Friday, November 19, 2004

Buridan's Ass

Joe at Oohlah's Blogspace recently mentioned Buridan's ass: caught between two equally-tempting piles of hay, the ass starves to death because it cannot choose between them. This is supposed to be a paradox. I may be missing something (as always, if I am then let me know!), but it strikes me as problematic only if we adopt an overly-abstract model of rationality. The supposed problem, I take it, is that absent any reason to prefer one option over another, it is irrational to choose either. The solution, I think, is to flesh out our abstractions with a little more practical detail.

Firstly, note that cognition comes at a cost - in terms of time, energy, and opportunity costs. So a rational agent should only cognize when the benefits of doing so outweigh these costs. Eventually one will reach a stage when further deliberation is no longer worth it, and one should engage in action instead. Thus grounding Buridan's Ass in an ecological context readily demonstrates its irrationality, for it continues to waste its resources assessing a choice that makes no difference.

Normally, once we realise that further deliberation is unproductive, we simply go ahead with our presently-favoured choice. The difficulty in this case is that, ex hypothesi, the ass has no favoured choice. One obvious solution would be to employ a random device, say, flip a coin. But I think even this is too much unnecessary effort. The ass should just pick one.

I think only a reasoner that had been abstracted away to the point of absurdity would find itself utterly 'frozen' in the situation of Buridan's ass. Any more realistic reasoner would be capable of making arbitrary decisions at ease (we certainly are!). Perhaps the sun shone more brightly on one side, or a bird was singing pleasantly to the other, or the agent was right-handed (hooved?). These are silly little things, of course, but any one would be enough to tip the scales and allow a decision to be made one way rather than the other.

Here one might complain that I have ignored the requirement that the agent (or ass) has no reason - not even a silly reason - to prefer one choice over the other. To this I would respond with a second appeal against abstraction, namely, to recognize that real-world cognition is a process in flux. Even if at one moment all its preferences perfectly balance out and the ass cannot choose one side over the other, we need only wait a moment for the next fluctuation to give rise to a slight imbalance.

The ass would not be constantly feeling exactly equal temptation for each pile of hay. That's just not how thinking works. Rather, the ass would be continually flickering back and forth in its preferences, as the equally-deserving bales of hay vied for its fickle favour. This more realistic view of cognition makes the problem disappear - for once our ass realises it's time to stop deliberating, it could simply go with whatever option happened to be favoured at that particular moment.

Update: Joe has more at Third Floor.


  1. Decision-making is firstly a temporal process, as you touched on at the end. I actually firmly believe rationality IS an abstract concept, and all we can do is aspire towards it.

    If you are being pursued by an axe-wielding maniac, and you come to two identical looking doors, the best decision is simply to MAKE a decision; it may be the worse path, but the worst possible path is weighing up which one is the best while the axe-murderer catches up. 

    Posted by Stephen Cooper

  2. What if the fluctuation of intrests between hte two bails of hay is such that the ass keeps wanting hte one he is not looking at. all that would take is for him to over value things in his memory over things in his sight (one would think the opposite would usually be true but one can think of many examples of "it was better in my day" sort of fond memories.
    If that is hte case then the ass opens himself up to making a choice and choses one but immediatly gets the urge to chose the other. The question is - is he capable of rejecting the urge because he is facing the other pile of hay? this seems to be how indecision often works - with hte person making an abortive attempt in each idrection a few times before deciding -
    and them maybe regreting it for no logical reason.
    Your argument of course solves the paradox in an absolute sense in that one should take the cost of cognitition into the equasion but of course the ability to do that IS cognition - if one was conserving mental power one would usually not bother to test if things required mental power - because it requires mental power to do so - thus leaving a subjective problem if not paradox. 

    Posted by geniusnz

  3. Stephen - I would still think that rationality has to be grounded in an ecological context for the concept to be any use. To take your axe-murderer example: do you really want to say it is rational for the victim to stop and weigh up their options before choosing a door?

    Genius - re: fluctuations, I was meaning to suggest that the ass stop thinking about it altogether once the appropriate 'time' is up. So later fluctuations would be irrelevant.

    You rightly note that we must also 'work out' when to stop working things out, a puzzle I'm not sure how to answer. I suspect that overall a brief test here (to work out roughly how much effort one ought to put into working out the original problem) would be beneficial to us. It would use up some mental power, sure, but not nearly as much as would working away at a problem for hours more than you needed to. Think of it as a sort of insurance policy. 

    Posted by Richard

  4. Richard,

    Thanks for taking the time to deal with this problem. I also want to say that I agree it is a problem that can be overcome practically. The problem is how to cash out what we mean by "practical."

    I would like to address only your first argument in this comment. I gather that your claim is that we should only cognize when the benefits outweigh the costs, and action should commence as soon as we reach a point at which deliberation is no longer worth it.

    First, I am not sure that I agree we should cognize only when the benefits outweigh the costs. Thinking about mathematical puzzles or thinking about how to deal with a dispute with a friend costs a great deal. We sometimes wonder why we waste our time thinking about these things, but we still do it. We do it because if we didn't do it, then we might say something we regret or deal with a mathematical puzzle incorrectly. In these cases, it seems that the costs outweigh the benefits, but we still perform the costly action.

