His solution seems to rely on the ability to precommit to a future action, such that the future action can be treated like an ordinary outcome:
It is obvious that in the situation thus presented one-boxing is rational. If my decision
determines or strongly influences the prediction, then I rationally decide to one-box, and when standing before the boxes I just do this. (p. 101f)
If people can just “make decisions early”, then one-boxing is, of course, the rational thing to do from the point of CDT. It effectively means you are no longer deciding anything when you are standing in front of the two boxes, you are just slavishly one-boxing as if under hypnotic suggestion, or as if being somehow forced to one-box by your earlier self. Then the “decision” or “act” here can be assigned a probability because it is assumed there is nothing left to decide, it’s effectively just an consequence of the real decision that was made much earlier, consistent with the view that an action in a decision situation may not be assigned a probability.
The real problem with the precommitment route is that it assumes the possibility of “precommitment”. Yet in reality, if you “commit” early to some action, and you are later faced with the situation where the action has to be executed, you are still left with the question of whether or not you should “follow through” with your commitment. Which just means your precommitment wasn’t real. You can’t make decisions in advance, you can’t simply force your later self to do things. The actual decision always has to be made in the present, and the supposed “precommitment” of your past self is nothing more than a suggestion.
The toxin puzzle is also referenced extensively in that aforementioned Spohn paper on one-boxing, and his paper is a response to the toxin puzzle as much as it is to two-boxing.
Spohn shows that you can draw causal graphs such that CDT can get rewards in both cases, though only under the assumption that true precommitment is possible. But Spohn doesn’t give arguments for the possibility of precommitment, as far as I can tell.
Isn’t the possibility and, moreover, computability of precommitmet just trivially true?
If you have programm DT(data), determinimg a decision according to a particular decision theory in the circumstances, specified by data, then you can easily construct a program PDT(data), determining the decision for the same decision theory but with precommitment:
This also seems trivially true to me. I’ve successfully precommited multiple times in my life and I bet you have as well.
What you are probably talking about is the fact that occasionally humans fail at precommitments. But isn’t it an isolated demand for rigor? Humans occasionally fail at following any decision theory, or fail at being rational in general. It doesn’t make all the decision theories and rationality itself incoherent concept which we thus can’t talk about.
Actually, when I think about it, isn’t deciding what decision theory to follow, itself a precommitment?
I often do things because I earlier decided to, overruling whatever feelings I may have in the moment. So from a psychological point of view, precommitment is possible. Why did I pause at Alderford? To let my fatigue clear sufficiently to let the determination to do 100 miles overcome it.
Kavka’s toxin puzzle only works if the intention-detecting machine works, and the argument against rationally drinking the toxin when the time comes could equally well be read as an argument against the possibility of such an intention-detecting machine. Its existence, after all, presupposes that the future decision can be determined at midnight, while the argument against drinking presupposes that it cannot be. An inconsistent thought experiment proves nothing. This example is playing much the same role in decision theory as Russell’s question to Frege did for set theory. It’s pointing to an inconsistency in intuitions around the subject.
Excluding reflectiveness is too strong a restriction, akin to excluding all forms of comprehension axiom from set theory. A precisely formulated limitation is needed that will rule out the intention-detecting machine while allowing the sorts of self-knowledge that people observably use.
But clearly you still made your final decision between 10 and 40 miles only when you were at Alderford. Not hours before that. Our past selves can’t simply force us to do certain things, the memory of a past “commitment” is only one factor that may influence our present decision making, but it doesn’t replace a decision. Otherwise, always when we “decide” to definitely do an unpleasant task tomorrow rather than today (“I do the dishes tomorrow, I swear!”), we would then tomorrow in fact always follow through with it, which isn’t at all the case. (The Kavka/Newcomb cases are even worse than this, because there it isn’t just irrational akrasia preventing us from executing past “commitments”, but instrumental rationality itself, at least if we believe that CDT captures instrumental rationality.)
