Ihor Kendiukhov

The CS interpretation cannot accommodate this, because the whole point of CS is that independence violations are contextually negligible, and in the cases that matter for EE and for real-world sequential decision-making, they are anything but.

Subheading Fallenstein's Why You Must Maximize Expected Utility, 2012

Benja Fallenstein's post is the most rigorous and carefully argued defense of expected utility maximization on LessWrong, and it is the one that most directly claims what the title says.

That you must maximize expected utility.

If the argument of this article is correct, Fallenstein's post is where the disagreement is sharpest.

Fallenstein's setup is this.

You have a genie, a perfect Bayesian AI, that must choose among possible actions on your behalf.

The Genie comprehends the set of all possible Vagiant lookup tables, complete plans specifying what to do in every conceivable situation, and selects the one that best satisfies your preferences.

Preferences are defined over outcomes, which are data structures containing all and only the information about the world that matters to your terminal values.

The Genie evaluates probability distributions over these outcomes.

Within this setup, Fallenstein argues for independence by analogy with conservation of expected evidence.

He writes, the axiom of independence is equivalent to saying that if you're evaluating a possible course of action, and one experimental result would make it seem more attractive than it currently seems to you, while the other experimental result would at least make it seem no less attractive, then you should already be finding it more attractive than you do.

He then addresses the parent-coin counterexample by arguing that if you care about the randomization mechanism, this should already be encoded in the outcome, not in the preference over lotteries.

This is a strong argument, and it is correct within its setup.

If you accept the timeless genie framing, where a perfect Bayesian evaluates all possible world history simultaneously and chooses among complete plans from a God's eye view, then independence is very nearly trivially true.

The genie faces a single, static decision over probability distributions.

There is no temporal sequence, no compounding, no intermediate node at which the genie might re-evaluate.

The genie simply picks the best plan, and the best plan is the one whose probability distribution over outcomes ranks highest.

In this setting, asking whether the common component should influence the evaluation is like asking whether an irrelevant column in a spreadsheet should affect which row you pick.

Obviously not, because you're evaluating the whole row at once.