Journal Article

Causation, Decision Theory, and Bell’s Theorem: A Quantum Analogue of the Newcomb Problem

Eric G. Cavalcanti

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 61, issue 3, pages 569-597
Published in print September 2010 | ISSN: 0007-0882
Published online April 2010 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axp050
Causation, Decision Theory, and Bell’s Theorem: A Quantum Analogue of the Newcomb Problem

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I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics.

Introduction

Newcomb’s Probleme

Causal Decision Theory

3.1 Regions of causal influence

3.2 Evidential and effective probabilities

The parallel with Bell’s theorem

4.1 Consequences of the analogy

4.1.1 The marble boxes game

4.1.2 Mechanism underlying the marble boxes game

4.1.3 The causalist’s decision

4.1.4 The Bell game

Communicated versus Non-communicated Predictions

Summary and Conclusion

Journal Article.  12146 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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