Abstract
We argue that causal decision theory (CDT) is no worse off than evidential decision theory (EDT) in handling entanglement, regardless of one’s preferred interpretation of quantum mechanics. In recent works, Ahmed (Evidence, decision, and causality, Cambridge University Press, Cambridge, 2014) and Ahmed and Caulton (Synthese, 191(18): 4315–4352, 2014) have claimed the opposite; we argue that they are mistaken. Bell-type experiments are not instances of Newcomb problems, so CDT and EDT do not diverge in their recommendations. We highlight the fact that a Causal Decision Theorist should take all lawlike correlations into account, including potentially acausal entanglement correlations. This paper also provides a brief introduction to CDT with a motivating “small” Newcomb problem. The main point of our argument is that quantum theory does not provide grounds for favouring EDT over CDT.
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Notes
See Giustina et al. (2015) for a notable recent example.
Cavalcanti (2010) makes a similar argument, though his conclusion is slightly different. He claims that the failure of CDT plus acausal interpretations of entanglement in EPR-type betting scenarios means that either CDT is false, or that CDT is capable of making a practical distinction between what were previously thought to be empirically equivalent metaphysical theses.
Nozick credits the physicist William Newcomb with the original formulation of the problem.
See e.g. Skyrms (2013). Chance here can be viewed as objective and prior to the agent’s credences, or epistemic and built out of a systematization of credences.
This is a version of an example that appeared in (Harper 1993, pp. 84–85).
If utilities are linear with these amounts of money, as they often are for modest amounts like this, then evidential decision theory will recommend one box so long as \(Cr(p1B | 1B){-}Cr(p1B |2B)\) is greater than 50/1000, or .05.
This would clearly be what Cusbert (2017) would identify as a case of ordinary ‘forwards’ causation.
In fact, when analyzing counterfactuals for which \(P(A \rightarrow S) \ne P(S|A)\), Gibbard and Harper (1978, p. 127) make reference only to worlds that “obey physical laws”, not to worlds in which causation plays any role.
As mentioned in (Ahmed and Caulton 2014, fn. 21)—and quoted below—Ahmed grants that CDT should deal with conditional chance in this way, and it thus appears clear that our interpretations of what CDT is do not differ drastically. However, here he views conditional chance as revealing only causal dependencies: “the extent to which the conditional chance of Y on X, Ch(Y|X), exceeds the unconditional chance Ch(Y) of Y, reflects the extent to which the occurrence of Xcausally promotes the occurrence of Y” [Ahmed and Caulton 2014, (p. 4328, emphasis original)].
Causal connections are allowed, so long as the agent does not have epistemic access to the detailed state of the world. In the de Broglie–Bohm theory, for example, the choice of experiment on one particle has a causal influence on the distant system. However, an agent cannot have precise knowledge of the true state of the world, and must therefore average over all compatible states. In effect, this averaging washes out any causal connection present in the agent’s credences.
A similar argument appears in Cavalcanti (2010), where Bell factorizability is imposed on the structure of CDT [cf. (Cavalcanti 2010, (Section 3.1, eq (11))]. Though the details may differ, we think our argument in this section should largely apply there as well. We think it unfair to impose factorizability on CDT, and to do so one must impose parameter independence, outcome independence, and the no conspiracy assumptions.
On a Bayesian view of setting credences, these outcomes should never receive exactly zero credence, but the past body of evidence can be made sufficiently large such that \(Cr(AB, het) \approx 0\).
Ahmed and Caulton (2014) use ‘hom’ and ‘het’ to indicate cases in which the outcomes on two receivers show the same reading (homogeneous) and different readings (hetergeneous), respectively.
Though these conditions are brought up in the context of B-type solutions, they claim that the same argument applies equally to (C2) solutions: “the foregoing argument of course applies as well to them as it does to (B2)-type theories: CDT and EDT will give conflicting advice...to any agent who accepts (C2)” (Ahmed and Caulton 2014, p. 4335)
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Acknowledgements
The authors would like to thank the philosophy of physics reading group at Western University for helpful feedback on early drafts, Wayne Myrvold for helpful discussions, and two anonymous reviewers for their comments, which helped to strengthen the argument of this paper. This research was supported by a Joseph-Armand Bombardier Doctoral CGS Award from the Social Sciences and Humanities Research Council of Canada (Adam Koberinski).
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Koberinski, A., Dunlap, L. & Harper, W.L. Do the EPR correlations pose a problem for causal decision theory?. Synthese 196, 3711–3722 (2019). https://doi.org/10.1007/s11229-017-1611-9
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DOI: https://doi.org/10.1007/s11229-017-1611-9