Newcomb’s problem isn’t a choice dilemma

Authors:

• Zhanglyu Li,
• Frank Zenker

Abstract

Newcomb’s problem involves a decision-maker faced with a choice and a predictor forecasting this choice. The agents’ interaction seems to generate a choice dilemma once the decision-maker seeks to apply two basic principles of rational choice theory (RCT): maximize expected utility (MEU); adopt the dominant strategy (ADS). We review unsuccessful attempts at pacifying the dilemma by excluding Newcomb’s problem as an RCT-application, by restricting MEU and ADS, and by allowing for backward causation. A probability approach shows that Newcomb’s original problem-formulation lacks causal information. This makes it impossible to specify the probability structure of Newcomb’s univocally. Once missing information is added, Newcomb’s problem and RCT re-align, thus explaining Newcomb’s problem as a seeming dilemma. Building on Wolpert and Benford (Synthese 190(9):1637–1646, 2013), we supply additional details and offer a crucial correction to their formal proof.