One useful definition of Bayesian vs Frequentist that I've found is the following. Suppose you run an experiment; you have a hypothesis and you gather some data.
I'm not sure whether this view holds up to criticism, but if so, I sure find the latter much more interesting than the former.
This has been the most fun, satisfying survey I've ever been part of :) Thanks for posting this. Can't wait to see the results!
One question I'd find interesting is closely related to the probability of life in the universe. Namely, what are the chances that a randomly sampled spacefaring lifeform would have an intelligence similar enough to ours for us to be able to communicate meaningfully, both in its "ways" and in general level of smarts, if we were to meet.
Given that I enjoyed taking part in this, may I suggest that more frequent and in-depth surveys on specialized topics might be worth doing?
Maybe we've finally reached the point where there's no work left to be done
If so, this is superb! This is the end goal. A world in which there is no work left to be done, so we can all enjoy our lives, free from the requirement to work.
The thought that work is desirable has been hammered into our heads so hard that it's a really, really dubious proposition that actually a world where nobody has to work is the ultimate goal. Not one in which everyone works. That world sucks. That's world in which 85% of us live today.
I've first read this about two years ago and it has been an invaluable tool. I'm sure it has saved countless hours of pointless arguments around the world.
When I realise that an inconsistency in how we interpret a specific word is a problem in a certain argument and apply this tool, it instantly transforms arguments which actually are about the meaning of the word to make them a lot more productive (it turns out it can be unobvious that the actual disagreement is about what a specific word means). In other cases it just helps get back on the right track in...
Addressed by making a few edits to the "Solution" section. Thank you!
All fair points. I did want to post this to main, but decided against it in the end. Didn't know I could move it to main afterwards. Will work on the title, after I've fixed the error pointed out by VincentYu.
I've reviewed the language of the original statement and it seems that the puzzle is set in essentially the real world with two major givens, i.e. facts in which you have 100% confidence.
Given #1: Omega was correct on the last 100 occurrences.
Given #2: Box B is already empty or already full.
There is no leeway left for quantum effects, or for your choice affecting in any way what's in box B. You cannot make box B full by consciously choosing to one-box. The puzzle says so, after all.
If you read it like this, then I don't see why you would possibly one-box....
I'm not sure I understand correctly, but let me phrase the question differently: what sort of confidence do we have in "99.9%" being an accurate value for Omega's success rate?
From your previous comment I gather the confidence is absolute. This removes one complication while leaving the core of the paradox intact. I'm just pointing out that this isn't very clear in the original specification of the paradox, and that clearing it up is useful.
To explain why it's important, let me indeed think of an AI like hairyfigment suggested. Suppose someone sa...
While I disagree that one-boxing still wins, I'm most interested in seeing the "no future peeking" and the actual Omega success rate being defined as givens. It's important that I can rely on the 99.9% value, rather than wondering whether it is perhaps inferred from their past 100 correct predictions (which could, with a non-negligible probability, have been a fluke).
To expand a bit on the first paragraph, I feel that such reasonable arguments are to many people about the same as the proof of Poincaré conjecture is to me: I fully understand the proposition, but I'm not nearly smart enough to follow the proof sufficiently well to be confident it's right.
Importantly, I can also follow the outline of the proof, to see how it's intended to work, but this is of course insufficient to establish the validity of the proof.
So the only real reason I happen to trust this proof is that I already have a pre-established trust in the...
I have found that the logical approach like this one works much more rarely than it doesn't, simply because it appears that people can manage not to trust reason, or to doubt the validity of the (more or less obvious) inferences involved.
Additionally, belief is so emotional that even people who see all the logic, and truly seem to appreciate that believing in God is completely silly, still can't rid themselves of the belief. It's like someone who knows household spiders are not dangerous in any way and yet are more terrified of them than, say, an elephant....
Of course I'd argue that the game of life is not an isolated universe if one can toggle cells in it, and if you consider the whole lot then there's nothing supernatural about the process of cells being toggled.
But this is a good example. I asked about what others mean by "supernatural" and this sounds very close indeed!
Sounds like a reasonable way of putting it. So a weapon shooting invisible (to the human eye) bullets would be classified as "supernatural" by someone from the stone age, because to them, killing someone requires direct contact with a visible weapon or projectile, that has appreciable travel time. Right?
Although "hard science" would have to be excluded from this, even though it contains lots of stuff that doesn't obey the same laws as most stuff we see.
I suppose it's not the most concise post I've ever written. Thanks for the feedback!
So from the negative votes I'm guessing that this is not something you guys find appropriate in "discussion"? It would help me as a newcomer if you also suggested what makes it bad :)
Even more important, I think, is the realization that, to decide how much you're willing to bet on a specific outcome, all of the following are essentially the same:
The bottom line is that you don't know what the next value will be, and that's the only thing that matters.
