So, in my experience it’s common for decision theorists in philosophy to take preferences to be over possible worlds and probability distributions over such (the specification of which includes the past and future), and when coarse-graining they take outcomes to be sets of possible worlds. (What most philosophers do is, of course, irrelevant to the matter of how it’s best to do things, but I just want to separate “my proposal” from what I (perhaps mistakenly) take to be common.) As you say, no agent remotely close to actual agents will have preferences where details down to the location of every particle in 10,000 BC make a difference, which is why we coarse-grain. But this fact doesn’t mean that maximally-specific worlds or sets of such shouldn’t be what are modeled as outcomes, as opposed to outcomes being ways the world can be at specific times (which I take to be your understanding of things; correct me if I’m wrong). Rather, it just means a lot of these possible worlds will end up getting the same utility because the agent is indifferent between them, and so we’ll be able to treat them as the same outcome.
I worry I might be misunderstanding your point in the last few paragraphs, as I don’t understand how having maximally-specific worlds as outcomes is counter to our commonsense thinking of decision-making. It is true I don’t have a felt preference between “I get $100 and the universe was in state S five billion years ago” and “I get $100 and the universe was in state T five billion years ago,” let alone anything more specific. But that is just to say I am indifferent—I weakly prefer either outcome to the other, and this fact is as intuitively accessible to me as the fact that I prefer getting $100 to getting $10. As far as I can tell, the only consequence of making things too fine-grained is that you include irrelevant details to which the agent is indifferent and you make the model needlessly unwieldy—not that it invokes a concept of preference divorced from actual decision-making.
Outside of sci-fi or thought experiments, I will never face a “decision problem” in which both of the options are complete specifications of the way the rest of my life might go, all the way up to the moment I die.
Every decision problem can be modeled as being between probability distributions over such histories, or over sets of such histories if we want to coarse-grain and ignore minute details to which the agent is indifferent. Now, of course, a real human never has precise probabilities associated with the most minute detail—but the same is true even if the outcomes are states-at-times, and even non-maximally-specific states-at-times. Idealizing that matter away seems to be something any model has to do, and I’m not seeing what problems are introduced specifically by taking outcomes to be histories instead of states-at-times.
The two cases that come to mind immediately are money pumps for non-transitive preferences and diachronic Dutch books. In both cases, the argument assumes an agent that makes multiple successive decisions on the basis of preferences which we assume do not vary with time (or which only vary with time in some specified manner, rather than being totally unconstrained as your proposal would have it).
But having outcomes be sets of maximally-specific world-histories doesn’t prevent us from being able to model sequential decisions. All we need to do so is to assume that the agent can make choices at different times which make a difference as to whether a more-or-less preferred world-history will obtain. For example, say I have a time-dependence preference of preferring to wear a green shirt on weekends and a red shirt on weekdays, so I’m willing to pay $1 to trade shirts every Saturday and Monday. This would not make me a money-pump, rather I’m just someone who’s willing to pay to keep their favorite shirt at the moment on. But allowing time-dependent preferences like this doesn’t prevent money-pump and diachronic Dutch book arguments from ever going through, for I still prefer wearing a red shirt next Monday to wearing a green shirt then, if everything else about the world-history is kept the same. If I in addition prefer wearing a yellow shirt on a weekday to wearing a red one, but then also prefer a green shirt on a weekday to a yellow one, then my preferences are properly cyclic and I will be a money-pump. For let’s say I have a ticket that entitles me to a red shirt next Monday; then suppose I trade that ticket for a yellow shirt ticket, then that one for a green shirt ticket, then I pay $1 to trade that for my original red shirt ticket. Assuming my preferences merely concern (i) what color shirt I wear on what day and (ii) my having more money than less, I will end up in a state that I think is worse than just having made no trade at all. This is so even though my preferences are not merely over shirt-colors and money, but rather coarse-grained sets of world-histories.
