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JenniferRM comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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This chapter showed that, if it appears that a Time Turner wasn't used, they don't try to use it. Presumably, the reverse is also true. If it appears that it is used, they use it.
I've always figured that the rules deciding which stable time loop were something along the lines of the more likely it is for an event to cause itself, the more likely it is that one happens. If you want a specific time loop to happen, such as giving yourself a paper that factors a given semiprime, you'd make it so that happening causes itself, by copying down the factors if they are correct, and make it so it not happening causes a paradox, by writing something else down. This way, a high portion of time loops are the ones you like.
That can't happen here. They try to cause whatever happened. This means that any stable time loop that isn't too difficult to carry out is equally likely to work. It's implied that there's some sort of force at work here. While it's conceivable that most of the stable time loops with Harry factoring a semiprime were in the same reference class as "DON'T MESS WITH TIME TRAVEL", Dumbledore later managed to use the effect to gain actual information: the time travel he was about to attempt shouldn't be attempted. What's interesting here, though, is that it seems to imply that this force isn't just something that manifests when they do something wrong. It always chooses the time loop. Or more accurately, the rules that I had assumed worked whenever someone wasn't messing with time travel never work. The theory was completely wrong, instead of being something that breaks down under odd circumstances.
And I still wonder: why did the force let Harry do everything he ever wanted to do with time travel before, but then stop him now.
That force just made a very dangerous move. Perhaps it's not trying to do anything like paradox avoidance, as the "DON'T MESS WITH TIME TRAVEL" suggested. Perhaps it's trying to avoid all future paradoxes, by making Harry end the world. I've read about one story where attempting to abuse time travel resulted in the sun going nova. This is might be the same idea, but on a larger scale.
Back in the story's early days I predicted that prime factoring wouldn't work, because then the story wouldn't be about rationality any more... it would be about time travel. If my theory and your theory are syncretized then "the force" here is simply "Eliezer's plot generation efforts which will output a story consistent with his broader authorial intent".
In this model, the way the characters might be able to choice-fully manipulate "the force that chooses time loops" to give them what they want is by being genre savvy enough to have their planning process be the one that functions as a positive example of science informed x-rationality leading to good outcomes, and the stable time loops that come into existence won't be super dramatic, but they will helpfully nudge them closer to x-rationality-demonstrating victories. Harry's unlocked time turner (as of Chapter 90) becomes more interesting in this light.
However, it seems like there's an element of irony in this framing, because there is almost no scientific evidence that I'm aware of in the heuristics and biases literature (nor inspirational essays in Eliezer's sequences) that the skill of genre-savvy-ness is useful in real life. On the downside I've heard that keeping a diary may have a causal role in depression. On the upside I've also heard that reading more novels than normal tends to give people better "other human modeling" skills that can translate into higher salaries. But neither of these sorts of prosaic angles seem central to LW culture?
In a sense, this goes without saying. All stories run on narrative causality. However, part of what makes a story interesting is that it follows consistent laws. There's no drama in a cliffhanger if gravity isn't here to stay. Similarly, the time loops are much more interesting if they're controlled by the characters' intents and abilities, rather than directly based on what fits the plot.
If it's not useful, then that just means that you're wrong genre savvy.