, Analysis, and Erkenntnis for permitting texts to be republished here. The book is dedicated to my father – tack pappa!

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