Ihor Kendiukhov

Strategy calibration.

The optimal strategy, the Kelly fraction, or more generally whatever the agonic mapping prescribes, depends on the probabilities.

When probabilities are known, you can tune your bet size precisely and achieve the optimal time average growth rate.

When probabilities are ambiguous, you cannot.

The Kelly criterion is uniquely optimal.

Any deviation from the correct Kelly fraction, whether you bet too aggressively or too conservatively, strictly reduces the time average growth rate.

If the true probability of black is 1 sixth and you bet as if it were 1 third, you are overbetting and your growth rate suffers.

If the true probability is 1 half and you bet as if it were 1 third, you are underbetting and your growth rate also suffers, less dramatically but still measurably.

Regardless of what the true probability turns out to be, as long as it differs from your point estimate, your trajectory-level performance is strictly worse than what you could have achieved with known probabilities.

So the agent who prefers known probabilities is, in effect, saying, I want to be able to optimize my strategy for the actual stochastic process I am embedded in, and I can only do that if I know the parameters of that process.

Heading.

How LessWrong has engaged with this.

The LessWrong community has discussed the independence axiom and related questions multiple times over the past 15 years, and the landscape is instructive.

The pieces are mostly there.

The right questions have been asked, the right concerns have been raised, and in one remarkable comment, the right conclusion has been stated almost verbatim.

But the pieces have never been assembled into a unified argument.

Subheading.

Armstrong's expected utility without the independence axiom, 2009.

Stuart Armstrong's post is, to my knowledge, the earliest serious treatment of dropping independence on less wrong, and it gets a lot right.

Armstrong correctly identifies independence as the most controversial VNM axiom and explores what kind of decision theory remains when you drop it.