# Transparent Newcomb Problem: Decision Theory Unpacked

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## Chapter 1: Understanding the Transparent Newcomb Problem

In this chapter, we delve into a scenario akin to Newcomb's Problem, but with a twist: Box B is already open. Omega states:

"I have anticipated whether you will choose to take the contents of Box A alone or both boxes upon discovering that Box B holds $1,000,000. If I predicted you would opt for only Box A, leaving the $1,000 from Box A, I placed $1,000,000 in Box B. Conversely, if I predicted you would take both boxes, then Box B remains empty."

Upon examining Box B, you find it contains $1,000,000. Given Omega's remarkable predictive ability, should you opt for only Box A or take both?

### Section 1.1: The Dilemma of Choice

In this scenario, Carl and Eve agree on the decision: you should opt for both boxes. Carl argues that the choice of one box or two does not influence the contents of Box B. Eve reinforces this by noting that the presence of $1,000,000 in Box B serves as compelling evidence of its existence.

What is Fiona's stance? From a subjunctive perspective, the situation hasn't changed much from the original Newcomb's Problem. Your decision unfolds at two distinct moments: first, in Omega's mind, and second, during your own choice.

If you choose to take only Box A, Omega predicts that you will do so, leading to $1,000,000 in Box B. However, if you decide to take both, she anticipates that as well, resulting in an empty Box B.

But here's the twist: you already see $1,000,000 in Box B. Choosing both boxes now cannot alter that fact! True, the intricacies of subjunctive dependence are intriguing. However, the evidence before you is undeniable.

This raises a critical contradiction: the problem states that you see $1,000,000 in Box B, yet asserts that Omega only placed it there if she predicted you would choose just one box. Given Omega's near-perfect predictions, it implies that $1,000,000 would not be in Box B if you chose both.

### Section 1.2: Resolving the Contradiction

This contradiction can be approached in two distinct ways.

The first resolution centers on the first point: you observe $1,000,000 in Box B, which has implications. If that amount is present, it indicates Omega placed it there, meaning she predicted you would choose only Box A.

So what does this imply? Remember the idea of subjunctive dependence. If Omega predicted you'd take only Box A and her predictions are highly accurate, it follows that you will indeed choose only Box A. The problem could be simplified to:

"Omega shows you two transparent boxes, A and B. She has placed $1,000 in Box A and $1,000,000 in Box B. You see that she predicted you will take only Box A, leading you to choose it and receive $1,000,000."

While this interpretation resolves the dilemma, it renders the problem rather mundane, eliminating any real decision-making.

The second approach emphasizes the second point: Omega only placed $1,000,000 in Box B if she predicted you would opt for just one box. Thus, if you choose only Box A, you see $1,000,000 in Box B, but if you select both boxes, it remains empty.

This perspective, albeit more unconventional, remains equally valid and preserves the intrigue of the problem, as it involves an actual decision. The correct choice, consistent with the original Newcomb's Problem, is to take only Box A.

Both interpretations lead to the same conclusion: the optimal decision is to choose just one box.

Another way to comprehend this resolution is to ponder: Would you prefer to be a one-box chooser or a two-box chooser in a scenario involving the Transparent Newcomb Problem?

If you lean towards one box, then encountering this problem leads Omega to predict your choice, resulting in $1,000,000 in Box B. Conversely, if you are a two-box chooser, Omega leaves Box B empty.

This means that two-boxers never see $1,000,000 in Box B! The scenario describedâ€”where you see $1,000,000 in Box Bâ€”becomes irrelevant for two-boxers. It's an impossible situation for them! Carl and Eve may decide to take both boxes in such a scenario, but they will never find themselves in it.

## Chapter 2: Insights from Decision Theory

The first video, "GAME THEORY: The Pinnacle of Decision Making," explores the intricacies of decision-making strategies and their implications in various scenarios, further illuminating concepts discussed in this chapter.

The second video, "What Were You Thinking? Decision Theory as Coherence Test - Prof. Itzhak Gilboa," delves into the coherence of decision-making processes, providing valuable insights relevant to the Transparent Newcomb Problem.

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