Causal Decision Theory

Causal Decision Theory (CDT) is a prominent branch of decision theory developed in the 1970s and 1980s by philosophers such as Allan Gibbard, William Harper, and David Lewis. It was designed specifically to resolve perceived flaws in Evidential Decision Theory (EDT), particularly in scenarios where an action correlates with an outcome but does not causally influence it.

The Core Principle of CDT

Unlike EDT, which calculates expected utility using standard conditional probabilities (which measure correlation), CDT calculates expected utility using causal probabilities or counterfactual conditionals. It asks: "What will my action *physically bring about*?" rather than "What will my action *be a sign of*?"

Mathematically, CDT replaces the conditional probability P(O | A) with a probability that represents the causal influence of action A on outcome O, often denoted using counterfactuals (e.g., the probability that O would occur if A were done):

EU(A) = ∑ P(A ➔ O) * U(O)

This ensures that an agent does not choose an action merely because it is a symptom of a good state, but only if the action is a causal instrument for achieving that state.

CDT and Newcomb's Paradox

CDT is the mathematical and philosophical engine behind "two-boxing" in Newcomb's Paradox. A causal decision-maker recognizes that the Predictor's placement of the money occurred in the past and is causally independent of the agent's current choice.

Because choosing to take both boxes cannot causally alter the contents of Box B, the causal probability of Box B containing $1,000,000 is identical whether the agent takes one box or two. Therefore, CDT dictates that taking both boxes is the only rational choice, as it guarantees an extra $1,000 in all possible causal branches.

The Challenge to CDT

While CDT successfully avoids the irrationalities of the "Smoking Lesion" problem, it faces a major challenge in Newcomb's Paradox: the "Why Aren't You Rich?" objection. Because the Predictor is highly accurate, causal decision-makers (two-boxers) almost always end up with $1,000, while evidential decision-makers (one-boxers) almost always end up with $1,000,000. This leads critics to argue that CDT's definition of "rationality" is self-defeating in practice.

If you found this valuable, consider supporting our work.