“The same” in what sense? Are you saying that what I described in the context of game theory is not surprising, or outlining a way to explain it in retrospect?
Communication won’t make a difference if you’re playing with a copy.
Well, if I understand the post correctly, you’re saying that these two problems are fundamentally the same problem, and so rationality should be able to solve them both if it can solve one. I disagree with that, because from the perspective of distributed computing (which I’m used to), these two problems are exactly the two kinds of problems that are fundamentally distinct in a distributed setting: agreement and symmetry-breaking.
Communication won’t make a difference if you’re playing with a copy.
Actually it could. Basically all of distributed computing assumes that every process is running the same algorithm, and you can solve symmetry-breaking in this case with communication and additional constraint on the scheduling of processes (the difficulty here is that the underlying graph is symmetric, whereas if you had some form of asymmetry (like three processes in a line, such that the one in the middle has two neighbors but the others only have one), they you can use directly that asymmetry to solve symmetry-breaking.
(By the way, you just gave me the idea that maybe I can use my knowledge of distributed computing to look at the sort of decision problems where you play with copies? Don’t know if it would be useful, but that’s interesting at least)
Well, if I understand the post correctly, you’re saying that these two problems are fundamentally the same problem
No. I think:
...the reasoning presented is correct in both cases, and the lesson here is for our expectations of rationality...
As outlined in the last paragraph of the post. I want to convince people that TDT-like decision theories won’t give a “neat” game theory, by giving an example where they’re even less neat than classical game theory.
Actually it could.
I think you’re thinking about a realistic case (same algorithm, similar environment) rather than the perfect symmetry used in the argument. A communication channel is of no use there because you could just ask yourself what you would send, if you had one, and then you know you would have just gotten that message from the copy as well.
I can use my knowledge of distributed computing to look at the sort of decision problems where you play with copies
I’d be interested. I think even just more solved examples of the reasoning we want are useful currently.
As outlined in the last paragraph of the post. I want to convince people that TDT-like decision theories won’t give a “neat” game theory, by giving an example where they’re even less neat than classical game theory.
Hum, then I’m not sure I understand in what way classical game theory is neater here?
I think you’re thinking about a realistic case (same algorithm, similar environment) rather than the perfect symmetry used in the argument. A communication channel is of no use there because you could just ask yourself what you would send, if you had one, and then you know you would have just gotten that message from the copy as well.
As long as the probabilistic coin flips are independent on both sides (you also mention the case where they’re symmetric, but let’s put that aside for the example), then you can apply the basic probabilistic algorithm for leader election: both copies flip a coin n times to get a n-bit number, which they exchange. If the numbers are different, then the copy with the smallest one says 0 and the other says 1; otherwise they flip a coin and return the answer. With this algorithm, you have probability ≥1−12n of deciding different values, and so you can get as close as you want to 1 (by paying the price in more random bits).
I’d be interested. I think even just more solved examples of the reasoning we want are useful currently.
Do you have examples of problems with copies that I could look at and that you think would be useful to study?
“The same” in what sense? Are you saying that what I described in the context of game theory is not surprising, or outlining a way to explain it in retrospect?
Communication won’t make a difference if you’re playing with a copy.
Well, if I understand the post correctly, you’re saying that these two problems are fundamentally the same problem, and so rationality should be able to solve them both if it can solve one. I disagree with that, because from the perspective of distributed computing (which I’m used to), these two problems are exactly the two kinds of problems that are fundamentally distinct in a distributed setting: agreement and symmetry-breaking.
Actually it could. Basically all of distributed computing assumes that every process is running the same algorithm, and you can solve symmetry-breaking in this case with communication and additional constraint on the scheduling of processes (the difficulty here is that the underlying graph is symmetric, whereas if you had some form of asymmetry (like three processes in a line, such that the one in the middle has two neighbors but the others only have one), they you can use directly that asymmetry to solve symmetry-breaking.
(By the way, you just gave me the idea that maybe I can use my knowledge of distributed computing to look at the sort of decision problems where you play with copies? Don’t know if it would be useful, but that’s interesting at least)
No. I think:
As outlined in the last paragraph of the post. I want to convince people that TDT-like decision theories won’t give a “neat” game theory, by giving an example where they’re even less neat than classical game theory.
I think you’re thinking about a realistic case (same algorithm, similar environment) rather than the perfect symmetry used in the argument. A communication channel is of no use there because you could just ask yourself what you would send, if you had one, and then you know you would have just gotten that message from the copy as well.
I’d be interested. I think even just more solved examples of the reasoning we want are useful currently.
Hum, then I’m not sure I understand in what way classical game theory is neater here?
As long as the probabilistic coin flips are independent on both sides (you also mention the case where they’re symmetric, but let’s put that aside for the example), then you can apply the basic probabilistic algorithm for leader election: both copies flip a coin n times to get a n-bit number, which they exchange. If the numbers are different, then the copy with the smallest one says 0 and the other says 1; otherwise they flip a coin and return the answer. With this algorithm, you have probability ≥1−12n of deciding different values, and so you can get as close as you want to 1 (by paying the price in more random bits).
Do you have examples of problems with copies that I could look at and that you think would be useful to study?
Changing the labels doesn’t make a difference classically.
Yes.
No, I think you should take the problems of distributed computing, and translate them into decision problems, that you then have a solution to.