A (hopefully) comprehensive solution to the Newcomb's problem

The Newcomb's problem has been discussed in the philosophical literature for more than fifty years. So far quarrels mainly oppose causalism on the one hand, and evidentialism on the other hand. This paper wants to explain why causalists are right from a certain point of view, and why they should one-box --- instead of keeping two-boxing. The Newcomb's problem can be thought in terms of possible worlds. I assume here that this problem does not happen in our world, but it occurs in a world where causality and rationality obey different rules. But, in any cases, when the predictor is reliable, the player must one-box.

Newcomb’s problem isn’t a choice dilemma

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.

Equal Opportunities in Newcomb’s Problem and Elsewhere

The paper discusses Ian Wells’s recent argument (Wells 2019) that there is a decision problem in which followers of Evidential Decision Theory end up poorer than followers of Causal Decision Theory despite having the same opportunities for money. It defends Evidential Decision Theory against Wells’s argument, on the following grounds. (i) Wells's has not presented a decision problem in which his main claim is true. (ii) Four possible decision problems can be generated from his central example, in each of which followers of Evidential Decision Theory do at least as well as followers of Causal Decision Theory (but the former typically have better opportunities for money). (iii) There is another case in which followers of Causal Decision Theory have the same opportunities for making money but end up worse than followers of Evidential Decision Theory.

Newcomb University: A play in one act

Counter-intuitive consequences of both causal decision theory and evidential decision theory are dramatized. Each of those theories is thereby put under some pressure to supply an error theory to explain away intuitions that seem to favour the other. Because trouble is stirred up for both sides, complacency about Newcomb’s problem is discouraged.

The philosopher’s paradox: How to make a coherent decision in the Newcomb Problem

We offer a novel argument for one-boxing in Newcomb’s Problem. The intentional states of a rational person are psychologically coherent across time, and rational decisions are made against this backdrop. We compare this coherence constraint with a golf swing, which to be effective must include a follow-through after the ball is in flight. Decisions, like golf swings, are extended processes, and their coherence with other psychological states of a player in the Newcomb scenario links her choice with the way she is predicted in a common cause structure. As a result, the standard argument for two-boxing is mistaken.

Frankfurt cases and the Newcomb Problem

A standard argument for one-boxing in Newcomb’s Problem is ‘Why Ain’cha Rich?’, which emphasizes that one-boxers typically make a million dollars compared to the thousand dollars that two-boxers can expect. A standard reply is the ‘opportunity defence’: the two-boxers who made a thousand never had an opportunity to make more. The paper argues that the opportunity defence is unavailable to anyone who grants that in another case—a Frankfurt case—the agent is deprived of opportunities in the way that advocates of Frankfurt cases typically claim.