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?
You are most welcome! Thank you for reading the series.
The road trip rest stop
Yes, I think this is a very good alternative formulation. I agree that it can feel more intuitive when framed like that, even though I do not hope too much that it will change minds of many people.
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?
You are most welcome! Thank you for reading the series.
Yes, I think this is a very good alternative formulation. I agree that it can feel more intuitive when framed like that, even though I do not hope too much that it will change minds of many people.