The Causal Decision Trap

Imagine a game set up by an exceptionally reliable predictor. You are presented with two boxes. One is transparent and contains a modest one thousand dollars. The other is opaque, and it either holds a cool million or nothing at all. You have two choices: take both boxes, or take only the opaque one. Here is the catch. The predictor made their bet long before you walked into the room, filling the opaque box only if they foresaw that you would take just that single box. By the time you sit down to choose, the money is already placed. It is either sitting there, or it is not.

A strictly logical agent using Causal Decision Theory looks at this setup and sees an easy win. They reason that the predictor's action is already locked in the past. Your choice today cannot physically reach backward in time to change what the predictor did. Therefore, taking both boxes is strictly better, guaranteeing you an extra thousand dollars no matter what. If the million is in the opaque box, you get a million and one thousand. If it is empty, you still walk away with an extra thousand. It is an airtight argument for taking everything on the table.

Yet the agent who follows this ironclad logic consistently walks away with far less money than someone who acts on mere correlation. The conflict exposes a deep fracture in how we define rationality itself. While the causal decision-maker focuses exclusively on physical impact, an alternative framework known as Evidential Decision Theory focuses on conditional probability. The evidential agent asks a different question: what does my choice say about me? They recognize that their choice and the predictor's past action are strongly correlated. By choosing to take only one box, they provide the best possible evidence that they are the kind of person who leaves the first box behind, aligning themselves with the payout.

This tension reveals that rationality is not a single, unified command. Instead, it splits into two distinct paths: one governed by strict physical causation, and the other by the diagnostic power of our choices. Sometimes, the world rewards those who act not on what their action directly causes, but on what it reveals.