Abstract - What this essay does and does not cover

This essay attempts a resolution to Newcomb’s problem in the case of a perfect predictor (aka limit case). The essay does give a solution, but the goal of this essay is more ambitious.

The goal is that a supporter of 1-boxing, a supporter of 2-boxing, and any undecided people would all unanimously come to an agreement with the conclusion of this essay (if they read it through and follow the argument). To that end, separate sections “Focusing on the source of confusion in Newcomb’s Problem with Perfect Predictor” and a section of illustrative examples are given . However, this essay follows a chronological order and skipping any section, besides the introduction and the final section with illustrative examples, is unadvised.

I argue that in the perfect predictor case, the apparent disagreement between 1-boxers and 2-boxers emerges from an incorrect placement of the decision node of the agent. The classical framing of the problem conflates a deterministic execution node with a decision node. Once this is recognized the source of the disagreement between 1-boxers and 2-boxers is dissolved.

After reading this essay, there are still two questions where readers might disagree. They are as follows:

Do humans have absolute free will?
Can humans voluntarily choose what to believe and what not to believe?

These are relevant questions. However, they are not questions about decision theory. They do not deal with maximization of utility under set circumstances. This essay aims to resolve Newcomb’s problem with a perfect predictor as a decision theory problem. If the reader finds that this essay has reduced the problem from a decision theory problem to a problem entirely about free will and belief formation, then I shall consider the aim of this essay to have been accomplished.

Introduction

While Newcomb’s problem is widely known, it is still helpful to look at the exact statement of the problem to make sure we are on the same page.

Let’s consider the version from Newcomb’s Problem and Regret of Rationality

A superintelligence from another galaxy, whom we shall call Omega, comes to Earth and sets about playing a strange little game. In this game, Omega selects a human being, sets down two boxes in front of them, and flies away.
Box A is transparent and contains a thousand dollars.
Box B is opaque, and contains ei

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