Can CDT rationalise the ex ante optimal policy via modified anthropics?

Abstract

In Newcomb's problem, causal decision theory (CDT) recommends two-boxing and thus comes apart from evidential decision theory (EDT) and ex ante policy optimisation (which prescribe one-boxing). However, in Newcomb's problem, you should perhaps believe that with some probability you are in a simulation run by the predictor to determine whether to put a million dollars into the opaque box. If so, then causal decision theory might recommend one-boxing in order to cause the predictor to fill the opaque box. In this paper, we study generalisations of this approach. That is, we consider general Newcomblike problems and try to form reasonable self-locating beliefs under which CDT's recommendations align with an EDT-like notion of ex ante policy optimisation. We consider approaches in which we model the world as running simulations of the agent, and an approach not based on such models (which we call 'Generalised Generalised Thirding', or GGT). For each approach, we characterise the resulting CDT policies, and prove that under certain conditions, these include the ex ante optimal policies.

Figures (9)

• Figure 1: The dependence function in the first version of \ref{['eg:SB_PD']}.
• Figure 2: A graph of \ref{['eg:SB_PD']}. The nodes show the states and the edges show the transitions (all deterministic). The utilities of the terminal states are the same as the states' labels.
• Figure 3: A graph of $4p(1-p)$.
• Figure 4: In red, we show the original dependence function $F(p)$. In blue, we show four increasingly good approximations to it. While the approximations get close to the original function, they become increasingly wiggly, and therefore have increasingly many new stationary points (that aren't stationary points of the original dependence function). Each of these would be a CDT+GSGT policy in our example problem. Using this idea, we can create a sequene of approximating dependence functions such that every policy in $[0,1]$ is the limit of some sequence of CDT+GSGT policies for the decision problems where the dependence function is replaced by its approximations.
• Figure 5: A graph of (our version of) the adversarial offer, with states shown as nodes, and transitions shown as edges.

Theorems & Definitions (130)

• Example 1
• Example 2
• Example 3
• Definition 1: Decision problem
• Remark 1: Observations and copies
• Example 4: continues= eg:SB_PD
• Definition 2: History
• Lemma 1
• Definition 3: Ex ante expected utility
• Remark 2