All that is needed for the pragmatic money-pump argument to go through is that my preferences are coarse-grained enough that we can speak of my making sequential choices as to which world-histories will obtain, such that facts about what choices I have made in these very cases do not influence the world-history in a way that makes a difference to my preferences. This seems pretty safe in the case of humans, and a result showing transitivity to be rationally required under such assumptions still seems important. Even in the case of a realistic agent who really likes paying to go through the A-B-C-A cycle, we could imagine alternate decision problems where they get to choose whether they get to go through that cycle during a future time-interval, and genuinely exploit them if those preferences are cyclic.
I worry that what I described above in the shirt-color example falls under what you mean by “or which only vary with time in some specified manner, rather than being totally unconstrained as your proposal would have it.” A world-history is a specification of the world-state at each time, similar in kind to “I wear a red shirt next Monday.” As I said before, the model would allow for weird fine-grained preferences over world-histories, but realistic uses of it will have as outcomes larger sets of world-histories like the set of histories where I wear a red shirt next Monday and have $1000, and so on. This is similar to how standard probability theory in principle allows one to talk about probabilities of propositions so specific that no one could ever think or care about them, but for practical purposes we just don’t include those details when we actually apply it.
I’m concerned that I may be losing track of where our disagreement is. So, just to recap: I took your arguments in the OP to be addressed if we understand outcomes (the things to which utilities are assigned) to be world-histories or sets of world-histories, so we can understand the difference between an agent who’s content with paying a dollar for every A-B-C-A cycle and an agent for whom that would be indicative of irrationality. You alleged that if we understand outcomes in this way, and not merely as possible states of the world with no reference to time, then (i) we cannot model sequential decisions, (ii) such a model would have an unrealistic portrayal of decision-making, and (iii) there will be too few constraints on preferences to get anything interesting. I reply: (i) sequential decisions can still be modeled as choices between world-histories, and indeed in an intuitive way if we make the realistic assumption that the agent’s choices in this very sequence by themselves do not make a difference to whether a world-history is preferred; (ii) the decisions do seem to be intuitively modeled if we coarse-grain the sets of world-histories appropriately; and (iii) even if money-pump arguments only go through in the case of agents who have a certain additional structure to their preferences, this additional structure is satisfied by realistic agents and so the restricted results will be important. If I am wrong about what is at issue, feel free to just correct me and ignore anything I said under false assumptions.
Thanks for the reply!
So, in my experience it’s common for decision theorists in philosophy to take preferences to be over possible worlds and probability distributions over such (the specification of which includes the past and future), and when coarse-graining they take outcomes to be sets of possible worlds. (What most philosophers do is, of course, irrelevant to the matter of how it’s best to do things, but I just want to separate “my proposal” from what I (perhaps mistakenly) take to be common.) As you say, no agent remotely close to actual agents will have preferences where details down to the location of every particle in 10,000 BC make a difference, which is why we coarse-grain. But this fact doesn’t mean that maximally-specific worlds or sets of such shouldn’t be what are modeled as outcomes, as opposed to outcomes being ways the world can be at specific times (which I take to be your understanding of things; correct me if I’m wrong). Rather, it just means a lot of these possible worlds will end up getting the same utility because the agent is indifferent between them, and so we’ll be able to treat them as the same outcome.
I worry I might be misunderstanding your point in the last few paragraphs, as I don’t understand how having maximally-specific worlds as outcomes is counter to our commonsense thinking of decision-making. It is true I don’t have a felt preference between “I get $100 and the universe was in state S five billion years ago” and “I get $100 and the universe was in state T five billion years ago,” let alone anything more specific. But that is just to say I am indifferent—I weakly prefer either outcome to the other, and this fact is as intuitively accessible to me as the fact that I prefer getting $100 to getting $10. As far as I can tell, the only consequence of making things too fine-grained is that you include irrelevant details to which the agent is indifferent and you make the model needlessly unwieldy—not that it invokes a concept of preference divorced from actual decision-making.
