Some problem statements in decision theory can be non universal. Like, they are possible as situations that can happen, but they are invalid as problems to ask what would you do in them.
Suppose Omega gives a single box with $100 to people who don’t say banana after seeing the explanation of the setup and the box. You encounter such situation. Would you say “banana”?
Like, it’s funky premise? It’s not applicable to all people? It would not give me such opportunity, so the premise is invalid.
It pre selects what kind of guys get to participate. So, some guys don’t. So, if you ask what those guys will do in that situation? It has invalid premise of them being in selection.
Newcomb’s problem is fine on that front, it accommodates every kind of strategy, namely, “see opaque and transparent boxes” → two box, and “see opaque and transparent boxes” → one box.
Transparent Newcomb’s problem needs adjustment for this selection effect danger, because in that case you can go against the prediction, e.g. one box if it’s empty and two box if they both are full. What Omega offers to those guys, huh?
One solution is “Omega leaves both full IFF you one box after seeing both full”, then some contrarians do receive only $1000 and leave with $0 after one boxing. Another “Omega leaves both full IFF no matter what you see you take one”—but this one is closer to counterfactual mugging.
Smoker’s lesion might be one such problematic problem. Agents will act on correlation they perceive, but in doing so, destroy the correlation. You can fix this by introducing staged information gain, like “People decided to collect the statistic each 10 years. This was the first time they did that. There is such correlation. Before next statistic collection, what do you do? ” or selection effects, like “even after acting on this correlation, correlation remains”—and this looks like it makes weird postulates, that might be non universal.
EDIT
XOR blackmail uses this selection effect deliberately. There is a selection effect to what kind of agents the letters arrives. If you received a letter, then you have termites XOR you will pay small fee. But it’s evidence about the state of the world not your decision, if you are the kind of person who would not pay. There is no way to act on this information and get out of bounds of what is postulated.
There’s nothing wrong with invalid premises or contrived scenarios. Even if a situation doesn’t exist, you can still ask what happens there, and what should happen there, and what the people who don’t exist should do. Some decisions “cause” agents that make them (situations where they are made) to have never existed (as in Transparent Newcomb), and some decision problems have such decisions as the correct ones (the laws of Nature don’t constrain what an agent gets to do, as an abstract algorithm).
That’s not my point. I claim that some problems are stated badly, stated incorrectly, illposed. Like “Would you glomp when it’s romcsing?” or “It’s raining in Brazil. How many times will you jump?”. It’s not about what happens in problem, it’s about what happens among people who consider it.
Please explain what makes a Banana problem well posed.
Transparent Newcomb … you can go against the prediction, e.g. one box if it’s empty and two box if they both are full. What Omega offers to those guys, huh?
The situation doesn’t exist for them, as a logical result of their behavior. They also don’t win.
XOR blackmail … There is no way to act on this information and get out of bounds of what is postulated.
The bounds of what is postulated can’t constrain what an algorithm actually does, even when the algorithm gets to know what was postulated in some sense, and is correct in that knowledge in some sense. The algorithm is still the only thing that determines the algorithm’s behavior, it screens off everything else. No other claims or predictions or stipulations get to determine the algorithm’s behavior. It gets to refute even a formal proof about what it does, causing the whole situation where that proof was present or stipulated to never have existed, even if it’s the whole world. The selection effect has no power over the behavior that the abstract algorithm chooses.
You can explicitly say what happens if you are not in selection, I guess. Like “Omega takes a look at you from stealth. If it thinks you would not say banana if given $100 and explanation of the setup, it approaches you and does it. Otherwise it leaves without turning off stealth or explaining anything”—then everyone is in selection again.
I think XOR problem is of this type. Smokers lesion deals with this incorrectly / underdefined. Transparent boxes Newcomb’s can be fixed in the same way. Although I think the one fixed with counterfactual predictor is better as a problem, although is a different one.
Some problem statements in decision theory can be non universal. Like, they are possible as situations that can happen, but they are invalid as problems to ask what would you do in them.
Like, it’s funky premise? It’s not applicable to all people? It would not give me such opportunity, so the premise is invalid.
It pre selects what kind of guys get to participate. So, some guys don’t. So, if you ask what those guys will do in that situation? It has invalid premise of them being in selection.
Newcomb’s problem is fine on that front, it accommodates every kind of strategy, namely, “see opaque and transparent boxes” → two box, and “see opaque and transparent boxes” → one box.
Transparent Newcomb’s problem needs adjustment for this selection effect danger, because in that case you can go against the prediction, e.g. one box if it’s empty and two box if they both are full. What Omega offers to those guys, huh?
One solution is “Omega leaves both full IFF you one box after seeing both full”, then some contrarians do receive only $1000 and leave with $0 after one boxing. Another “Omega leaves both full IFF no matter what you see you take one”—but this one is closer to counterfactual mugging.
Smoker’s lesion might be one such problematic problem. Agents will act on correlation they perceive, but in doing so, destroy the correlation. You can fix this by introducing staged information gain, like “People decided to collect the statistic each 10 years. This was the first time they did that. There is such correlation. Before next statistic collection, what do you do? ” or selection effects, like “even after acting on this correlation, correlation remains”—and this looks like it makes weird postulates, that might be non universal.
EDIT
XOR blackmail uses this selection effect deliberately. There is a selection effect to what kind of agents the letters arrives. If you received a letter, then you have termites XOR you will pay small fee. But it’s evidence about the state of the world not your decision, if you are the kind of person who would not pay. There is no way to act on this information and get out of bounds of what is postulated.
There’s nothing wrong with invalid premises or contrived scenarios. Even if a situation doesn’t exist, you can still ask what happens there, and what should happen there, and what the people who don’t exist should do. Some decisions “cause” agents that make them (situations where they are made) to have never existed (as in Transparent Newcomb), and some decision problems have such decisions as the correct ones (the laws of Nature don’t constrain what an agent gets to do, as an abstract algorithm).
That’s not my point. I claim that some problems are stated badly, stated incorrectly, illposed. Like “Would you glomp when it’s romcsing?” or “It’s raining in Brazil. How many times will you jump?”. It’s not about what happens in problem, it’s about what happens among people who consider it.
Please explain what makes a Banana problem well posed.
The situation doesn’t exist for them, as a logical result of their behavior. They also don’t win.
The bounds of what is postulated can’t constrain what an algorithm actually does, even when the algorithm gets to know what was postulated in some sense, and is correct in that knowledge in some sense. The algorithm is still the only thing that determines the algorithm’s behavior, it screens off everything else. No other claims or predictions or stipulations get to determine the algorithm’s behavior. It gets to refute even a formal proof about what it does, causing the whole situation where that proof was present or stipulated to never have existed, even if it’s the whole world. The selection effect has no power over the behavior that the abstract algorithm chooses.
You can explicitly say what happens if you are not in selection, I guess. Like “Omega takes a look at you from stealth. If it thinks you would not say banana if given $100 and explanation of the setup, it approaches you and does it. Otherwise it leaves without turning off stealth or explaining anything”—then everyone is in selection again.
I think XOR problem is of this type. Smokers lesion deals with this incorrectly / underdefined. Transparent boxes Newcomb’s can be fixed in the same way. Although I think the one fixed with counterfactual predictor is better as a problem, although is a different one.