A Bleg Concerning the Utility of Information

Consider the following scenario.

Scenario One (the “control” scenario).  In the morning you tune your television to the Weather Channel and find the forecaster saying (what’s true) that all meteorolgical signs point towards rain in the afternoon.  You trust the forecaster and so you accept the information that all meteorological signs point towards rain in the afternoon.  With this new information you make the rational (by stipulation) decision to take an umbrella with you to work.  As it happens, it does rain that afternoon and you benefit from having brought the umbrella.

Question: was the information that all meteorological signs point to rain useful information with respect to your decision whether to bring an umbrella?  Obvious answer: yes.

Scenario Two (the “experimental” scenario).  

In the morning you tune your television to the Weather Channel and find the forecaster saying (what’s true) that all meteorolgical signs point towards rain in the afternoon.  You trust the forecaster and so you accept the information that all meteorological signs point towards rain in the afternoon.  With this new information you make the rational (by stipulation) decision to take an umbrella with you to work.  But, despite the fact that all signs pointed to rain, it does not rain that afternoon, and so you incur some cost by having brought the umbrella.

Question: was the information that all meteorological signs point to rain useful information with respect to your decision whether to bring an umbrella?  It seems to me that there isn’t an obvious answer here.  After some thought, Heather and I think that maybe we should say something like this: with respect to deciding what to do, that information was useful, but with respect to getting what you want, that information was not useful.

Does that sound right to anyone else?  Anyone have a better idea?  Any thoughts at all?  We’d love to hear them!

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7 Responses to A Bleg Concerning the Utility of Information

  1. a says:

    this is interesting! i agree with you and heather, because it seems like any information that aids you in arriving at a rational decision is useful. but i’m not as sure about it being useful in ‘getting what you want,’ partly because i can think of a number of things one might want in this situation, and whether the information is useful or not depends on what those are. so i might want to be prepared in the event it rains, or i might want to wear my nice coat without having to worry about getting it wet. in the latter case i kind of think the information is useful both in deciding what to do and in getting what you want, because in bringing the umbrella i get to both avoid spending my day at the office worrying about my coat and enjoy the satisfaction of wearing my nice coat. on the other hand, a policy of acting in accordance with the meteorologist’s predictions is probably, over time, a useful strategy for getting what you want, but i’m not sure how that impacts your case, because i suspect you are talking about the particular information you get on one particular day.

    i could go on and on about this… can you tell i have a draft i have to finish today? thanks for the procrastination material!

  2. dtlocke says:

    Hi, Alex. Thanks for the thoughts. In the interest of being concise, I left out what would have probably been the useful clarification that all issues concerning other ‘things one might want in this situation’ should be set aside. I’m just trying to get at whether the information is useful qua this one decision with respect to the mentioned benefits and desires. (Imagine, if you like, an idealized agent who dis/values only these things.) I could spell that out in more detail if you like, but I think you get the point. Also, yes, I am interested in just this one piece of information on this one particular day.

    What I’m trying to get at is this question: is the mere fact that a piece of information rationally leads you to do what, in fact, has the worse consequences, enough to undermine the utility of that information? If so, in what respect?

  3. David says:

    Are you thinking of the agent in question as an expected utility maximizer? If so, then I’m having trouble seeing how the information wouldn’t be useful for getting what you want if (a) what you (ultimately) want is to do the thing that maximizes expected utility, and (b) the information is useful for deciding what to do which act maximizes expected utility, It’s true that when you make decisions with the aim of maximizing expected utility, the world doesn’t always bring the state of the world that you’d like, but does that mean that you didn’t get what you want? I guess it’s going to matter how you fill in ‘getting what you want’.

    If you mean ‘getting the state of the world you most desire’, then the information isn’t useful for that. But it’s hard to see how your information could ever be ‘useful’ for that. Getting what you want in this sense depends upon some chancy event coming about over which you – and your information – have no control.

