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No, introducing the concept of "indexical sample space" does not capture the thirder position, nor language.

And what does it not capture in thirder position, in your opinion? 

You do not need to introduce a new type of space, with new definitions and axioms. The notion of credence (as defined in the Sleeping Beauty problem) already uses standard mathematical probability space definitions and axioms.

So thirder think. But they are mistaken, as I show in the previous posts.

Thirder credence fits the No-Coin-Toss problem where Monday and Tuesday don't happen during the same iteration of the experiment and on awakening the person indeed learns that "they are awaken Today", which can be formally expressed as an event $MondayxorTuesday$.

Not so with Sleeping Beauty, where the participant completely aware that Monday awakening on Tails is followed by Tuesday awakening, therefore, event $MondayxorTuesday$ doesn't happen in 50% cases, so instead of learning that the Beauty is awakened today she can only learn that she is awakened at least once.

In Sleeping Beauty problem being awakened Today isn't a thing you can express via probability space. It's something that can happen twice in the same iteration of the experiment, just like getting a ball in the example from the post. And so we need a new mathematical model to formally talk about this sort of things, therefore weighted probability space.

I suppose you've read all my posts on the topic. What is the crux of our disagreement here?

Really interesting! I particularly liked the part on reading out loud: even though I’d heard it used to be more common (and that there’s even a French 19th c. novelist who had set up a specific ‘shouting room’ in his garden for shouting his texts out loud and see if they sounded good), but I’d never actually noticed it had so many advantages. Maybe I should do it more. Heck, it might even help me stay focused more easily on what I read?

I see there might be limits to what is possible.

On the other hand, I have the impression often the limits to what the students can learn (in economics) come more from us teaching in absurdly simplified cases too remote from reality and from what's plausible so that the entire thing we teach remains a purely abstract empty analytical beast. While I only guess even young ones are capable of understanding the more subtle mechanisms - in their few individual steps often not really complicated! - if only we taught them with enough empathy for the students & for the reality we're trying to model.

As you write, with as little math as absolutely necessary.

I’m confused: if the dating apps keep getting worse, how come nobody has come up with a good one, or at least a clone of OkCupid? Like, as far as I can understand not even “a good matching system is somehow less profitable than making people swipe all the time (surely it’d still be profitable on the absolute scale)” or “it requires a decently big initial investment” can explain a complete lack of good products in a very demanded area. Has anyone digged into it / tried to start a good dating app as a summer project?

Yeah, that's my understanding as well.

But does the probability decrease fast enough?

The LessWrong Review [? · GW] runs every year to select the posts that have most stood the test of time. This post is not yet eligible for review, but will be at the end of 2024. The top fifty or so posts are featured prominently on the site throughout the year. Will this post make the top fifty?

The problem with something like e.g. funding applications is that unless deep honesty (which I agree would lead to the best outcomes!) is actively rewarded, then whoever is that honest ends up being a sucker who loses to those who express more confidence, even if unwarranted. This in fact I'd say is a big problem with funding and investments, because the shallowness of the honesty required (in fact, the encouragement of all sorts of truth twisting this side of outright lying) creates a situation in which it's very easy for people to slide directly into fraud or at least delusion about their own prospects as soon as things go awry.

You can "bookmark" a post, is that equivalent to your desired "read later"?

Ok, then I agreed. I was interpreting the advice in a different way, but your interpretation looks more reasonable.