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What is the semantics of assigning probabilities to future events?
Dmitriy Vasilyuk10

That's perfect, I was thinking along the same lines, with a range of options available for sale, but didn't do the math and so didn't realize the necessity of dual options. And you are right of course, there's still quite a bit of arbitrariness left. In addition to varying the distribution of options there is, for example, freedom to choose what metric the forecasters are supposed to optimize. It doesn't have to be EV, in fact in real life it rarely should be EV, because that ignores risk aversion. Instead we could optimize some utility function that becomes flatter for larger gains, for example we could use Kelly betting.

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Learning Russian Roulette
Dmitriy Vasilyuk10

Learning that "I am in the sleeping beauty problem" (call that E) when there are N people who aren't is admittedly not the best scenario to illustrate how a normal update is factored into the SSA update, because E sounds "anthropicy". But ultimately there is not really much difference between this kind of E and the more normal sounding E* = "I measured the CMB temperature to be 2.7K". In both cases we have:

  1. Some initial information about the possibilities for what the world could be: (a) sleeping beauty experiment happening, N + 1 or N + 2 observers in tota
... (read more)
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1Bunthut
Not what I meant. I would say anthropic information tells you where in the world you are, and normal information tell you what the world is like. An anthropic update, then, reasons about where you would be, if the world were a certain way, to update on world-level probabilities from anthropic information. So sleeping beauty with N outsiders is a purely anthropic update by my count. Big worlds generally tend to make updates more anthropic. One way to interpret the SSA criterion is to have beliefs in such a way that in as many (weighed by your prior) worlds as possible, you would as right as possible in the position of an average member of your reference class. If you "control" the beliefs of members in your reference class, then we could also say to believe in such a way as to make them as right as possible in as many worlds as possible.  "Agents which are born with my prior" (and maybe "and using this epistemology", or some stronger kind of identicalness) is a class whichs beliefs are arguably controlled by you in the timeless sense. So if you use it, you will be doing a UDT-like optimizing. (Of course, it will be a UDT that  believes in SSA.) Maybe, but if there is a general form that can produce many kinds of anthropics based on how its free parameter is set, then calling the result of one particular value of the parameter SIA and the results of all others SSA does not seem to cleave reality at the joints.
Learning Russian Roulette
Dmitriy Vasilyuk20

You have described some bizarre issues with SSA, and I agree that they are bizarre, but that's what defenders of SSA have to live with. The crucial question is:

For the anthropic update, yes, but isn't there still a normal update?

The normal updates are factored into the SSA update. A formal reference would be the formula for P(H|E) on p.173 of Anthropic Bias, which is the crux of the whole book. I won't reproduce it here because it needs a page of terminology and notation, but instead will give an equivalent procedure, which will hopefully be more transpare... (read more)

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1Bunthut
I didn't consider that illustrative of my question because "I'm in the sleeping beauty problem" shouldn't lead to a "normal" update anyway. That said I haven't read Anthropic Bias, so if you say it really is supposed to be the anthropic update only then I guess. The definition in terms of "all else equal" wasn't very informative for me here. But background knowledge changes over time, and a change in reference class could again lead to absurdities like this. So it seems to me like the sensible version of this would be to have your reference class always be "agents born with the same prior as me", or indentical in an even stronger sense, which would lead to something like UDT. Now that I think of it SSA can reproduce SIA, using the reference class of "all possible observers", and considering existence a contingent property of those observers.
Learning Russian Roulette
Dmitriy Vasilyuk10

Can you spell that out more formally? It seems to me that so long as I'm removing the corpses from my reference class, 100% of people in my reference class remember surviving every time so far just like I do, so SSA just does normal bayesian updating.

