Decision Theories: A Semi-Formal Analysis, Part II
Or: Causal Decision Theory and Substitution
Previously:
0. Decision Theories: A Less Wrong Primer
1. The Problem with Naive Decision Theory
Summary of Post: We explore the role of substitution in avoiding spurious counterfactuals, introduce an implementation of Causal Decision Theory and a CliqueBot, and set off in the direction of Timeless Decision Theory.
In the last post, we showed the problem with what we termed Naive Decision Theory, which attempts to prove counterfactuals directly and pick the best action: there's a possibility of spurious counterfactuals which lead to terrible decisions. We'll want to implement a decision theory that does better; one that is, by any practical definition of the words, foolproof and incapable of error...

I know you're eager to get to Timeless Decision Theory and the others. I'm sorry, but I'm afraid I can't do that just yet. This background is too important for me to allow you to skip it...
Over the next few posts, we'll create a sequence of decision theories, each of which will outperform the previous ones (the new ones will do better in some games, without doing worse in others0) in a wide range of plausible games.
Newcomb's problem happened to me
Okay, maybe not me, but someone I know, and that's what the title would be if he wrote it. Newcomb's problem and Kavka's toxin puzzle are more than just curiosities relevant to artificial intelligence theory. Like a lot of thought experiments, they approximately happen. They illustrate robust issues with causal decision theory that can deeply affect our everyday lives.
Yet somehow it isn't mainstream knowledge that these are more than merely abstract linguistic issues, as evidenced by this comment thread (please no Karma sniping of the comments, they are a valuable record). Scenarios involving brain scanning, decision simulation, etc., can establish their validy and future relevance, but not that they are already commonplace. For the record, I want to provide an already-happened, real-life account that captures the Newcomb essence and explicitly describes how.
So let's say my friend is named Joe. In his account, Joe is very much in love with this girl named Omega… er… Kate, and he wants to get married. Kate is somewhat traditional, and won't marry him unless he proposes, not only in the sense of explicitly asking her, but also expressing certainty that he will never try to leave her if they do marry.
Now, I don't want to make up the ending here. I want to convey the actual account, in which Joe's beliefs are roughly schematized as follows:
- if he proposes sincerely, she is effectively sure to believe it.
- if he proposes insincerely, she will 50% likely believe it.
- if she believes his proposal, she will 80% likely say yes.
- if she doesn't believe his proposal, she will surely say no, but will not be significantly upset in comparison to the significance of marriage.
- if they marry, Joe will 90% likely be happy, and will 10% likely be unhappy.
He roughly values the happy and unhappy outcomes oppositely:
- being happily married to Kate: 125 megautilons
- being unhapily married to Kate: -125 megautilons.
So what should he do? What should this real person have actually done?1 Well, as in Newcomb, these beliefs and utilities present an interesting and quantifiable problem…
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