Thirders believe that this awakening should be treated as randomly sampled from three possible awakening states. Halfers believe that this awakening should be treated as randomly sampled from two possible states, corresponding to the result of a coin toss. This is an objective disagreement, that can be formulated in terms of probability theory and at least one side inevitably has to be in the wrong. This is the unresolved issue that we can’t simply dismiss because both sides have a point.
If you make some assumptions about sampling, probability theory will give one answer, with other assumptions probability theory will give another answer. So both can be defended with probability theory, it depends on the sampling assumptions. And there isn’t necessarily any sampling assumption that’s objectively correct here.
By the way I normally agree with thirders in terms of my other assumptions about anthropics, but in the case of Sleeping Beauty since it’s particularly formulated to separate the multiple awakenings from impacting on the rest of the world including the past and future, I think the halfer sampling assumption isn’t necessarily crazy.
If you make some assumptions about sampling, probability theory will give one answer, with other assumptions probability theory will give another answer.
True, but then you may happen to have issues with some of your other assumptions. And in Sleeping Beauty case, as I’m going to show in my next post, indeed there are troubles justifying thirders sampling assumption with other conditions of the setting
So both can be defended with probability theory, it depends on the sampling assumptions. And there isn’t necessarily any sampling assumption that’s objectively correct here.
Not neccessarily. But still possible. And this is a direction that needs to be properly explored.
By the way I normally agree with thirders in terms of my other assumptions about anthropics, but in the case of Sleeping Beauty since it’s particularly formulated to separate the multiple awakenings from impacting on the rest of the world including the past and future, I think the halfer sampling assumption isn’t necessarily crazy.
I’m giving you a strong upvote for this. It’s rare to find a person who notices that Sleeping Beauty is quite different from other “antropic problems” such as incubator problems.
And in Sleeping Beauty case, as I’m going to show in my next post, indeed there are troubles justifying thirders sampling assumption with other conditions of the setting
I look forward to seeing your argument.
I’m giving you a strong upvote for this. It’s rare to find a person who notices that Sleeping Beauty is quite different from other “antropic problems” such as incubator problems.
Thanks! But I can’t help but wonder if one of your examples of someone who doesn’t notice is my past self making the following comment (in a thread for one of your previous posts) which I still endorse:
I certainly agree that one can have philosophical assumptions such that you sample differently for Sleeping Beauty and Incubator problems, and indeed I would not consider the halfer position particularly tenable in Incubator, whereas I do consider it tenable in Sleeping Beauty.
But … I did argue in that comment that it is still possible to take a consistent thirder position on both. (In the comment I take the thirder position for sleeping beauty for granted, and argue for it still being possible to apply to Incubator (rather than the other way around, despite being more pro-thirder for Incubator), specifically to rebut an argument in that earlier post of yours that the classic thirder position for Sleeping Beauty didn’t apply to Incubator).
Some clarification of my actual view here (rather than my defense of conventional thirderism):
In my view, sampling is not something that occurs in reality, when the “sampling” in question includes sampling between multiple entities that both exist. Each of the entities that actually exists actually exists, and any “sampling” between multiple of such entities occurs (only) in the mind of the observer. (However, can still mix with conventional sampling, in the mind of the observer). Which sampling assumption you use in such cases is in principle arbitrary but in practice should probably be based on how much you care about the correctness of the beliefs of each of the possible entities you are uncertain about being.
Halferism or thirderism for Sleeping Beauty are both viable, in my view, because one could argue for caring equally about being correct at each awakening (resulting in thirderism) or one could argue for caring equally about being correct collectively in the awakenings for each of the coin results (resulting in halferism). There isn’t any particular “skin in the game” to really force a person to make a commitment here.
If you make some assumptions about sampling, probability theory will give one answer, with other assumptions probability theory will give another answer. So both can be defended with probability theory, it depends on the sampling assumptions. And there isn’t necessarily any sampling assumption that’s objectively correct here.
By the way I normally agree with thirders in terms of my other assumptions about anthropics, but in the case of Sleeping Beauty since it’s particularly formulated to separate the multiple awakenings from impacting on the rest of the world including the past and future, I think the halfer sampling assumption isn’t necessarily crazy.
True, but then you may happen to have issues with some of your other assumptions. And in Sleeping Beauty case, as I’m going to show in my next post, indeed there are troubles justifying thirders sampling assumption with other conditions of the setting
Not neccessarily. But still possible. And this is a direction that needs to be properly explored.
I’m giving you a strong upvote for this. It’s rare to find a person who notices that Sleeping Beauty is quite different from other “antropic problems” such as incubator problems.
I look forward to seeing your argument.
Thanks! But I can’t help but wonder if one of your examples of someone who doesn’t notice is my past self making the following comment (in a thread for one of your previous posts) which I still endorse:
https://www.lesswrong.com/posts/HQFpRWGbJxjHvTjnw/anthropical-motte-and-bailey-in-two-versions-of-sleeping?commentId=dkosP3hk3QAHr2D3b
I certainly agree that one can have philosophical assumptions such that you sample differently for Sleeping Beauty and Incubator problems, and indeed I would not consider the halfer position particularly tenable in Incubator, whereas I do consider it tenable in Sleeping Beauty.
But … I did argue in that comment that it is still possible to take a consistent thirder position on both. (In the comment I take the thirder position for sleeping beauty for granted, and argue for it still being possible to apply to Incubator (rather than the other way around, despite being more pro-thirder for Incubator), specifically to rebut an argument in that earlier post of yours that the classic thirder position for Sleeping Beauty didn’t apply to Incubator).
Some clarification of my actual view here (rather than my defense of conventional thirderism):
In my view, sampling is not something that occurs in reality, when the “sampling” in question includes sampling between multiple entities that both exist. Each of the entities that actually exists actually exists, and any “sampling” between multiple of such entities occurs (only) in the mind of the observer. (However, can still mix with conventional sampling, in the mind of the observer). Which sampling assumption you use in such cases is in principle arbitrary but in practice should probably be based on how much you care about the correctness of the beliefs of each of the possible entities you are uncertain about being.
Halferism or thirderism for Sleeping Beauty are both viable, in my view, because one could argue for caring equally about being correct at each awakening (resulting in thirderism) or one could argue for caring equally about being correct collectively in the awakenings for each of the coin results (resulting in halferism). There isn’t any particular “skin in the game” to really force a person to make a commitment here.