Sure, as discussed for example here: https://www.lesswrong.com/tag/self-sampling-assumption, if there are two theories, A and B, that predict different (non-zero) numbers of observers in your reference class, then on SSA that doesn't matter. Instead, what matters is what fraction of observers in your reference... (read more)

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1Bunthut
For the anthropic update, yes, but isn't there still a normal update? Where you just update on the gun not firing, as an event, rather than your existence? Your link doesn't have examples where that would be relevant either way. But if we didn't do this normal updating, then it seems like you could only learn from an obervation if some people in your reference class make the opposite observation in different worlds. So if you use the trivial reference class, you will give everything the same probability as your prior, except for eliminating worlds where noone has your epistemic state and renormalizing. You will expect to violate bayes law even in normal situations that dont involve any birth or death. I don't think thats how its meant to work.
Learning Russian Roulette
Dmitriy Vasilyuk10

Reference class issues.

SSA, because that one me is also 100% of my reference class.

I think it's not necessarily true that on SSA you would also have to believe B, because the reference class doesn't necessarily have to involve just you. Defenders of SSA often have to face the problem/feature that different choices of a reference class yield different answers. For example, in Anthropic Bias Bostrom argues that it's not very straightforward to select the appropriate reference class, some are too wide and some (such as the trivial reference class) often too n... (read more)

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1Bunthut
Can you spell that out more formally? It seems to me that so long as I'm removing the corpses from my reference class, 100% of people in my reference class remember surviving every time so far just like I do, so SSA just does normal bayesian updating. I did mean to use the trivial reference class for the SSA assesment, just not in a large world. And, it still seems strange to me that it would change the conclusion here how large the world is. So even if you get this to work, I don't think it reproduces my intuition. Besides, if the only reason we successfully learn from others is that we defined our reference class to include them - well, then the assumption we can't update against is just "what reference class were in". I'd similarly count this as a non-solution thats just hard-wiring the right answer.
What is the semantics of assigning probabilities to future events?
Answer by Dmitriy Vasilyuk20

I find this question really interesting. I think the core of the issue is the first part:

First, how can we settle who has been a better forecaster so far? 

I think a good approach would be betting related. I believe different reasonable betting schemes are possible, which in some cases will give conflicting answers when ranking forecasters. Here's one reasonable setup:

  • Let A = probability the first forecaster, Alice, predicts for some event.
  • Let B = probability the second forecaster, Bob, assigns (suppose B > A wlog).
  • Define what's called an option: ba
... (read more)
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3Michal
I like the idea of defining a betting game 'forecasters vs cosmic bookie'. Then saying 'the probability that people will land on Mars by 2040 is 42%' translates into semantics 'I am willing to buy an option for Y<42 cents that would be worth $1 if we land on Mars by 2040 or $0 otherwise'. To compare several forecasters we can consider a game in which each player is offered to buy some options of this kind. Suppose that for each x in {1, \dots, 99} each player is allowed to buy one option for x cents. If one believes that the probability of an event is 30% then it is profitable for them to buy the 29 cheapest options and nothing more (it does not matter if one buys the option for 30 cents or not).   To make the calculations simpler, we can make the prices continuous. So one is allowed to buy an option-interval [0,x] for some real x in [0,1]: by integration its price should be x22 and the pay-off is x if the event occurs. If the 'true' probability of the event is y then the expected profit equals yx−x22. One can easily see that if you know the value of y then the optimal strategy sets x=y. The larger mistake you make, the lower is your expected profit. The value of the game is the sum of all the profits and being a good forecaster means that one can design a strategy with high expected revenue. An important drawback of this approach is that when you correctly estimate the probability of successful Mars landing to be 42%, then the optimal strategy gives expected profit 0.4222. However, if the question would be 'what is the probability that people would FAIL to land on Mars by 2040?', then the same knowledge gives you answer 58% and the expected profit is different: 0.5822. Hence, the bookie should also sell options that pays when the event does not occur or, equivalently, always consider each question together with its dual, i.e., the question about the event not happening. Now it begins to look like a proper mathematical formalization of forecasting. Still, the pr