[EM] Kemeny challenge

[Warren Smith]

KEMENY CHALLENGE
=================

Here is an attempt by me to intentionally create small elections for
which it is difficult to determine the Kemeny winner.

Consider this pairwise matrix:
    http://www.RangeVoting.org/Tourn27.html
and replace all the +1s by random numbers in the interval
    [A, B]
and all the -1s by ditto but negated, to get the pairwise margins matrix
for a 27-candidate election.
Here B>A>0 are two parameters chosen by the Devil to try to cause
these problems to be hardest [I'd originally suggested A=9million
B=10million, but maybe some other choice like A=0 and B=10billion
would tend to make it harder]. Also of course randomly permute the 27
candidate-names in a way unknown to the solver, before giving the
problem to the solver [equivalently permute both the rows and columns
of the 27x27 matrix by one random permutation].

THE CHALLENGE: Find the Kemeny winner or order...  can anybody do
either reliably for 27-candidate elections of this class, or is this
usually beyond humankind's abilities?



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