General

[quote=Al3xL3g3nd]Ah gotcha.
It's assuming pain and time are connected so you must chose which weighs more, the pain or the time. If you chose pain, transitivity doesn't hold and if you chose time, it does.[/quote]

Thank you for being the non-skeptic and answering the question how 99% of the 10,000+ lectured individuals answered the question.

You're partially right. Although transitivity does not seem to hold regardless of whether you choose pain or time as your deciding fact, you do raise an important question about how we should consider duration and pain felt across a duration. This is why I wanted to tell you guys to draw a graph. Essentially, if you are to draw this (and this kind of gets into set theory if you're familiar with it from math class) on a graph where x is your duration and y is your intensity. You'll notice that the area under the curve can give different stories depending on how we evaluate and define our sets. In some cases, it will say that it is undefined or simply put that you can't compare the two things.

It's like looking at something really wide and something really tall and asking which is bigger? You can't compare two things if in one you're comparing width and the other you're comparing height.

[quote=CaptCandy]
@SirJayGatsby: I got your point, but I just used two numbers just as an example earlier.

OT:
1. Crate 1
2. 3
3. Never
4. The second one (is Maplestory right?)[/Quote]

Well, given your answers some might call you crazy but more to the point you seem to be agreeing with the conclusion that transitivity does not hold. It's just that for you, we'd work backward to the most extreme case being the one we think is intuitively better (from your perspective) while the one with no pain is the worst (also from your perspective). If you want to avoid the transitivity problem you have to answer inconsistently. ie,

1. Crate 2
2. 3
3. 1
4. 2 (yes maplestory)

@SirJayGatsby: I got your point, but I just used two numbers just as an example earlier.

OT:
1. Crate 1
2. 3
3. Never
4. The second one (is Maplestory right?)

1. none.
2. worst. no pain no gain.
3. i don't play sports.
4. neither.
5. what's their values?

[quote=CaptCandy]@SirJayGatsby: I didn't answer question 4 for a reason. It's because I don't know how to quantify the two pains (whether case 1 > or < case 2), because life is full of qualitative rather than quantitative data. Except for one thing. You said the wax would be 1 degree cooler, and the pain would be smaller by a "hair less" amount. What is "hair less"? Could it be infinitesimally small? We simply don't know, because "hair less" is qualitative, so I could not answer question 4.[/quote]

You're only avoiding the question. It does not matter how much a hair less is or not. All that is trying to get across to you is that the difference in pain between any two cases so, n and n+1, is a really small amount such that it is just barely noticeable or able to be felt. You could, for your own purposes, get really technical about it and say that the difference is whatever the smallest feelable threshold for pain is but that does not really matter either because I could just an example where you are choosing things that are not experience-based.

I chose this example because it has to do with a question in value theory and normative ethics that I'm working on for law school.

If you'd like we can do the same case with another example over PM or something. To answer your question about the rock paper scissors thing, you told me nothing of the relation between Rock and Paper.

What the fudge am I reading?

http://xkcd.com/169/

@SirJayGatsby: I didn't say which pain I would choose in question 4 for a reason. It's because I don't know how to quantify the two pains (whether case 1 > or < case 2), because life is full of qualitative rather than quantitative data. Except for one thing. You said the wax would be 1 degree cooler, and the pain would be smaller by a "hair less" amount. What is "hair less"? Could it be infinitesimally small? We simply don't know, because "hair less" is qualitative, so I could not answer question 4.

Also, I just used two numbers as an example.
And yeah, I understand what you're doing, it's calculus III where I'm from.

In case 1, I lose 1 year of life out of like 100. While in case 2, I lose 4 year of life out of 100. So my total utility changes by about 3% between those two.

[quote=SirJayGatsby]Dude, all you have to do is pick between B and C. I already know you'll choose instance 2 over instance 3. All you're doing now is trying to find some sort of catch or avoid stating the obvious because you want to say transitivity holds. You've already agreed with enough for me to show you that it does not hold. I only wanted to go further with question 4 so that it was clear to you. But you're already ruining the game just by trying to find some catch or create one where there is not.[/quote]
Ah gotcha.
It's assuming pain and time are connected so you must chose which weighs more, the pain or the time. If you chose pain, transitivity doesn't hold and if you chose time, it does.

You guys are taking this out of the context of a "game" by trying to find a trick when there is not one so we may as well do the explanation so you can still take something away from it,

The most important case is the 4th one. Notice that you chose instance 1, we'll call this A, over instance 2, we'll call this B. Thus you've said, A > B. In the third case in question 4 you were all going to choose instance 3, we'll call that C. Thus what you've said is B > C. We can continue this game in question four by continually reducing the pain such that the difference between n and n+1 is only a hair of pain (whatever is the minimum amount of pain such that it is able to be felt by the human body) while increasing the duration of the pain (Doubling, squaring, tripling, whatever floats your boat). The point is that somewhere along the possible instances we'll come to a situation where the pain you feel is minuscule, perhaps you barely feel it at all but it will be for an extremely long time. However because you chose that pain A > B and B > C, A would have to be better than this case too IF TRANSITIVITY HOLDS.

