I wish I could say this in a nicer way, but here it is: this post has not clarified UDT for me one bit, and I seem to be more confused now about the topic than I previously was.
The diagrams and lack of explanation of how I’m supposed to interpret them are a large part of why this isn’t helpful to me at all.
Thanks—it’s helpful even to have negative feedback like this, to get a better idea of where to ‘pitch’ any future posts I make.
For what it’s worth, my post presupposes basic knowledge of probability theory, conditional probabilities and Bayesian reasoning, and enough familiarity with and understanding of the problems mentioned to more or less ‘instantly see’ how they are related to my diagrammatic depictions.
I guess that won’t be very helpful, but I’d be happy to answer any specific questions you may have.
Well, I upvoted both your post and Morendil’s comment. I have all the prerequisites you mention, but your diagrams and explanations didn’t help me at all. Your post doesn’t seem to have any insight that would make anything easier to understand than it was before. But discussion of UDT is always very welcome.
Well, if you understand “choose the strategy that maximizes your unconditional expected utility”, with it being implicit that other beings in the universe may be able to ‘see’ your strategy regardless of whether or not you’ve executed it yet, then you pretty much understand UDT.
If you already understood this before my post, then it won’t have been helpful. If you aren’t able to understand that, even after reading my post, but have the prerequisites, then something’s going wrong somewhere.
I’ve only skimmed it so far, and I like the diagrams, but I think they would be helped tremendously by doing something to the Util boxes that indicates their relative goodness.
I agree—AlephNeil, you should add payoffs to the diagrams and perhaps textual descriptions of the games.
I also think that this analysis should be polished up and published in a philosophy or game theory journal, assuming that it’s sound and that no one else came up with it before. Newcomb-like problems are much debated in philosophy, and finding a reformulation where the “rational” strategy is to one-box may be a fairly big deal.
Thanks, but it’s not my theory—it’s by Wei Dai and Vladimir Nesov.
you should add payoffs to the diagrams and perhaps textual descriptions of the games.
Yes, in hindsight this would have made the post much more accessible. Somehow I was imagining that this community has been ‘bathed’ in these problems for so long that nearly everyone would instantly ‘get’ the diagrams… or if they didn’t then it would be easy and fun to ‘fill in the gaps’, rather than difficult and confusing.
As regards probability it may be useful to think of me as a possibly confused student. This is stuff I’m learning, and there are bound to be gaps in my knowledge.
What do you mean by “unconditional expected utility”?
I understand expectation (probability weighted sum of possible values), I understand utility (measure of satisfaction of an agent’s preferences), and I understand conditioning as a basic operation in probability.
In particular, how does your distinction between NDT and UDT play out in numbers in (say) the Sleeping Beauty scenario? How exactly is NDT inadequate there?
The Sleeping Beauty scenario is problematic to discuss because it’s posed as a question about probabilities rather than utilities. Let’s consider Parfit’s Hitchhiker instead. If you’d like some concrete numbers, suppose you get 0 utility if you’re left in the desert, 10 if you’re taken back to civilisation, but then lose 1 if you have to pay. So the utilities in the ‘Util’ boxes on my diagram are 9, 10, 0, in that order.
Now, if you have an opportunity to act at all, then you can say with certainty where you are in the tree-diagram: you’re at the one-and-only Player node. This corresponds to “I’ve already been taken to my destination, and now I need to decide whether to pay the driver.” Conditional upon being at that node, it’s obvious that you maximise your utility by not paying (10 instead of 9).
However, if you make no assumptions about ‘the state of the world’ (i.e. whether or not you were offered a ride) and ask “Which of the two strategies maximizes my expected utility at the outset?” then the strategy where you pay up will get utility 9, and the one that doesn’t will get 0.
So looking at the unconditional expected utility basically means that you deliberately ‘forget’ the information you have about where you are in the game and just look for “a strategy for the blue box” that will maximize your utility over many start-to-finish iterations of the game.
I don’t know where the probabilities are supposed to be in that graphical model, so I don’t know how to apply my understanding of “expectation”. I’m not even sure what I’m supposed to be uncertain about, so I’m not sure how to apply my understanding of “probability”.
I don’t know what the semantics of nodes and arrows are, either. Labeling the arrows and the “Util” boxes would help.
The Sleeping Beauty scenario is problematic to discuss
That might justify removing it from the OP, or at least moving it out of the critical path across the inferential distance.
because it’s posed as a question about probabilities rather than utilities
It isn’t clear how you can discuss expectations without discussing probabilities?
In the case of Newcomb’s Problem—if Omega is only assumed to have some finite accuracy, say .9 - I can at least start to see how to make it about probabilities and expectations. I’ll take a shot at it sometime.