A more general remark, somewhat related to reflexivity (reflectivity?): In the Where Luce and Krantz paper, Spohn also criticizes Jeffrey for allowing the assignment of probabilities to acts, because for Jeffrey, everything (acts, outcomes, states) is a proposition. And any boolean combination of propositions is a proposition. In his framework, any proposition can be assigned a probability and a utility. But I’m pretty sure Jeffrey’s theory doesn’t strictly require that act probabilities are defined. Moreover, even if they are defined, it doesn’t require them for decisions. That is, for outcomes O and an action A, to calculate the utility U(A) he only requires probabilities of the form P(O|A), which we can treat as a basic probability instead of, frequentist style, a mere abbreviation for the ratio formula P(O∧A)P(A). So P(A) and P(O∧A) can be undefined. In his theory U(A)=P(O|A)U(O∧A)+P(¬O|A)U(¬O∧A) is a theorem. I’m planning a post on explaining Jeffrey’s theory because I think it is way underappreciated. It’s a general theory of utility, rather than just a decision theory which is restricted to “acts” and “outcomes”. To be fair, I don’t know whether that would really help much with elucidating reflectivity. The lesson would probably be something like “according to Jeffrey’s theory you can have prior probabilities for present acts but you should ignore them when making decisions”. The interesting part is that his theory can’t be simply dismissed because others aren’t as general and thus are not a full replacement.
A precisely formulated limitation is needed that will rule out the intention-detecting machine while allowing the sorts of self-knowledge that people observably use.
Maybe the first question is then what form of “self-knowledge” people do, in fact, observably use. I think we treat memories of past “commitments”/intentions more like non-binding recommendations from a close friend (our “past self”), which we may very well just ignore. Maybe there is an ideal rule of rationality that we should always adhere to our past commitments, at least if we learn no new information. But I’d say “should” implies “can”, so by contraposition, “not can” implies “not should”. Which would mean if precommitment is not possible for an agent it’s not required by rationality.
His solution seems to rely on the ability to precommit to a future action, such that the future action can be treated like an ordinary outcome:
If people can just “make decisions early”, then one-boxing is, of course, the rational thing to do from the point of CDT. It effectively means you are no longer deciding anything when you are standing in front of the two boxes, you are just slavishly one-boxing as if under hypnotic suggestion, or as if being somehow forced to one-box by your earlier self. Then the “decision” or “act” here can be assigned a probability because it is assumed there is nothing left to decide, it’s effectively just an consequence of the real decision that was made much earlier, consistent with the view that an action in a decision situation may not be assigned a probability.
The real problem with the precommitment route is that it assumes the possibility of “precommitment”. Yet in reality, if you “commit” early to some action, and you are later faced with the situation where the action has to be executed, you are still left with the question of whether or not you should “follow through” with your commitment. Which just means your precommitment wasn’t real. You can’t make decisions in advance, you can’t simply force your later self to do things. The actual decision always has to be made in the present, and the supposed “precommitment” of your past self is nothing more than a suggestion.
(The impossibility of precommitment was illustrated in Kavka’s toxin puzzle.)
The toxin puzzle is also referenced extensively in that aforementioned Spohn paper on one-boxing, and his paper is a response to the toxin puzzle as much as it is to two-boxing.
Spohn shows that you can draw causal graphs such that CDT can get rewards in both cases, though only under the assumption that true precommitment is possible. But Spohn doesn’t give arguments for the possibility of precommitment, as far as I can tell.
Isn’t the possibility and, moreover, computability of precommitmet just trivially true?
If you have programm DT(data), determinimg a decision according to a particular decision theory in the circumstances, specified by data, then you can easily construct a program PDT(data), determining the decision for the same decision theory but with precommitment:
The only thing that is required is an if-statement and memory object which can be implemented via a dictionary.
Yes, but I was taking about humans. An AI might have a precommitment ability.
