> Imagine that you’re at the Institute for sleeping beauty studies, and thousands of beauties, beaus and gender non-specific beautiful people are put through this experiment every week. There are two types of people- people who always say 2/3 and people who always say 1/2. Note that overall, the people who say 2/3 every time they are woken up will be in the heads condition upon that waking event… two-thirds of the time.
(Apologies, I haven't read up on this at all, so I'm probably making mistakes or repeating things said elsewhere, or both.)
I'm inclined to take the most boring road and dispute the wording. :-\ If 2000 people are put into the study (with a non-quantum coin), then about 1000 people will wake up in the heads condition and about 1000 in the tails condition. Those in the heads case will respond to the question twice and those in the tails case will respond to it once.
So if we're averaging across people (in a sense involving a consistent identity across time), then the people who answer 1/2 will have better average Brier scores (0.25 vs 0.278). But if we're averaging across responses to the question (or across "people" in a sense involving only experiential mind-moments), then the responses saying 2/3 will have better average Brier scores (0.222 vs 0.25).
I suspect the quantum case is easier to think about mainly because it suppresses the intuition of a consistent identity across time.
Here’s a series of posts going into detail on anthropic problems and analyzing different approaches to them: https://www.lesswrong.com/posts/RnrpkgSY8zW5ArqPf/sia-greater-than-ssa-part-1-learning-from-the-fact-that-you
This series presents lots of interesting anthropic situations, and (if you like thinking about this kind of thing) should be quite fun to read.
Hello Ursus Philisophicus,
I just wanted to say I really appreciate your newsletterblog. It's always interesting, and almost always intelligible even to an idiot like myself.
Also, I love that picture of the sleeping bear! AI I assume?
Thanks
Yes! Midjourney. A sleeping Bearty.
> Imagine that you’re at the Institute for sleeping beauty studies, and thousands of beauties, beaus and gender non-specific beautiful people are put through this experiment every week. There are two types of people- people who always say 2/3 and people who always say 1/2. Note that overall, the people who say 2/3 every time they are woken up will be in the heads condition upon that waking event… two-thirds of the time.
(Apologies, I haven't read up on this at all, so I'm probably making mistakes or repeating things said elsewhere, or both.)
I'm inclined to take the most boring road and dispute the wording. :-\ If 2000 people are put into the study (with a non-quantum coin), then about 1000 people will wake up in the heads condition and about 1000 in the tails condition. Those in the heads case will respond to the question twice and those in the tails case will respond to it once.
So if we're averaging across people (in a sense involving a consistent identity across time), then the people who answer 1/2 will have better average Brier scores (0.25 vs 0.278). But if we're averaging across responses to the question (or across "people" in a sense involving only experiential mind-moments), then the responses saying 2/3 will have better average Brier scores (0.222 vs 0.25).
I suspect the quantum case is easier to think about mainly because it suppresses the intuition of a consistent identity across time.