Warren Smith wrote:
REMARK 1:
Range is known to be better than every rank-order ballot voting system
for honest voters under the "RNEM" probability model, where "better"
is measured by Bayesian Regret. This proven by WD Smith in recent
papers for each N=3,4,5,...,31.
Permitting rank-order ballots to include equalities has no effect on
this because in the RNEM exactly-equal utilities occur with
probability=0, hence honest rank-order
voters would not use them.
So in these senses, range is better for both honest & strategic voters
than every
rank-order method meeting the criteria in the theorem, measured by
Bayesian Regret.
In the BR sense, what's the best voting system that meets the criteria
you listed? Range fails in the same way as Borda - someone who's ranked
top by a majority may still not be elected. If we consider Approval
votes complete (i.e. that approving A and B and not approving C means
the voter truly can't decide which is better of A and B), then I suppose
Approval would win this one. Otherwise, which method? It would have to
be a ranked or rated method.
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