[EM] Re: question/comments re DMC

[Araucaria Araucana]

On 28 Aug 2005 at 17:19 UTC-0700, Warren Smith wrote:
> --(also true of range)
> I'm a bit worried here.  Heitzig was telling me DMC could be done with
> 	equality rankings
> like A>B=C>D=>F too.  However...  in the plain Condorcet world, permitting equalities
> *and* using winning votes makes a big difference and you need to do *Both*
> to reap the benefits.  So I would like to know how DMC handles that, in view
> of the previous remark 9 that DMC eliminated  the margins/winnign
> votes debate.

There are those who maintain that when candidates are equal-ranked,
each should get half a vote.  As far as I can tell, all those who
support this position are marginal-votes proponents.

If approval cutoff is implemented using an extra fictional
Not-Approved candidate, with votes "for X against Not-Approved"
counted as approval, then the half-vote-split equal-rank tabulation
artificially inflates X's approval rating.  X might then avoid being
eliminated (in DMC) by a truly higher approved candidate.

In my winning-votes-biased opinion, equal ranking should be considered
as an abstention in the contest, tabulated as *no* vote for either
candidate.  As it happens, this Does The Right Thing on an approval
cutoff ballot, no extra gimmicks required.

Furthermore, ER-half-vote-split loses information.  Once the totals
are accumulated, you can no longer tell how many equal-rank votes were
cast.  But that information is still available directly from the
pairwise matrix if you use ER-equals-abstention:

    (X=Y) = total - (X>Y + Y>X)

where

    (X=Y): total number of equal ranks
    total: total number of ballots
    X>Y  : total number of ballots ranking X over Y
    Y>X  : total number of ballots ranking Y over X

Shouldn't a voting method try to avoid entropy, rather than increasing
it?  :-)

Q
-- 
araucaria dot araucana at gmail dot com
http://www.metafilter.com/user/23101
http://wiki.electorama.com/wiki/User:Araucaria
Q = Qoph = "monkey/knot" -- see http://www.ship.edu/~cgboeree/alphabet.html