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This is one of the worst comments I've seen on LessWrong and I think the fact that this is being upvoted is disgraceful. (Note: this reply refers to a comment that has since been deleted.)
This note is for readers who are unfamiliar with The_Lion:
This user is a troll who has been banned multiple times from Less Wrong. He is unwanted as a participant in this community, but we are apparently unable to prevent him from repeatedly creating new accounts. Administrators have extensive evidence for sockpuppetry and for abuse of the voting system. The fact that The_Lion's comment above is heavily upvoted is almost certainly entirely due to sockpuppetry. It does not reflect community consensus
Cloud Atlas is my favorite movie ever and I recommend it to anyone reading this. In fact, it is my opinion that it is one of the most important pieces of early 21st century art.
The downvote is however not for your bad taste in movies, but for intentionally misgendering Lana. More generally, you can consider it payback for your efforts to make Less Wrong an unwelcoming place. I care about this community, and you are doing your best to break it.
At this stage, I call for an IP ban.
As expected, my karma fell by 38 points and my "positive percentage" fell from 97% to 92% shortly after leaving this comment
Lana Wachowski.
Has he done anything impressive since transitioning? Really since the first Matrix movie?
Cloud Atlas is my favorite movie ever and I recommend it to anyone reading this. In fact, it is my opinion that it is one of the most important pieces of early 21st century art.
The downvote is however not for your bad taste in movies, but for intentionally misgendering Lana. More generally, you can consider it payback for your efforts to make Less Wrong an unwelcoming place. I care about this community, and you are doing your best to break it.
At this stage, I call for an IP ban.
In response to
comment
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on
Map:Territory::Uncertainty::Randomness – but that doesn’t matter, value of information does.
Generally if you approach probability as an extension of logic, probability is always relative to some evidence. Hardcore frequency dogmatists like John Venn for example thought that this is completely wrong: "the probability of an event is no more relative to something else than the area of a field is relative to something else."
So thinking probabilities existing as "things itself" taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities. Lets say I take HIV-test and it comes back positive. You dont find it weird to say that it is not OK to judge probabilities of me having the HIV based on that evidence?
In response to
comment
by
on
Map:Territory::Uncertainty::Randomness – but that doesn’t matter, value of information does.
So thinking probabilities existing as "things itself" taken to the extreme could lead one to the conclusion that one cant say much for example about single-case probabilities.
Thinking probabilities can exists in the territory leads to no such conclusion. Thinking probabilities exist only in the territory may lead to such a conclusion, but that is a strawman of the points that are being made.
It would be insane to deny that frequencies exist, or that they can be represented by a formal system derived from the Kolmogorov (or Cox) axioms.
It would also be insane to deny that beliefs exist, or that they can be represented by a formal system derived from the Kolmogorov (or Cox) axioms.
I think this confusion would all go away if people stopped worrying about the semantic meaning of the word "probability" and just specified whether they are talking about frequency or belief. It puzzles me when people insist that the formal system can only be isomorphic to one thing, and it is truly bizarre when they take sides in a holy war over which of those things it "really" represents. A rational decision maker genuinely needs both the concept of frequency and the concept of belief.
For instance, an agent may need to reason about the proportion (frequency) P of Everett branches in which he survives if he makes a decision, and also about how certain he is about his estimate of that probability. Let's say his beliefs about the probability P follow a beta distribution, or any other distribution bounded by 0 and 1. In order to make a decision, he may do something like calculate a new probability Q, which is the expected value of P under his prior. You can interpret Q as the agent's beliefs about the probability of dying, but it also has elements of frequency.
You can make the untestable claim that all Everett branches have the same outcome, and therefore that Q is determined exclusively by your uncertainty about whether you will live or die in all Everett branches. This would be Bayesian fundamentalism. You can also go to the other extreme and argue that Q is determined exclusively by P, and that there is no reason to consider uncertainty. That would be Frequentist fundamentalism. However, there is a spectrum between the two and there is no reason we should only allow the two edge cases to be possible positions. The truth is almost certainly somewhere in between.
