Fixing the Decision Problem: A Constraint-Based Framework for Newcomb's Problem

Newcomb’s Problem is usually treated as a conflict between competing principles of rational choice: one-boxing follows the strong predictive relation between choice and outcome, while two-boxing follows the dominance argument that the contents of the boxes are already fixed. This paper asks an earlier question: what exactly is the decision problem that those principles are being asked to evaluate? We develop a constraint-based framework in which the decision problem is fixed before any decision rule is applied. The specification includes the available actions and payoff states, the agent’s objective, the external information available at deliberation, the agent’s information about itself, the structural rules of the environment, and the actions, mechanisms, and deliberative resources actually available to the agent. This separates facts about how the world operates from the information the agent possesses about those facts, and separates the objective of the decision from the principle used to pursue it. The framework is then used to isolate predictor reliability as a decision-relevant informational constraint. Holding the monetary objective, payoff structure, prediction-to-box-filling rule, and causal ordering fixed while varying predictor reliability changes the rational pressure on the choice: reversed prediction favors two-boxing, informational neutrality leaves the dominance advantage intact, and perfect prediction supports one-boxing. Because the causal structure remains fixed throughout these cases while the prescription changes, causal fixity alone cannot determine the rational choice. Returning to Nozick’s original formulation, the paper examines what a defense of two-boxing would have to establish under the original constraints. Causal dominance identifies the extra thousand dollars available when the earlier state is held fixed, but does not by itself establish why that fixed-state comparison should receive decisive priority over the agent’s near-certain predictive information. Introspection can alter the problem only when the relevant self-information, its reliability, and its relation to the predictor are specified. Counterfactual reasoning can represent a world in which the past is held fixed and the final act changes, but representing such a world does not give the agent a mechanism for selecting it. The profitable two-boxing outcome ultimately requires the predictor’s forecast and the agent’s final action to diverge. Under Nozick’s original specification, the objective remains monetary maximization and the agent is given exceptionally strong information associating one-boxing with the million-bearing state and two-boxing with the empty state. No additional informational or deliberative resource in the original problem establishes the profitable two-boxing mismatch, while causal fixity by itself does not establish the normative priority of fixed-state evaluation. The framework therefore supports one-boxing under Nozick’s original constraints. The broader contribution is methodological. Decision-theoretic evaluation is downstream of problem specification. Competing theories may genuinely disagree about how the same fixed problem should be evaluated, but they may also be evaluating different informational, structural, or deliberative specifications without making that difference explicit. Modified cases remain useful as controlled tests: changing predictor reliability, observability, self-information, or available mechanisms can reveal which constraints are doing the work, provided the modified problem is not silently substituted for the original. The framework therefore offers a common structure for analyzing Newcomb’s Problem and other decision problems involving prediction, correlation without causation, self-information, counterfactual dependence, and strategic interaction.