Dear Forest:
check

http://www.rangevoting.org/DhillonM.html

I was never really able to fully understand this paper.
You, having more motivation and/or ability, might be able+wanting to.
Then you can explain it to us all.
(Note, the paper pdf is linked to the bottom of that web page, so
you do not have to go to a library.)

It seems to do something like what you were asking for.  It proves (or
claims to - I'm a bit hesitant to endorse since I never fully
understood)  that "normalized range voting" is the unique voting
method satisfying a set of Arrow-like criteria, including an IIAC
idea quite like yours.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html
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