In general, when you are asked "What is the probability that the coin came up heads" we interpret this as "how much are you willing to pay for a contract that will be worth 1 dollar if the coin came up heads, and nothing if it came up tails"
Nobody who thinks that the probability is at 75% will buy into the prediction market when the prediction market is at 75%.
A better way to phrase it would be to say: "If you are forced to buy a share in the prediction market, the probability of the event is that probability where you don't care which side of the bet you take."
Sure, this is true, thanks for noticing. Sorry about the inaccurate/incorrect wording. It does however not affect the main idea.
In response to
Open Thread, January 11-17, 2016
I finally gave in and opened a Tumblr account at http://dooperator.tumblr.com/ . This open-thread comment is just to link my identity on Less Wrong with my username on websites where I do not want my participation to be revealed by a simple Google search for my name, such as SlateStarCodex and Tumblr.
You can arrange the situation so that the two probabilities are 1/10,000 and 1/2. Then just ask, "Do you think the coin came up heads or tails"? If they say they are not sure, they agree with the halfer position.
In other words, "how sure are you" does mean something besides how much you want to bet.
There is a difference between "How sure are you that if we looked at the coin now, it is heads?" and "How sure are you that if we looked at the coin only once, at the end of the experiment, it is heads?"
In the first variant, the thirder position is unambiguously true.
I the second variant, I suspect that you really need more precision in the words to answer it. I think a halfer interpretation of this question is at least plausible under some definitions of "how sure"
Unless "how sure" refers explicitly to well specified bet, many attempts to define it will end up being circular.
In response to
Variations on the Sleeping Beauty
This post caused me to type up some old, unrelated thoughts about Sleeping Beauty. I posted it as a comment to the stupid questions thread at http://lesswrong.com/lw/n3v/stupid_questions_2nd_half_of_december/d14z . I'd very much appreciate any feedback on this idea. This comment is just to catch the attention of readers interested in Sleeping Beauty who may not see the comment in the stupid questions thread.
In response to
Stupid Questions, 2nd half of December
I have an intuition that I have dissolved the sleeping beauty paradox as semantic confusion about the word "probability". I am aware that my reasoning is unlikely to be accepted by the community, but I am unsure what is wrong with it. I am posting this to the "stupid questions" thread to see if helps me gain any insight either on Sleeping Beauty or on the thought process that led to me feeling like I've dissolved the question.
When the word "probability" is used to describe the beliefs of an agent, we are really talking about how that agent would bet, for instance in an ideal prediction market. However, if the rules of the prediction market are unclear, we may get semantic confusion.
In general, when you are asked "What is the probability that the coin came up heads" we interpret this as "how much are you willing to pay for a contract that will be worth 1 dollar if the coin came up heads, and nothing if it came up tails". This seems straight forward, but in the sleeping beauty problem, the agent may make the same bet multiple times, which introduces ambiguity.
Person 1 may interpret then the question as follows: "Every time you wake up, there is a new one dollar bill on the table. How much are you willing to pay for a contract that gives you the dollar if the coin came up heads?". In this interpretation, you get to keep all the dollars you won throughout the experiment.
In contrast, person 2 may interpret the question as follows "There is one dollar on the table. Every time you wake up, you are given a chance to revise the price you are willing to pay for the contract, but all earlier bets are cancelled such that only the last bet counts". In this interpretation, there is only one dollar to be won.
Person 1 will conclude that the probability is 1/3, and person 2 will conclude that the probability is 1/2. However, once they agree on what bet they are asked to make, the disagreement is dissolved.
The first definition is probably better matched to current usage of the word. This gives most rationalists a strong intuition that the thirder position is "correct". However, if you want to know which definition is most useful or applicable, this really depends on the disguised query, and on which real world scenario the parable is meant to represent. If the payoff utility is only determined once (at the end of the experiment), then the halfer definition could be more useful?
ETA: After reading the Wikipedia:Talk section for Sleeping Beauty, it appears that this idea is not original and that in fact a lot of people have reached the same conclusion. I should have read that before I commented...
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...katydee?
Whoops, my apologies. Thanks for noticing. Corrected