I also use a simple version of this, with a key extra step at the end:
1) have a decision you are unsure about.
2) perform randomisation (I usually just use a coin).
3) notice how the outcome makes you feel. If you find that you wish the coin landed the other way, override the decision and do what you secretly wanted to do all along.
You might think the third step defeats the purpose of the exercise, but so long as you actually commit to following the randomisation most of the time, it gives you direct access to very useful information. It also sets up the right incentive, wherein you never really need to work your willpower against your desires (except, I guess, the desire to deliberate more).
I mostly use this for a slightly different use case – inconsequential decisions like where to eat or small purchases, where taking a lot of time to optimise isn’t worth it. Your mileage may vary with more important decisions, but I see no reason in principle this couldn’t work.
I agree. That’s what I meant when I wrote there will be TMs that artificially promote S itself. However, this would still mean that most of S’s mass in the prior would be due to these TMs, and not due to the natural generator of the string.
Furthermore, it’s unclear how many TMs would promote S vs S’ or other alternatives. Because of this, I don’t now whether the prior would be higher for S or S’ from this reasoning alone. Whichever is the case, the prior no longer reflects meaningful information about the universe that generates S and whose inhabitants are using the prefix to choose what to do; it’s dominated by these TMs that search for prefixes they can attempt to influence.
I agree that this probably happens when you set out to mess with an arbitrary particular S, I.e. try to make some S’ that shares a prefix with S as likely as S.
However, some S are special, in the sense that their prefixes are being used to make very important decisions. If you, as a malicious TM in the prior, perform an exhaustive search of universes, you can narrow down your options to only a few prefixes used to make pivotal decisions, selecting one of those to mess with is then very cheap to specify. I use S to refer to those strings that are the ‘natural’ continuation of those cheap-to-specify prefixes.
There are, it seems to me, a bunch of other equally-complex TMs that want to make other strings that share that prefix more likely, including some that promote S itself. What the resulting balance looks like is unclear to me, but what’s clear is that the prior is malign with respect to that prefix—conditioning on that prefix gives you a distribution almost entirely controlled by these malign TMs. The ‘natural’ complexity of S, or of other strings that share the prefix, play almost no role in their priors.
The above is of course conditional on this exhaustive search being possible, which also relies on there being anyone in any universe that actually uses the prior to make decisions. Otherwise, we can’t select the prefixes that can be messed with.
The trigger sequence is a cool idea.
I want to add that the intended generator TM also needs to specify a start-to-read time, so there is symmetry there. Whatever method a TM needs to use to select the camera start time in the intended generator for the real world samples, it can also use in the simulated world with alien life, since for the scheme to work only the difference in complexity between the two matters.
There is additional flex in that unlike the intended generator, the reasoner TM can sample its universe simulation at any cheaply computable interval, giving the civilisation the option of choosing any amount of thinking they can perform between outputs, if they so choose.