    If you mean ‘being in a world where you expect to maximize your utility’, then your information is useful for that. This seems like a plausible rendering of ‘getting what you want’ if you consider that, in the 2nd scenario, you’re unlikely to think that you should have chosen differently. It’s true you might wish you didn’t have your umbrella with you, but having this wish is compatible with also thinking that you made the right decision all things considered. And insofar as ‘getting what you want’ means making decisions that are expected to maximize your utility, then the information is useful for getting what you want in the second case.

  4. dtlocke says:

    David, yes I am thinking of the agent as an expected utility maximizer and your above distinction hits the nail on the head!

    But things aren’t quite so simple. First, agents don’t simply want to maximize expected utility—rather, they want the things to which value is in the first instance assigned (e.g., being kept dry in the rain). Second, notice that information doesn’t help you to maximize expected utility–you can already do that; you just calculate expected utility using your current credences and then do the action with the highest expected utility. So if there is a sense in which the information in scenario one is useful, it’s not via helping you to maximize *expected* utility. Rather, it seems to be useful in the sense that, once you take it on board, the new expected utilities of your actions will be such that the action with highest expected utility is the action that has the highest utility (simpliciter). But that feature isn’t present in the second scenario and, hence, it seems that the information in the second scenario is not useful in the way that the same information in the first scenario is useful.

  5. Steve C. says:

    “Question: was the information that all meteorological signs point to rain useful information with respect to your decision whether to bring an umbrella?”

    Hey Dustin,
    It sounds to me like you’re using “useful” to indicate promotion of the attainment of an end. Are you? (I thought this based on your proposed answer, which seems to invoke two different ends: getting what you want, deciding what to do.)

    In any case, if that’s a helpful way to think about usefulness, then I think the reason the question above admits of no obvious answer (as you observed) is that it’s a vague question. It isn’t obvious what end is implicated by “useful with respect to a decision.” We could make it more precise by specifying what the end in question is. It seems like there are going to be a number of potential ends that might be associated with a decision. I think one of them, as Dave pointed out, might be to do the thing with highest expected utility. Don’t good poker players often prefer to play “rationally” even if that means having bad luck on occasion? Isn’t that acting with the aim of maximizing expected utility, rather than actual utility? If so, a person might make all of her decisions in this way, ultimately caring more about being satisfied with the quality of her decisions than with optimal outcomes. But, as you pointed out, often an end is more a matter of actual utility.

  6. dtlocke says:

    Hi, Steve. Thanks for the thoughts. The only thing I think I can disagree with is the second or your rhetorical questions:

    “Don’t good poker players often prefer to play “rationally” even if that means having bad luck on occasion? Isn’t that acting with the aim of maximizing expected utility, rather than actual utility?”

    No, acting with the aim of maximizing expected utility *is* acting with the aim of maximizing actual utility. From the agent’s perspective, these are one and the same thing. It’s just that, as it happens, acting with the aim of maximizing expected utility/actual utility doesn’t always mean maximizing utility (as my scenario two and your poker player example show).

    As far as what I mean by ‘useful’, I don’t want to beg any questions by stipulating a certain meaning; rather, I just mean whatever it is we ordinarily mean when we say something like ‘that was useful information’. One way to put the question I’m asking is, “What *do* we mean by ‘useful’ when we say that?”

  7. Richard says:

    I’m tempted to say the information wasn’t genuinely useful at all. You made use of it, for sure, but this turned out to be counterproductive, i.e. lacking in instrumental utility. (This is so even with regard to ‘deciding what to do’ — after all, you made the wrong decision, however reasonable your mistake might have been in light of the misleading evidence. Without this misleading info, you still would have ‘decided what to do’, and you might have even done a better job of it!)

    I guess one might use the term differently, to simply designate information that provides one with relevant evidence for one’s decision (or something along those lines).

    If the question really is vague or ambiguous between these two interpretations, then isn’t that just to say that there is no one definite thing “we mean” here? Once the disambiguations are offered, there’s nothing more to settle, is there?

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