One point though: You are writing that the 1-5 agent would walk into room 1 against a low-accuracy frustrator, right? Shouldn't it be the opposite, against a low accuracy frustrator he chooses 2, and if the predictor is more accurate than t he chooses 1? Is this just a typo or am I missing something?
Flo have you engaged at all with Olé Peters’ work on non-ergodicity and path dependence and its implications for decision theory? He calls it “ergodicity economics” but I think this is a confused label since it’s specifically non-ergodicity which is being emphasized.
As someone not super familiar with decision theory I'm a little confused about how the agent with 1-5 must never take option 3 in the frustrater case. Isn't the relevant credence not their credence that box 1 has x, but that box 1 has x given that they pick box 1?
Great question. Whether Box 1 has x is causally independent of the agent’s choice; therefore, a Causal Decision Theorist will find it unnecessary to conditionalize on the act. For the CDTer, it would be like considering the probability that it rains vs. the probability that it rains *given* that I take an umbrella; since the act doesn’t affect the relevant state to begin with, we don’t need the conditional.
But why is it relevant whether or not it is causally independent? I understand that in general the rationale behind CDT is that what you choose now can't change what is already the case (which is why they 2 box). But in this case the conditionalising just seems to be about working out what is already the case. What if instead we were conditionalising on being very close to picking box 1? We start thinking P(p) is 0.5, then just before I take 1 I realise that this is evidence against p, so I update it to something much less than 0.5? Is this sort of phenomenon not something the CDTer can take into account at all?
What do you think about causal ratificationism (e.g., weatherson’s gamified decision theory)? It seems like it probably recommends blowing oneself up less frequently than the others do, at least
Note that for the Transparent Newcomb problem Statewide Dominance does not apply because the states and their probability are not causally independent on most usual understandings of causality, for choosers who respond to what their eyes interact with.
Prove it for the easier case imagine the predictor announces that tomorrow the chooser will face either the standard or the transparent Newcomb problem and that all preparations and predictions have been made.
Now suppose that the chooser is an EDTer and so when they get to the venue the next day they see it is transparent and the money is absent. Well then they decide to one box, but that means the predictor caused the money to be present absent signaling their prediction and then in the same causal chain the chooser saw that and so choose to two box as a result. So now the prediction both directly causes the absence of money and the choice the chooser made. Therefore causal independence is violated.
Further you can't argue that it is merely the transparency of the box that causes it because in order to know the box is transparent the chooser must be able to see the contents, if instead of nothing or the million dollars, the chooser saw a fish say they'd just conclude not that it was transparent Newcomb problem, but something had gone wrong. So knowing the prediction is a key part of the causal chain.
Okay now can we apply this to the narrower case of interest. Well suppose the predictor is fallible, how might he screw up? Well, he might have missed the box altogether when dolling out money and dropped the million dollars on the ground outside the box, if he did that the chooser is presumably going to scoop it up off the ground etc. Relatively for this proof he might forget to take the opaque screen out. So even if he announced he was doing the transparent problem the EDTer is still going to be aware of and keep his eyes peeled for possible screw-ups, so the box being transparent and what was put in the box is going to cause him to change his choices and that means again the states of the system (contents of box and prediction versus what is chosen) are no longer causally independent. Causality is about subjunctive conditionals (on many analysis) and so even in the case where the chooser sees nothing amiss, their disposition to see something amiss that could have happened (given the predictor's fallibility) is still an instance of the subjunctive conditional and so an instance of causal connection.
Anyway this is another reason I think the transparent Newcomb's problem is mis-analyzed in these situations. I have others.
Another question is what even is a cause. For example, if a cause is nothing more than constant conjunction then the infallible predictor being the constant conjunction of prediction and choice just are causally related. Either the prediction is causing the outcome (choice) or the outcome is causing the prediction. This actually seems to have been Nozick's initial analysis. So we really need to specify what we mean by cause.
We also have gnarly quantum mechanical cases Harper et al suggested that even if EPR correlations are not causal, it is okay to think that outcomes that depend on them are not independent in the appropriate sense for CDT to treat them as independent https://philpapers.org/rec/KOBDTE-2 .
Also are we including mathematically and logical necessity under causal necessity. I think those are distinct I think the states could be mathematically dependent without being causally dependent in some common senses of word cause (Newcomb seems to have had this in mind in some of his analysis of his problem when he introduced it to people like Nozick).
An interesting issue is to try and state a principle that given the same information and motivations one should endorse the same choices independent of ones temporal position (or indeed your personal identity). So CDT as sometimes stated violates this by suggesting you should make a different decision before the money is placed and after. This is almost certainly wrong it wouldn't matter if the money is only placed at the very moment of choice so long as it were causally independent of the choice according to the CDTer. These iterated dilemmas show how some decision theories violate this (you take a decision on iteration A on the analysis that you will do X in iteration B, but then on arriving at B you choose Y instead even though you've learned nothing new about the overall situation).
Really cool article
One point though: You are writing that the 1-5 agent would walk into room 1 against a low-accuracy frustrator, right? Shouldn't it be the opposite, against a low accuracy frustrator he chooses 2, and if the predictor is more accurate than t he chooses 1? Is this just a typo or am I missing something?
