[EM] very simple email poll
heitzig-j at web.de
Mon Mar 5 02:57:14 PST 2007
ad 2., you wrote:
> >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?
That is very interesting. I expected this argument for question 1 not 2.
I think here the answer is obvious: The ratings are about single
options, not lotteries; so, for them to reflect preferences about
lotteries, one must assume something about how the rating of the
lottery would look like given the ratings of the options. Standard
utility theory (which I have often critizized) claims that the rating
of the lottery would be just the expected rating of the options, in
this case 17 for both voters.
However, in my view, the individual ratings are not the right place to
code the value of fairness into, since fairness is not an individual
but a social thing. Hence the greater amount of fairness of the coin
toss should be reflected in its social rating instead, as it will be
when some social welfare function is used to compute the social rating.
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