[EM] Saharon Shelah with own version of Arrow Theorem... I wonder what it is?

[Warren Smith]

Saharon Shelah is one of the best logicians in the world.
Which normally means nobody pays attention to him and his
work is very hard to penetrate.  There's nothing like modern
mathematical logic for
really driving you straight to the nuthouse.

But it seems Shelah wrote a 46 page (!!) paper on Arrow's theorem in voting:
  http://arxiv.org/abs/math/0112213

Not easy to read.  Apparently the point is this.
Arrow's original theorem considered rank-orderings as votes and also as
the output of the voting method.
Shelah calls these "rational."
What if we allow "irrational" votes?

"Irrational" means on every subset of the candidates, there is a
"best" candidate.
Normally that would simply be the first element of the subset ("first"
according to some
ordering).  However, Shelah abnormally says each subset could have
some best (or otherwise distinguished) element without any overall
ordering enforcing
logical consistency...

Even in a very general framework of that ilk, Shelah still is able to prove
an "impossibility theorem"...  but so far I have not been able to translate it
into anything I feel I comprehend.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)