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arXiv:0802.1390

Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?

Huw Price

Published Jun 24, 2010• 85 citations
arXivHTMLPDF

Abstract

Abstract Critics object that the Everett view cannot make sense of quantum probabilities, in one or both of two ways: either it cannot make sense of probability at all, or it cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections by appealing to an Everettian version of Savage's rational decision theory. Deutsch argues not only that an analogue of classical decision under uncertainty makes sense in an Everett world; but also that under reasonable assumptions, the betting odds of a rational Everettian agent should be constrained by the Born rule. Deutsch's proposal has been defended and developed by David Wallace, and in a different form by Hilary Greaves. This chapter offers some objections to the Deutsch–Wallace–Greaves argument, focussing in particular on the supposed analogy with classical decision under uncertainty.

DOI
10.1093/acprof:oso/9780199560561.003.0014

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Abstract Critics object that the Everett view cannot make sense of quantum probabilities, in one or both of two ways: either it cannot make sense of probability at all, or it cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections by appealing to an Everettian version of Savage's rational decision theory. Deutsch argues not only that an analogue of classical decision under uncertainty makes sense in an Everett world; but also that under reasonable assumptions, the betting odds of a rational Everettian agent should be constrained by the Born rule. Deutsch's proposal has been defended and developed by David Wallace, and in a different form by Hilary Greaves. This chapter offers some objections to the Deutsch–Wallace–Greaves argument, focussing in particular on the supposed analogy with classical decision under uncertainty.
It is often objected that the Everett interpretation of QM cannot make sense of quantum probabilities, in one or both of two ways: either it can't make sense of probability at all, or it can't explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, but also that under reasonable assumptions, the credences of a rational agent in an Everett world should be constrained by the Born rule. David Wallace has developed and defended Deutsch's proposal, and greatly clarified its conceptual basis. In particular, he has stressed its reliance on the distinguishing symmetry of the Everett view, viz., that all possible outcomes of a quantum measurement are treated as equally real. The argument thus tries to make a virtue of what has usually been seen as the main obstacle to making sense of probability in the Everett world. In this note I outline some objections to the Deutsch-Wallace argument, and to related proposals by Hilary Greaves about the epistemology of Everettian QM. (In the latter case, my arguments include an appeal to an Everettian analogue of the Sleeping Beauty problem.) The common thread to these objections is that the symmetry in question remains a very significant obstacle to making sense of probability in the Everett interpretation.
It is often objected that the Everett interpretation of QM cannot make adequate sense of quantum probabilities, in one or both of two senses: either it cannot make sense of probability at all, or cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, and that under reasonable assumptions, the credences of a rational agent in an Everett world should be constrained by the Born rule. David Wallace has recently developed and defended Deutsch's proposal, and greatly clarified its conceptual basis. In this note I outline some concerns about the Deutsch argument, as presented by Wallace, and about related proposals by Hilary Greaves. In particular, I argue that the argument is circular, at a crucial point.
Following the work of D. Deutsch, D. Wallace has proposed a derivation of the Born rule in the context of the Everett interpretation. However, it seems to require a genuine uncertainty of the observers, which is difficult to justify in this deterministic framework. H. Greaves proposed another point of view, which does not imply any uncertainty of the observers, but renders the Deutsch-Wallace derivation pointless. I will propose a slightly different framework (without any uncertainty of the observers), which consists in interpreting directly the squared modulus of the amplitudes as proportions of worlds (without supposing that any counting of discrete worlds can be defined); it requires to examine the principles of rationality associated with the notion of proportion of observers in thought experiments involving non-quantum fission of the observers. I will then analyse the role of the Deutsch-Wallace derivation in this framework, which consists in an ordering of the rationality principles in the quantum splitting case (distinguishing the primitive principles from the derived ones).
Building on work originally carried out by David Deutsch, the chapter develops a mathematically rigorous framework for discussing the quantum probability rule in terms of the preferences between various courses of action of rational agents. Within this framework, the chapter proves formally that any rational agent who believes in the truth of Everettian quantum mechanics and who knows (or thinks they know) the current quantum state of their branch will act as if future branching was a probabilistic process with the probabilities given by the standard quantum-mechanical probability rule (the ‘Born rule’). The chapter concludes by analysing other proposed rules for action in a quantum universe and showing where they violate the axioms for quantum decision making which it proposes and defends.
Abstract There is a compelling intellectual case for exploring whether purely unitary quantum theory defines a sensible and scientifically adequate theory, as Everett originally proposed. Many different and incompatible attempts to define a coherent Everettian quantum theory have been made over the past fifty years. However, no known version of the theory (unadorned by extra ad hoc postulates) can account for the appearance of probabilities and explain why the theory it was meant to replace — Copenhagen quantum theory — appears to be confirmed, or more generally why our evolutionary history appears to be Born-rule typical. This chapter reviews some ingenious and interesting recent attempts in this direction by Wallace, Greaves–Myrvold, and others, and explains why they don't work. An account of one-world randomness, which appears scientifically satisfactory, and has no many-worlds analogue, is proposed. A fundamental obstacle to confirming many-worlds theories is illustrated by considering some toy many-worlds models. These models show that branch weights can exist without having any role in either rational decision-making or theory confirmation, and also that the latter two roles are logically separate. Wallace's proposed decision theoretic axioms for rational agents in a multiverse and claimed derivation of the Born rule are examined. It is argued that Wallace's strategy of axiomatizing a mathematically precise decision theory within a fuzzy Everettian quasiclassical ontology is incoherent. Moreover, Wallace's axioms are not constitutive of rationality either in Everettian quantum theory or in theories in which branchings and branch weights are precisely defined. In both cases, there exist coherent rational strategies that violate some of the axioms.