Causation, decision theory, and Bell's theorem: a quantum analogue of the Newcomb problem

TL;DR

This paper explores the analogy between causal decision theory and quantum mechanics, showing that agents following CDT may be compelled to bet against quantum mechanics in entangled systems, challenging assumptions in decision theory or quantum causality.

Contribution

It establishes a formal analogy between CDT and LHV theories, revealing implications for decision theory and interpretations of quantum causality.

Findings

Agents following CDT should bet against quantum mechanics in certain scenarios.

The analogy links decision theory assumptions with quantum causal models.

Implications for the validity of decision theory and quantum causal interpretations.

Abstract

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 (LHV) 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.