Newcomb’s problem isn’t a choice dilemma

Synthese 199 (1-2):5125-5143 (2021)
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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 : maximize expected utility ; adopt the dominant strategy. 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 :1637–1646, 2013), we supply additional details and offer a crucial correction to their formal proof.

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Frank Zenker
Nankai University

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The Foundations of Statistics.Leonard Savage - 1954 - Wiley Publications in Statistics.
Causality: Models, Reasoning and Inference.Judea Pearl - 2000 - New York: Cambridge University Press.
The Paradoxes of Time Travel.David Lewis - 1976 - American Philosophical Quarterly 13 (2):145-152.

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