Painful Puzzle

[Borodog]

Well, the trick is in the statement of the choices I think. The situation doesn't seem to be analogous to, "I prefer redheads to brunettes, I prefer brunettes to blondes, therefore I prefer redheads to blondes."

So, "I prefer some pain for some time to slightly less pain for twice that time, I prefer some pain for some time to slightly less pain for twice that time, I prefer some pain for some time to slightly less pain for twice that time, . . . , I prefer some pain for some time to slightly less pain for twice that time, therefore I prefer some pain for some time to far less pain for twice that time" does not follow.

But in that case, it doesn't look like I'm arguing against the transitivity of choice so much as the form of the choices.

[Bork]

I think I follow you, but I am not sure I agree.
Are you saying somewhere along the lines the form of the dilemma changes? I dont see how this could be. What makes the form different? Is it something about the non-linear nature of pain?

I more leaning more towards what math economist said that there is some point where the pain goes from being bearable to unbearable and at that point you might decide that you are happy to double the length in exchange for the small decrease in intensity.

Maybe these are stylistic variants on the same objection. Im still a bit confused.

[Borodog]

[ QUOTE ]
Im still a bit confused.

[/ QUOTE ]

Me too. I'll keep thinking about it, and try to get back with something that makes more sense tomorrow.

[Borodog]

[ QUOTE ]
I more leaning more towards what math economist said that there is some point where the pain goes from being bearable to unbearable and at that point you might decide that you are happy to double the length in exchange for the small decrease in intensity.

[/ QUOTE ]

I'm pretty sure I don't agree with this. I can't see anyone (except maybe a masochist) choosing 99% of the pain for 200% of the time over 100% of the pain for 100% of the time.

[MathEconomist]

The more I think about it, the more I think this might be hypothetical bias. A billion years is a long time, even if the pain isn't really that bad. It's easy to commit to minor pain for a billion years without really understanding what that entails when we only live for a hundred or so. I'm also fairly sure that pain would be valued non-linearly (though of course what scale you use for something unmeasurable like pain is entirely arbitrary, so I suppose you could simply define it to be linear).

[atrifix]

[ QUOTE ]
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?

[/ QUOTE ]I have no idea, because I have no idea what the worst possible pain or almost almost worst possible pain would feel like.

[ QUOTE ]
This is because preferability is transitive. If you prefer B over C, and A over B, then you prefer A over C.

[/ QUOTE ]This is just false.

[soon2bepro]

[ 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.

[Bork]

[ QUOTE ]
This is because preferability is transitive. If you prefer B over C, and A over B, then you prefer A over C.


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This is just false.

[/ QUOTE ]

People keep saying preference isn't transitive without giving reasons why they think this. It seems clear to me at any given time if you prefer A over B, and B over C, that you also prefer A over C. Whats the counterexample I am missing?

[Borodog]

[ QUOTE ]
It seems clear to me at any given time if you prefer A over B, and B over C, that you also prefer A over C. Whats the counterexample I am missing?

[/ QUOTE ]

I think there's part of the problem.

[MCS]

Transitivity of preferences is a fundamental assumption of economic theory. However, people sometimes answer survey questions like this in an inconsistent way. This leads some to argue preferences are not transitive, but others argue that STATED preference is not identical to REVEALED preference, and that the latter is what we should examine.