This also seems trivially true to me. I’ve successfully precommited multiple times in my life and I bet you have as well.
What you are probably talking about is the fact that occasionally humans fail at precommitments. But isn’t it an isolated demand for rigor? Humans occasionally fail at following any decision theory, or fail at being rational in general. It doesn’t make all the decision theories and rationality itself incoherent concept which we thus can’t talk about.
Actually, when I think about it, isn’t deciding what decision theory to follow, itself a precommitment?
I often do things because I earlier decided to, overruling whatever feelings I may have in the moment. So from a psychological point of view, precommitment is possible. Why did I pause at Alderford? To let my fatigue clear sufficiently to let the determination to do 100 miles overcome it.
Kavka’s toxin puzzle only works if the intention-detecting machine works, and the argument against rationally drinking the toxin when the time comes could equally well be read as an argument against the possibility of such an intention-detecting machine. Its existence, after all, presupposes that the future decision can be determined at midnight, while the argument against drinking presupposes that it cannot be. An inconsistent thought experiment proves nothing. This example is playing much the same role in decision theory as Russell’s question to Frege did for set theory. It’s pointing to an inconsistency in intuitions around the subject.
Excluding reflectiveness is too strong a restriction, akin to excluding all forms of comprehension axiom from set theory. A precisely formulated limitation is needed that will rule out the intention-detecting machine while allowing the sorts of self-knowledge that people observably use.
But clearly you still made your final decision between 10 and 40 miles only when you were at Alderford. Not hours before that. Our past selves can’t simply force us to do certain things, the memory of a past “commitment” is only one factor that may influence our present decision making, but it doesn’t replace a decision. Otherwise, always when we “decide” to definitely do an unpleasant task tomorrow rather than today (“I do the dishes tomorrow, I swear!”), we would then tomorrow in fact always follow through with it, which isn’t at all the case. (The Kavka/Newcomb cases are even worse than this, because there it isn’t just irrational akrasia preventing us from executing past “commitments”, but instrumental rationality itself, at least if we believe that CDT captures instrumental rationality.)
A more general remark, somewhat related to reflexivity (reflectivity?): In the Where Luce and Krantz paper, Spohn also criticizes Jeffrey for allowing the assignment of probabilities to acts, because for Jeffrey, everything (acts, outcomes, states) is a proposition. And any boolean combination of propositions is a proposition. In his framework, any proposition can be assigned a probability and a utility. But I’m pretty sure Jeffrey’s theory doesn’t strictly require that act probabilities are defined. Moreover, even if they are defined, it doesn’t require them for decisions. That is, for outcomes O and an action A, to calculate the utility U(A) he only requires probabilities of the form P(O|A), which we can treat as a basic probability instead of, frequentist style, a mere abbreviation for the ratio formula P(O∧A)P(A). So P(A) and P(O∧A) can be undefined. In his theory U(A)=P(O|A)U(O∧A)+P(¬O|A)U(¬O∧A) is a theorem. I’m planning a post on explaining Jeffrey’s theory because I think it is way underappreciated. It’s a general theory of utility, rather than just a decision theory which is restricted to “acts” and “outcomes”. To be fair, I don’t know whether that would really help much with elucidating reflectivity. The lesson would probably be something like “according to Jeffrey’s theory you can have prior probabilities for present acts but you should ignore them when making decisions”. The interesting part is that his theory can’t be simply dismissed because others aren’t as general and thus are not a full replacement.
Maybe the first question is then what form of “self-knowledge” people do, in fact, observably use. I think we treat memories of past “commitments”/intentions more like non-binding recommendations from a close friend (our “past self”), which we may very well just ignore. Maybe there is an ideal rule of rationality that we should always adhere to our past commitments, at least if we learn no new information. But I’d say “should” implies “can”, so by contraposition, “not can” implies “not should”. Which would mean if precommitment is not possible for an agent it’s not required by rationality.
That is the question at issue.