    Second, the point at which deliberation turns into action is vague. How do we know that we've deliberated enough about a problem? In the case of Buridan's Ass, I've always taken it that we cannot set some point in time when deliberation has become futile. If we do decide that enough is enough and pick one of the two options, we run the risk of acting arationally at best or irrationally at worst.

    If we set a point - say, I'm going to think about this for 1 minute and whatever I decide to do I will do - then we have to ask ourselves why we picked that criterion to settle the issue. If we don't have a reason for the criterion, then we face the challenge again on a different level - on a meta-level (for lack of some better term).

    Though I agree that this is the way to settle the issue, I am not sure how to conclude that this is what we ought to do. There's the arational/irrational worry and having to deal with a meta-level Buridan's Ass problem. 

    Posted by Joe

  5. Joe, thanks for the feedback. To respond to your two main points:

    "In these cases, it seems that the costs outweigh the benefits"

    I disagree. Unless one adopts an impoverished view of wellbeing, I'd say that resolving a social dispute or solving a mathematical puzzle can both count as significant benefits, which well outweigh the costs involved. (Up to a point, that is. One can imagine anything being taken "too far", though, such as if it were to turn into an obsession.)

    "I've always taken it that we cannot set some point in time when deliberation has become futile. If we do decide that enough is enough and pick one of the two options, we run the risk of acting arationally at best or irrationally at worst."

    If all the evidence available to the ass leads it to consider both options equally desirable (and he has no reason to think he's missing something crucial), then that would immediately suggest that further deliberation is not worth the bother. The difference in expected values is negligible, so it doesn't much matter which is chosen.

    So I think your objection about possibly making an arational or irrational choice here neglects my original point that cognitive costs must be taken into account as a factor in 'rational' calculations. Since the costs here clearly outweigh the expected benefits (which are near-zero), it would actually be irrational of the ass to continue deliberating!

    More generally though, I do concede that knowing when to stop deliberating could be problematic. Perhaps the rational agent would need to keep a 'running tally' (of sorts) of the various values and their associated probabilities. If he judges that there's a high enough chance that he's making a wrong enough decision, then he would want to continue deliberating until he's more "confident" of the results.

    Do you think something along those lines might work? 

    Posted by Richard

  6. Richard,

    I do think that you're line of reasoning is working well toward a resolution of Buridan's Ass, but I want to take issue with the idea you mention in your last comment that "the difference in expected values is negligible, so it doesn't much matter which is chosen."

    First, I think this is the right statement to make, but I am not sure how it works to get the ass out of continuing to deliberate. If there is no difference in expected values between A and B, then it seems we cannot distinguish between A and B. If it seems that we cannot distinguish between A and B and we want one or the other over having none, then what do we have to determine which one we want?

    Well, this leads to two scenarios: If we don't pick one, then we've violated our wanting at least one A or B over having none. If we choose A or B over the other, then we seem to have chosen A or B randomly. I guess my problem - all along - has been why is it rational to choose randomly? Does this sort of thing need an explanation?

    I like your idea that the cognitive costs might be too much for the ass, but I am not sure when to call something "too much" or "too little" deliberation. I have to think about your proposal about "running tallys" some more before I comment on that. My initial reaction is that we've only drawn the problem one-step back by proposing such a way out. 

    Posted by Joe

  7. "If it seems that we cannot distinguish between A and B and we want one or the other over having none, then what do we have to determine which one we want?"

    That could be where my second point (the one about 'fluctuations') comes in handy. Perhaps in actual fact we will always have some faint preference for one over the other.

    But if we accept the "exactly equally desirable" abstraction for the sake of argument, then I guess I need to respond to the problem you raise. I do think it's rational to choose randomly in such a case, simply because that's what must be done to get the desired result (of either A or B).

    I guess what I want to say here is that if the choices really are indistinguishable, then choosing A is equivalent to choosing B. It simply doesn't matter which you choose, or how you choose it. (There is no "one we want"; rather, we want either.) So, given that any choice at all is rational in such a situation, it follows that a random choice is rational.

    (Sound plausible? Or do you think I've pulled a fast one here?) 

    Posted by Richard

  8. Richard,

    It does sound plausible, though I'm going to try to stir up trouble by addressing your last argument - try to play devil's advocate.

    I think your argument is the one that most will agree is the way around the problem of Buridan's Ass, but there might be some people who consider it a "fast one."

    I'll probably blog on it at the beginning of next week on my blog. Stay tuned - if interested. And thanks for your comments! You've been very helpful!


    Posted by Joe

  9. "I'll probably blog on it at the beginning of next week on my blog."

    I look forward to it! 

    Posted by Richard

  10. Those of us in the second rate mind catagory,who must suffer the indignities of daily diligence, have a phrase that sums up this entire argument. It's call "Paralysis by Analysis." STOP PREPARING!
    Regards, Jim


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