Every decision problem can be modeled as being between probability distributions over such histories, or over sets of such histories if we want to coarse-grain and ignore minute details to which the agent is indifferent. Now, of course, a real human never has precise probabilities associated with the most minute detail—but the same is true even if the outcomes are states-at-times, and even non-maximally-specific states-at-times. Idealizing that matter away seems to be something any model has to do, and I’m not seeing what problems are introduced specifically by taking outcomes to be histories instead of states-at-times.
But having outcomes be sets of maximally-specific world-histories doesn’t prevent us from being able to model sequential decisions. All we need to do so is to assume that the agent can make choices at different times which make a difference as to whether a more-or-less preferred world-history will obtain. For example, say I have a time-dependence preference of preferring to wear a green shirt on weekends and a red shirt on weekdays, so I’m willing to pay $1 to trade shirts every Saturday and Monday. This would not make me a money-pump, rather I’m just someone who’s willing to pay to keep their favorite shirt at the moment on. But allowing time-dependent preferences like this doesn’t prevent money-pump and diachronic Dutch book arguments from ever going through, for I still prefer wearing a red shirt next Monday to wearing a green shirt then, if everything else about the world-history is kept the same. If I in addition prefer wearing a yellow shirt on a weekday to wearing a red one, but then also prefer a green shirt on a weekday to a yellow one, then my preferences are properly cyclic and I will be a money-pump. For let’s say I have a ticket that entitles me to a red shirt next Monday; then suppose I trade that ticket for a yellow shirt ticket, then that one for a green shirt ticket, then I pay $1 to trade that for my original red shirt ticket. Assuming my preferences merely concern (i) what color shirt I wear on what day and (ii) my having more money than less, I will end up in a state that I think is worse than just having made no trade at all. This is so even though my preferences are not merely over shirt-colors and money, but rather coarse-grained sets of world-histories.
All that is needed for the pragmatic money-pump argument to go through is that my preferences are coarse-grained enough that we can speak of my making sequential choices as to which world-histories will obtain, such that facts about what choices I have made in these very cases do not influence the world-history in a way that makes a difference to my preferences. This seems pretty safe in the case of humans, and a result showing transitivity to be rationally required under such assumptions still seems important. Even in the case of a realistic agent who really likes paying to go through the A-B-C-A cycle, we could imagine alternate decision problems where they get to choose whether they get to go through that cycle during a future time-interval, and genuinely exploit them if those preferences are cyclic.
I worry that what I described above in the shirt-color example falls under what you mean by “or which only vary with time in some specified manner, rather than being totally unconstrained as your proposal would have it.” A world-history is a specification of the world-state at each time, similar in kind to “I wear a red shirt next Monday.” As I said before, the model would allow for weird fine-grained preferences over world-histories, but realistic uses of it will have as outcomes larger sets of world-histories like the set of histories where I wear a red shirt next Monday and have $1000, and so on. This is similar to how standard probability theory in principle allows one to talk about probabilities of propositions so specific that no one could ever think or care about them, but for practical purposes we just don’t include those details when we actually apply it.
I’m concerned that I may be losing track of where our disagreement is. So, just to recap: I took your arguments in the OP to be addressed if we understand outcomes (the things to which utilities are assigned) to be world-histories or sets of world-histories, so we can understand the difference between an agent who’s content with paying a dollar for every A-B-C-A cycle and an agent for whom that would be indicative of irrationality. You alleged that if we understand outcomes in this way, and not merely as possible states of the world with no reference to time, then (i) we cannot model sequential decisions, (ii) such a model would have an unrealistic portrayal of decision-making, and (iii) there will be too few constraints on preferences to get anything interesting. I reply: (i) sequential decisions can still be modeled as choices between world-histories, and indeed in an intuitive way if we make the realistic assumption that the agent’s choices in this very sequence by themselves do not make a difference to whether a world-history is preferred; (ii) the decisions do seem to be intuitively modeled if we coarse-grain the sets of world-histories appropriately; and (iii) even if money-pump arguments only go through in the case of agents who have a certain additional structure to their preferences, this additional structure is satisfied by realistic agents and so the restricted results will be important. If I am wrong about what is at issue, feel free to just correct me and ignore anything I said under false assumptions.