Thanks for this, it really helped.
it doesn't guarantee that we have time, resources, or inclination to actually calculate it
Here's how I understand this point, that finally made things clearer:
Yes, there exists a more accurate answer, and we might even be able to discover it by investing some time. But until we do, the fact that such an answer exists is completely irrelevant. It is orthogonal to the problem.
In other words, doing the calculations would give us more information to base our prediction on, but knowing that we can do the calculation doesn't...
Perhaps - obviously each coin is flipped just once, i.e. Binomial(n=1,p), which is the same thing as Bernoulli(p). I was trying to point out that for any other n it would work the same as a normal coin, if someone were to keep flipping it.
And just as it gets really interesting, that chapter ends. There is no solution provided for stage 4 :/
Bayesianism tells us that there is a unique answer in the form of a probability for the next coin to be heads
I'm obviously new to this whole thing, but is this a largely undebated, widely accepted view on probabilities? That there are NO situations in which you can't meaningfully state a probability?
For example, let's say we have observed 100 samples of a real-valued random variable. We can use the maximum entropy principle, and thus use the normal distribution (whcih is maximal-entropy for unbounded reals). We then use standard methods to estimate popu...
I read this to say that you can't calculate a value that is guaranteed to break even in the long term, because there isn't enough information to do this. (which I tend to agree with)
If I were trying to make a profit then I'd need to know how much to charge for entry. If I could calculate that then yes, I'd offer the bet regardless of how many heads came out of 100 trials.
But this is entirely beside the point; the purpose of this thought experiment is for me to show which parts of bayesianism I don't understand and solicit some feedback on those parts.
In particular, a procedure that I could use to actually pick a break-even price of entry would be very helpful.
You take the evidence, and you decide that you pay X. Then we run it lots of times. You pay X, I pick a random coin and flip it. I pay your winnings. You pay X again, I pick again, etc. X is fixed.
Preferably, let other people play the game first to gather the evidence at no cost to myself.
For the record, this is not permitted.
My take at it is basically this: average over all possible distributions
It's easy to say this but I don't think this works when you start doing the maths to get actual numbers out. Additionally, if you really take ALL possible distributions then you're already in trouble, because some of them are pretty weird - e.g. the Cauchy distribution doesn't have a mean or a variance.
...distribution about which we initially don’t kn
The properties of the pool are unknown to you, so you have to take into account the possibility that I've tuned them somehow. But you do know that the 100 coins I drew from that pool were drawn fairly and randomly.
I have clarified my post to specify that for each flip, I pick a coin from this infinite pool at random. Suppose you also magically know with absolute certainty that these givens are true. Still $10?
This is a good point, and I've pondered on this for a while.
Following your logic: we can observe that I'm not spending all my waking time caring about A (people dying somewhere for some reason). Therefore we can conclude that the death of those people is comparable to mundane things I choose to do instead - i.e. the mundane things are not infinitely less important than someone's death.
But this only holds if my decision to do the mundane things in preference to saving someone's life is rational.
I'm still wondering whether I do the mundane things by rational...
The original description of the problem doesn't mention if you know of Omega's strategy for deciding what to place in box B, or their success history in predicting this outcome - which is obviously a very important factor.
If you know these things, then the only rational choice, obviously and by a huge margin, is to pick only box B.
If you don't know anything other than box B may or may not contain a million dollars, and you have no reasons to believe that it's unlikely, like in the lottery, then the only rational decision is to take both. This also seems to...
I don't know. I don't suppose you claim to know at which point the number of dust specks is small enough that they are preferable to 50 years of torture?
(which is why I think that Idea 2 is a better way to reason about this)
Argh, I have accidentally reported your comment instead of replying. I did wonder why it asks me if I'm sure... Sorry.
It does indeed appear that the only rational approach is for them to be treated as comparable. I was merely trying to suggest a possible underlying basis for people consistently picking dust specks, regardless of the hugeness of the numbers involved.
I think Torture vs Dust Specks makes a hidden assumption that the two things are comparable. It appears that people don't actually think like that; even an infinite amount of dust specks are worse than a single person being tortured or dying. People arbitrarily place some bad things into a category that's infinitely worse than another category.
So, I'd say that you aren't preferring morality; you are simply placing 50 years of torture as infinitely worse than a dust speck; no number people getting dust specks can possibly be worse than 50 years of torture.
Idea 1: dust specks, because on a linear scale (which seems to be always assumed in discussions of utility here) I think 50 years of torture is more than 3^^^3 times worse than a dust speck in one's eye.
Idea 2: dust specks, because most people arbitrarily place bad things into incomparable categories. The death of your loved one is deemed to be infinitely worse than being stuck in an airport for an hour. It is incomparable; any amount of 1 hour waits are less bad than a single loved one dying.
Indeed, terse "explanations" that handwave more than explain are a pet peeve of mine. They can be outright confusing and cause more harm than good IMO. See this question on phrasing explanations in physics for some examples.