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#1
01-20-2006, 05:52 PM
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Painful Puzzle
Would you rather have 1 year of the worst possible physical pain or two years of almost the worst possible pain?
Would you rather have 2 years of almost the worst possible pain or 4 years of almost almost the worst possible pain? You pick the shorter duration in both cases do you not? Now if we repeat the pattern and you accept the premises for a huge amount of steps we would get some point where you would choose the 1 year of terrible pain over a billion years of a tiny bit of pain. This is because preferability is transitive. If you prefer B over C, and A over B, then you prefer A over C. So is it true that you would pick the one year over the billion years? If not where is the flaw in the reasoning? Interestingly, the same puzzle can be formulated for pleasure with perhaps different results. 
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#2
01-20-2006, 06:29 PM
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Re: Painful Puzzle
C is not always C in your reasoning. You change C yet you still assign the same value to it
If you ask me, the results are obviously opposite. I would try to maximize pleasure and minimize pain. Ultimately, for any of this to have any meaning, you have to assign real values to the level of pain and pleasure (which you can't, because only an individual knows how much pain or pleasure he's feeling and he can't communicate that entirely), saying "the almost worst pain" is not a real value: everyone can understand that in a different way
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#5
01-20-2006, 07:38 PM
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Re: Painful Puzzle
The standard assumption is that preferences are transitive. If they aren't, you get some weird results (If A prefered to B, B prefered to C, C prefered to A we have a real problem. Because presumably if you strictly prefer one thing to another, you'd be willing to trade some small amount of money to switch. But with this cycle I can make an infinte amount of money from you.) Whether or not people actually have transitive preferences is a subject of some debate.
In this case, the problem isn't necessarily non-transitivity. My guess is that at some point, you stop trading more pain for less time. Also, there is a hypothetical bias problem, especially when we're talking about billions of years and terrible pain.
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#6
01-20-2006, 08:22 PM
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Re: Painful Puzzle
[ QUOTE ]
[ QUOTE ] [ QUOTE ] This is because preferability is transitive. If you prefer B over C, and A over B, then you prefer A over C. [/ QUOTE ] I don't think this is true. [/ QUOTE ] Care to elaborate? [/ QUOTE ] Sorry; it made sense to me at the time. [img]/images/graemlins/wink.gif[/img] What I meant was that your argument essentially only has one step, yet produces an illogical result, therefore I'm pretty sure the one step was wrong. The first situation is that you are offered a choice between two very similar levels of pain (perhaps infinitesimally different) but durations that differ by a factor of two. Clearly you will always choose the shorter duration, no matter what the level of pain. In the second situation you are given a choice between durations that still differ by a factor of two, and an enormously large difference in pain. Clearly you choose the drastically lower pain level. I don't think it's the case that a series of choices of the first kind is equivalent to one choice of the second kind, if that makes any sense.
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#7
01-20-2006, 08:35 PM
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Re: Painful Puzzle
Well how exactly are the cases different? One is intense pain for a relatively short amount of time, and the other is almost no pain for a very long time. I think most of us would choose the latter over the former. The problem is in the first step and second and third etc. we choose the shorter time.
At what point do we reject the shorter by 1/2 duration of pain in exchange for slightly less intense pain? I dont see how anyone would ever make this choice. The intensity is going down by a static but tiny amount and the duration is doubling. Why would anyone ever make this trade? The problem is there has to be some point where we change our mind or else the transitivity of preference is wrong.
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#8
01-20-2006, 07:38 PM
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Re: Painful Puzzle
[ QUOTE ]
C is not always C in your reasoning. You change C yet you still assign the same value to it If you ask me, the results are obviously opposite. I would try to maximize pleasure and minimize pain. Ultimately, for any of this to have any meaning, you have to assign real values to the level of pain and pleasure (which you can't, because only an individual knows how much pain or pleasure he's feeling and he can't communicate that entirely), saying "the almost worst pain" is not a real value: everyone can understand that in a different way [/ QUOTE ] I dont think you are correct with your point about the puzzle being meaningless. You say it is not a real value because everyone can interpret it a different way. I agree that 'almost the worst possible pain' is a vague term which denotes a range of pain, but that doesnt mean you don't understand what it means. If I say so-and-so is bald this isn't an exact term but saying so-and-so is bald obviously means something. Please understand it in whatever way you like, it doesn't have to refer to an exact amount of pain for the statement to be used in a meaningful way. You will do whichever minimizes overall pain? What if you had to choose between 100% maximum possible pain for 1 year or 10% maximum possible pain for 10 years? They have the same amount of pain right? What about 1% for a 100 years vs 1 year at 100%?
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#9
01-20-2006, 11:10 PM
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Re: Painful Puzzle
[ QUOTE ]
You will do whichever minimizes overall pain? What if you had to choose between 100% maximum possible pain for 1 year or 10% maximum possible pain for 10 years? They have the same amount of pain right? What about 1% for a 100 years vs 1 year at 100%? [/ QUOTE ] That's much better. However I don't think the puzzle here would be hard (and besides, the point that you assign the same value to C when changing it still stands). There seems to be no pain minimization possible here. However, so long as I was to live 100 years (meaning option C wouldn't minimize pain), I'd take 1 year @ 100%, all the way. Of course it could be argued that 100 years @ 1% means you get accustomed to the pain so you reach a point where it doesn't hurt; or that a year of 100% drives you insane so you're unable to live the rest of your life happily, but those arguments are assumed not to be true in my answer; since that would mean pain minimization (or, in other words, happiness maximization) IS possible. On the other point: Preference IS transferable, so long as the preference is rational. When it's based on whims it doesn't have to be; but that's because it's not really a preference, just a whim [img]/images/graemlins/smile.gif[/img]. But as I said, you change C and still call it C, which is wrong: One would take a billion years of tiny pain over all your first three options, and any of the in-between, too.
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#10
01-20-2006, 08:36 PM
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Re: Painful Puzzle
Two problems. First, a billion years doesn't matter to anyone since the lifespan of a person is only around 100 years let's say. So the series can only go on so long. Secondly, in essence, your argument might make sense for someone who wants to just "suck it up," but many people have a pain threshold which, once crossed, dramactically increases the severity of pain. But let's never mind that, and worry only about the first problem.
Some people may choose 1 year of terrible pain over 100 years of pain which is constantly nagging. This doesn't seem like such a big deal. It's the same as someone taking a million dollars over one year or over 30 years. It's personal choice. Your argument doesn't work when you don't take the limit to infinity. And as any smart non-Mathematician will tell you: Infinity does not really exist.
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