To make the case of minuscule pain I'm talking about more clear, it's basically saying you choose between these:

The most excruciating pain of your life for 1 year and after which you forget the pain and are healed from all injuries by a pill. In the second case, you will experience a minuscule pain for a very long time (let's say 90 yrs) and afterward take a pill and forget it. It is clear that in this case, we'd rather choose the second torture case than the first.

If what we know about transitivity is true: A > B > C > D > E > F > G > H > I > J > K > L > M >... then you would have to say that the FIRST pain which is the most excruciating of your life is better than the case where the pain is minuscule and there-in lies the problem.

Either transitivity is false or you need to offer an explanation as to why you all choose the less harsh pain in such a way as to make it worse than A.

@SirJayGatsby: Umm, how about Rock > Scissors, and Scissors > Paper. Is rock > paper?

Or Water > Fire, Fire > Plant; water > plant?

[quote=Al3xL3g3nd]The point is you can take a pill afterwards that makes the pain go away and makes you forget that it ever happened. The utilitarian would then chose the first case because it is less time spent since pain isn't a factor anymore.[/quote]
Dude, all you have to do is pick between B and C. I already know you'll choose instance 2 over instance 3. All you're doing now is trying to find some sort of catch or avoid stating the obvious because you want to say transitivity holds. You've already agreed with enough for me to show you that it does not hold. I only wanted to go further with question 4 so that it was clear to you. But you're already ruining the game just by trying to find some catch or create one where there is not.

[quote=SirJayGatsby]You should hold this thought if you're well-versed in mathematics (calc 4) or just save this line of thinking because its a good way to think about these things, but make the choice I asked first. So I can show where this leads.[/quote]
The point is you can take a pill afterwards that makes the pain go away and makes you forget that it ever happened. The utilitarian would then chose the first case because it is less time spent since pain isn't a factor anymore.

[quote=CaptCandy]@SirJayGatsby: Greater magnitude does not mean greater value.

Example: -100 > -400, but their magnitudes (absolute value) is |-100| < |-400|.

So, in example 4, the magnitude of utility in case 2 might be greater (the absolute value of a larger negative number is greater), but the value of utility in case 1 is greater than the value of utility in case 2 (-100 > -400, but |-100| < |-400|)

So yeah, I don't understand, what's your point?[/quote]

You should hold this thought if you're well-versed in mathematics (calc 4) or just save this line of thinking because its a good way to think about these things, but make the choice I asked first. So I can show where this leads.

@SirJayGatsby: Greater magnitude does not mean greater value.

Example: -100 > -400, but their magnitudes (absolute value) is |-100| < |-400|.

So, in example 4, the magnitude of utility in case 2 might be greater (the absolute value of a larger negative number is greater), but the value of utility in case 1 is greater than the value of utility in case 2 (-100 > -400, but |-100| < |-400|)

5. A>B>C, A>C, but it can be that |A| < |C|.

So yeah, I don't understand, what's your point?

[quote=Al3xL3g3nd]How does answering the first case in Q4 prove that transitivity doesn't hold?
This just seems like a would you rather. It doesn't actually prove anything.[/quote]

Would you choose B or C? I'll give you the logic once you choose.

[quote=SirJayGatsby]Thanks for playing guys. As I predicted, you all hold an inconsistent set of beliefs. Namely, you believe in transitivity when it is clearly false. So here's the proof.

You said, A > B > C, therefore A > C. That's basic use of the transitivity property and it would be true IF transitivity holds. But what you all told me is that it does NOT hold by answering the FIRST case in question Four rather than case two.

Edit: If you would like me to elaborate more, just say so and I will.[/quote]
How does answering the first case in Q4 prove that transitivity doesn't hold?
This just seems like a would you rather. It doesn't actually prove anything.

[quote=Blackest]Most of these are obvious, so what's the catch.

@sirjaygatsby: elaborate more. pls[/quote]

I could give you the answer but let me continue the game as to make the problem more evident.

We'll continue with case 4.

The first two instances of torture exist but now you have a third option. You can either take the torture from instance two (in question 4) or you can experience instance three. Instance three is a hair less pain than that in torture two. You will experience this pain for 16 years. Notice that the pain still is almost exactly as excruciating as in instance one (of question 4). Which would you prefer? Instance 2 or Instance 3?

Previously, you chose 1 > 2, or A > B. Now I'm asking you to choose between 2 or 3, or B and C.

You didn't explain it very well?
Are you trying to say you can either choose either A (all the first options) or B (all the second options) or C (all the third options)? O.o

Most of these are obvious, so what's the catch.

@sirjaygatsby: elaborate more. pls

Thanks for playing guys. As I predicted, you all hold an inconsistent set of beliefs. Namely, you believe in transitivity when it is clearly false. So here's the proof.

You said, A > B > C, therefore A > C. That's basic use of the transitivity property and it would be true IF transitivity holds. But what you all told me is that it does NOT hold by answering the FIRST case in question Four rather than case two.

Edit: If you would like me to elaborate more, just say so and I will.

[quote=Assumptions]1. Crate 3
2. First case
3. Take the pill as soon as possible
4. First case
5. Yes

I'm confused[/quote]
I got the same answer as you did..