[EM] very simple email poll
Abd ul-Rahman Lomax
abd at lomaxdesign.com
Sun Mar 4 14:06:10 PST 2007
At 07:26 AM 3/4/2007, Jobst Heitzig wrote:
>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.
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