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First off, thank you for this series. You've thoroughly dissolved the paradox for me. I was initially a thirder despite suspicions about Elga's original argument (he seemed to equivocate between being awakened in general and being first awakened/awakened on Monday), because the probabilities for Lewis' halfer argument (the 1/2, 1/4, 1/4 split) made no sense no matter how I did the math. I now understand that both sides were making the same error in their models, and that while the thirder position is correctly measuring something, it's not your credence in the coin landing heads.
Second, as I was thinking about this solution, I came up with an isomorphic problem that might better clarify the key insight of Tails&Monday and Tails&Tuesday being the same event. I don't think it's worth a whole post, but I'd like your thoughts on it.
The road trip rest stop
You and a friend are taking a late night road trip from Townsburg to Cityville to catch a concert. Your friend graciously offers to drive the whole way, so you decide to go to sleep.
Before departing, your friend tells you that he'd like to stop at rest stops A and B on the way, but if the traffic out of Townsburg is congested (which you expect at a 50% chance), he'll only have time to stop at A. Either way, he promises to wake you up at whatever rest stop(s) he stops at.
You're so tired that you fall asleep before seeing how the traffic is, so you don't know which rest stops your friend is going to stop at.
Some time during the night, your friend wakes you up at a rest stop. You're groggy enough that you don't know if you've been woken up for another rest stop previously, and it's too dark to tell whether you're at A or B. At this point, what is your credence that the traffic was bad?
and have no particular reason to think those people are very unusual in terms of cooking-skill
Yeah, that's what I was trying to get at with the typical-friend-group stuff. The people you know well aren't a uniform sample of all people, so you have no reason to conclude that their X-skill is normal for any arbitrary X.
The problem (or maybe just my problem) is that when I say "average" it feels like it's activating my concept of "mathematical concept of sum/count", even though the actual thing I'm thinking of is "typical member of class extracted from my mental model". I find myself treating "average" as if it came from real data even if it didn't.
(including just using the default settings, or uninstalling the app and choosing an easier one).
I feel like this was meant to be in jest, but if you were serious: my goal was to beat the stage with certain self-imposed constraints, so relaxing those constraints would've defeated the purpose of the exercise.
Anyways, it wasn't my friend's specific change that was surprising, it was the fact that he had come up with an optimization at all. My strategy was technically viable but incredibly tedious, and even though I knew it was tedious I was planning on trying it as-is anyways. It was like I was committed to eating a bowl of soup with a fork and my friend pointed out the existence of spoons. The big realization was that I had a dumb strategy that I (on some level) knew was dumb, but I didn't have the "obvious" next thought of trying to make it better.