[EM] very simple email poll

[Abd ul-Rahman Lomax]

At 07:26 AM 3/4/2007, Jobst Heitzig wrote:
>Hello folks,
>
>I would be very glad if all of you would take one minute's time to 
>answer this very simple email poll!

Well, the problem with ad-hoc polls is that the answers depend on the 
questions, and ask the wrong questions, you'll get misleading answers.

>Consider a situation with three options A,B,C and only two voters, 
>whose ratings* are as follows:
>
>voter 1: A 100, C 50, B 0
>voter 2: B 100, C 50, A 0
>
>Now please answer these three questions with "yes" or "no":
>
>1. Is C socially preferable to A? ___

If we accept the conditions stated as below, that there is no more 
information, there is absolutely no way to tell. However, considering 
general conditions and a peer society, it is highly likely that the 
preferable option is C. This is because the utilities are so 
drastically different. If, for example, the options are:

A 1 gets all the food, 2 starves
B 2 gets all the food, 1 starves
C both get enough

It's pretty clear that option C is generally preferable. But what if 
option C is that both die, since there is only enough food for one person.

This is a zero-sum game, and, let me suggest, it is not one which is 
generally soluble with an election method....

Real elections and real choices are, far more often, not zero-sum 
games. Nor are the utilities so drastically opposed; we will see such 
expressed utilities in Range Voting, but this is because of 
normalization and magnification. It is generally assumed that people 
won't want to make choices that push all the chips into one corner, 
and it is assumed that people *may* behave as if this is what they 
want, because, with rule of law, it won't actually happen. Usually. 
We allow and even encourage self-interest, justified by an assumption 
that pursuit of self-interest results in common good.

It's obviously an assumption that does not hold under all conditions.

Faced with the election scenario, I wonder what would happen if 1 and 
2 sit down and talk. Why in the world would two people use a Range 
election method to actually make the decision? Especially given such 
opposing utilities? Rather, these people need to seek better 
solutions than A, B, and C. They might exist.

>2. Is tossing a coin to decide between A and B socially preferable to A? ___

It might be perceived as fair. Let's look at this situation in 
another way. Let's assume that the utilities are normalized. 
Actually, on an "absolute" scale, the ratings would look like this:

voter 1: A 18, C 17, B 16
voter 2: B 18, C 17, A 16

Sum of utilities is the same no matter what choice is made. Now, here 
is the paradox: if we assign a value to "fairness," to these two 
voters feeling that they were treated fairly, such that neither 
resents the other, we might see A or B as being inferior to C. But 
why was this not reflected in the ratings? Given the conditions of 
the problem, and assuming that the ratings are made *with knowledge*, 
we are stuck.

Looking from the outside of this system, I might think that C is 
better because then A and B aren't likely to fight. But, of course, 
this utility may have been incorporated into the ratings.

Other things being equal, though, my instinctive reaction is that C 
is the best solution. However, if both voters consent, then the coin 
toss may be better. It depends on what these choices are and how 
important they are. Even if they are life and death, choosing the one 
who drops off the lifeboat has often been done by drawing straws.

>3. Is C socially preferable to tossing a coin to decide between A and B? ___

*If* it is perceived as fair by 1 and 2.

>*If you want, you may interpret the ratings as the best information 
>we have about "individual utility".

I considered this and played with it.