It’s worth repeating Spohn’s arguments from Where Luce and Krantz Do Really Generalize Savage’s Decision Model:
Now, probably anyone will find it absurd to assume that someone has
subjective probabilities for things which are under his control and which
he can actualize as he pleases. I think this feeling of absurdity can be
converted into more serious arguments for our principle:
First, probabilities for acts play no role in decision making. For, what
only matters in a decision situation is how much the decision maker likes
the various acts available to him, and relevant to this, in turn, is what he
believes to result from the various acts and how much he likes these
results. At no place does there enter any subjective probability for an act.
The decision maker chooses the act he likes most—be its probability as it
may. But if this is so, there is no sense in imputing probabilities for acts to
the decision maker. For one could tell neither from his actual choices nor
from his preferences what they are. Now, decision models are designed to
capture just the decision maker’s cognitive and motivational dispositions
expressed by subjective probabilities and utilities which manifest themselves in and can be guessed from his choices and preferences. Probabilities for acts, if they exist at all, are not of this sort, as just seen, and
should therefore not be contained in decision models.
The strangeness of probabilities for acts can also be brought out by a
more concrete argument: It is generally acknowledged that subjective
probabilities manifest themselves in the readiness to accept bets with
appropriate betting odds and small stakes. Hence, a probability for an act
should manifest itself in the readiness to accept a bet on that act, if the
betting odds are high enough. Of course, this is not the case. The agent’s
readiness to accept a bet on an act does not depend on the betting odds,
but only on his gain. If the gain is high enough to put this act on the top of
his preference order of acts, he will accept it, and if not, not. The stake of
the agent is of no relevance whatsoever.
One might object that we often do speak of probabilities for acts. For
instance, I might say: “It’s very unlikely that I shall wear my shorts
outdoors next winter.” But I do not think that such an utterance expresses
a genuine probability for an act; rather I would construe this utterance as
expressing that I find it very unlikely to get into a decision situation next
winter in which it would be best to wear my shorts outdoors, i.e. that I find
it very unlikely that it will be warmer than 20°C next winter, that someone
will offer me DM 1000.- for wearing shorts outdoors, or that fashion
suddenly will prescribe wearing shorts, etc. Besides, it is characteristic of such utterances that they refer only to acts which one has not yet to decide
upon. As soon as I have to make up my mind whether to wear my shorts
outdoors or not, my utterance is out of place.
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.
It’s worth repeating Spohn’s arguments from Where Luce and Krantz Do Really Generalize Savage’s Decision Model:
And yet it seems that Spohn no longer believes this.
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.