Holy smokes, a bad typo (thinko?) at that. I meant the error rate is some s < t; thank you so much!
Flo have you engaged at all with Olé Peters’ work on non-ergodicity and path dependence and its implications for decision theory? He calls it “ergodicity economics” but I think this is a confused label since it’s specifically non-ergodicity which is being emphasized.
Anyway I’d be really curious how it struck you.
I have not! Might check it out
Here was the original paper I think: https://cyclostationarity.com/wp-content/uploads/2022/08/Peters2019-TheErgodicityProblemInEconomics_COMMENTED.pdf
Hi, interesting post, thank you.
As someone not super familiar with decision theory I'm a little confused about how the agent with 1-5 must never take option 3 in the frustrater case. Isn't the relevant credence not their credence that box 1 has x, but that box 1 has x given that they pick box 1?
Great question. Whether Box 1 has x is causally independent of the agent’s choice; therefore, a Causal Decision Theorist will find it unnecessary to conditionalize on the act. For the CDTer, it would be like considering the probability that it rains vs. the probability that it rains *given* that I take an umbrella; since the act doesn’t affect the relevant state to begin with, we don’t need the conditional.
But why is it relevant whether or not it is causally independent? I understand that in general the rationale behind CDT is that what you choose now can't change what is already the case (which is why they 2 box). But in this case the conditionalising just seems to be about working out what is already the case. What if instead we were conditionalising on being very close to picking box 1? We start thinking P(p) is 0.5, then just before I take 1 I realise that this is evidence against p, so I update it to something much less than 0.5? Is this sort of phenomenon not something the CDTer can take into account at all?
What do you think about causal ratificationism (e.g., weatherson’s gamified decision theory)? It seems like it probably recommends blowing oneself up less frequently than the others do, at least
Note that for the Transparent Newcomb problem Statewide Dominance does not apply because the states and their probability are not causally independent on most usual understandings of causality, for choosers who respond to what their eyes interact with.
Prove it for the easier case imagine the predictor announces that tomorrow the chooser will face either the standard or the transparent Newcomb problem and that all preparations and predictions have been made.
Now suppose that the chooser is an EDTer and so when they get to the venue the next day they see it is transparent and the money is absent. Well then they decide to one box, but that means the predictor caused the money to be present absent signaling their prediction and then in the same causal chain the chooser saw that and so choose to two box as a result. So now the prediction both directly causes the absence of money and the choice the chooser made. Therefore causal independence is violated.
Further you can't argue that it is merely the transparency of the box that causes it because in order to know the box is transparent the chooser must be able to see the contents, if instead of nothing or the million dollars, the chooser saw a fish say they'd just conclude not that it was transparent Newcomb problem, but something had gone wrong. So knowing the prediction is a key part of the causal chain.
Okay now can we apply this to the narrower case of interest. Well suppose the predictor is fallible, how might he screw up? Well, he might have missed the box altogether when dolling out money and dropped the million dollars on the ground outside the box, if he did that the chooser is presumably going to scoop it up off the ground etc. Relatively for this proof he might forget to take the opaque screen out. So even if he announced he was doing the transparent problem the EDTer is still going to be aware of and keep his eyes peeled for possible screw-ups, so the box being transparent and what was put in the box is going to cause him to change his choices and that means again the states of the system (contents of box and prediction versus what is chosen) are no longer causally independent. Causality is about subjunctive conditionals (on many analysis) and so even in the case where the chooser sees nothing amiss, their disposition to see something amiss that could have happened (given the predictor's fallibility) is still an instance of the subjunctive conditional and so an instance of causal connection.
Anyway this is another reason I think the transparent Newcomb's problem is mis-analyzed in these situations. I have others.
Another question is what even is a cause. For example, if a cause is nothing more than constant conjunction then the infallible predictor being the constant conjunction of prediction and choice just are causally related. Either the prediction is causing the outcome (choice) or the outcome is causing the prediction. This actually seems to have been Nozick's initial analysis. So we really need to specify what we mean by cause.
We also have gnarly quantum mechanical cases Harper et al suggested that even if EPR correlations are not causal, it is okay to think that outcomes that depend on them are not independent in the appropriate sense for CDT to treat them as independent https://philpapers.org/rec/KOBDTE-2 .
Also are we including mathematically and logical necessity under causal necessity. I think those are distinct I think the states could be mathematically dependent without being causally dependent in some common senses of word cause (Newcomb seems to have had this in mind in some of his analysis of his problem when he introduced it to people like Nozick).
An interesting issue is to try and state a principle that given the same information and motivations one should endorse the same choices independent of ones temporal position (or indeed your personal identity). So CDT as sometimes stated violates this by suggesting you should make a different decision before the money is placed and after. This is almost certainly wrong it wouldn't matter if the money is only placed at the very moment of choice so long as it were causally independent of the choice according to the CDTer. These iterated dilemmas show how some decision theories violate this (you take a decision on iteration A on the analysis that you will do X in iteration B, but then on arriving at B you choose Y instead even though you've learned nothing new about the overall situation).