Newcomb's Problem Without a Fixed Past: A Decision Rule From Observer-Indexed Determinacy

Newcomb’s problem has divided decision theory for five decades over a single question: whether a predictor’s already-made choice is fixed at the moment the agent decides. Evidential and causal decision theory give opposite verdicts, and the disagreement has proved stable because both camps accept the premise that the prediction, having occurred in the past, is determinate in the present. This paper proposes a decision rule that removes that premise rather than adjudicating between the camps. On the proposal, determinacy is indexed to an observer’s information state rather than to a position in time, so that an event’s having occurred earlier does not by itself make its content settled for a later deciding agent: an unread past outcome is a blank entry, and a blank entry is unsettled regardless of where its referent sits in time. The one-boxing verdict then follows from the structure of the decision rather than from the news value of the act (as in evidential decision theory) or from any backward causation (which the proposal does not invoke). The account converges with the one-box verdict of timeless and functional decision theory while supplying the ontological anchor those theories leave implicit, and it dissolves the standard randomization objection through a joint-consistency constraint rather than by stipulation. The rule is the decision-theoretic face of a general treatment of determinacy as observer-relative; a second route to the same verdict, through a principle of anthropic typicality, is sketched and its distinctness from classical anthropic reasoning emphasized. Neither route is offered as a proof that one-boxing is correct; both are offered as accounts of why, once a widely shared assumption about the past is dropped, the verdict ceases to be paradoxical.