I wish I could say this in a nicer way, but here it is: this post has not clarified UDT for me one bit, and I seem to be more confused now about the topic than I previously was.
The diagrams and lack of explanation of how I’m supposed to interpret them are a large part of why this isn’t helpful to me at all.
Thanks—it’s helpful even to have negative feedback like this, to get a better idea of where to ‘pitch’ any future posts I make.
For what it’s worth, my post presupposes basic knowledge of probability theory, conditional probabilities and Bayesian reasoning, and enough familiarity with and understanding of the problems mentioned to more or less ‘instantly see’ how they are related to my diagrammatic depictions.
I guess that won’t be very helpful, but I’d be happy to answer any specific questions you may have.
Well, I upvoted both your post and Morendil’s comment. I have all the prerequisites you mention, but your diagrams and explanations didn’t help me at all. Your post doesn’t seem to have any insight that would make anything easier to understand than it was before. But discussion of UDT is always very welcome.
Well, if you understand “choose the strategy that maximizes your unconditional expected utility”, with it being implicit that other beings in the universe may be able to ‘see’ your strategy regardless of whether or not you’ve executed it yet, then you pretty much understand UDT.
If you already understood this before my post, then it won’t have been helpful. If you aren’t able to understand that, even after reading my post, but have the prerequisites, then something’s going wrong somewhere.
I’ve only skimmed it so far, and I like the diagrams, but I think they would be helped tremendously by doing something to the Util boxes that indicates their relative goodness.
I agree—AlephNeil, you should add payoffs to the diagrams and perhaps textual descriptions of the games.
I also think that this analysis should be polished up and published in a philosophy or game theory journal, assuming that it’s sound and that no one else came up with it before. Newcomb-like problems are much debated in philosophy, and finding a reformulation where the “rational” strategy is to one-box may be a fairly big deal.
Thanks, but it’s not my theory—it’s by Wei Dai and Vladimir Nesov.
Yes, in hindsight this would have made the post much more accessible. Somehow I was imagining that this community has been ‘bathed’ in these problems for so long that nearly everyone would instantly ‘get’ the diagrams… or if they didn’t then it would be easy and fun to ‘fill in the gaps’, rather than difficult and confusing.
As regards probability it may be useful to think of me as a possibly confused student. This is stuff I’m learning, and there are bound to be gaps in my knowledge.
What do you mean by “unconditional expected utility”?
I understand expectation (probability weighted sum of possible values), I understand utility (measure of satisfaction of an agent’s preferences), and I understand conditioning as a basic operation in probability.
In particular, how does your distinction between NDT and UDT play out in numbers in (say) the Sleeping Beauty scenario? How exactly is NDT inadequate there?
The Sleeping Beauty scenario is problematic to discuss because it’s posed as a question about probabilities rather than utilities. Let’s consider Parfit’s Hitchhiker instead. If you’d like some concrete numbers, suppose you get 0 utility if you’re left in the desert, 10 if you’re taken back to civilisation, but then lose 1 if you have to pay. So the utilities in the ‘Util’ boxes on my diagram are 9, 10, 0, in that order.
Now, if you have an opportunity to act at all, then you can say with certainty where you are in the tree-diagram: you’re at the one-and-only Player node. This corresponds to “I’ve already been taken to my destination, and now I need to decide whether to pay the driver.” Conditional upon being at that node, it’s obvious that you maximise your utility by not paying (10 instead of 9).
However, if you make no assumptions about ‘the state of the world’ (i.e. whether or not you were offered a ride) and ask “Which of the two strategies maximizes my expected utility at the outset?” then the strategy where you pay up will get utility 9, and the one that doesn’t will get 0.
So looking at the unconditional expected utility basically means that you deliberately ‘forget’ the information you have about where you are in the game and just look for “a strategy for the blue box” that will maximize your utility over many start-to-finish iterations of the game.
I don’t know where the probabilities are supposed to be in that graphical model, so I don’t know how to apply my understanding of “expectation”. I’m not even sure what I’m supposed to be uncertain about, so I’m not sure how to apply my understanding of “probability”.
I don’t know what the semantics of nodes and arrows are, either. Labeling the arrows and the “Util” boxes would help.
That might justify removing it from the OP, or at least moving it out of the critical path across the inferential distance.
It isn’t clear how you can discuss expectations without discussing probabilities?
In the case of Newcomb’s Problem—if Omega is only assumed to have some finite accuracy, say .9 - I can at least start to see how to make it about probabilities and expectations. I’ll take a shot at it sometime.