[EM] Range Voting "unbeatable"?

[Warren Smith]

>> Warren defines BR in such a way that Range is unbeatable
>> given sincere votes.
> Absolutely...

--Sorry: these claims, although stated with the utmost apparent
confidence by their authors, are utterly false.   Range voting is
beatable, and has been beaten, with honest voters -- and I was the one
who did that!

Consult paper #101 here
http://www.math.temple.edu/~wds/homepage/works.html
e.g. see the plot
http://www.math.temple.edu/~wds/homepage/BestVrange.html#RegPlot
and the table
http://www.math.temple.edu/~wds/homepage/BestVrange.html#BigResultsTable
and note that the BRBH (best ratings-based voting system for honest
voters, which I explicitly derive in the 3-candidate RNEM case) does
beat plain range voting, with 100% honest voters, having
BRBH regret = 0.067454
versus
Range Voting Regret = 0.096864 = 1.436*BRBHregret.

Further, certain systems also beat range voting with *strategic*
voters, for example
range+top2runoff system with 2 rounds beats plain range (i.e. has
lower BR) if there are about 75% or more strategic voters in the mix.

Do these imply that we should abandon range voting?
At present, I do not think so, and here's why.

BRBH does beat range, but only if the honesty-fraction in the
electorate exceeds 91%.
And the regret reduction is fairly small.  If however, we have only a
small fraction of sincere voters, range is greatly superior to BRBH
(by a lot more than a factor of 1.4).

Range+top2runoff does beat range if the strategy-fraction is large, but it
doesn't beat it by much (10-30% regret reduction); meanwhile range
beats range+top2runoff by a lot more than that if the honesty-fraction
is large.

And both BRBH and range+top2runoff are a lot more complicated than
(and harder to "sell" than) plain range voting.

So in view of this, at present I still think plain range voting is a
pretty good choice.



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