Q,
I've made a slight change on the DMC page on electowiki.
I've extended the definition somewhat: the ballot is a combination of ordinal
ranking (equal ranks allowed) and approval rating. The approval rating
information can be either binary approval (approved/not-approved) or
finer-grained cardinal ratings ([1,0,-1] or [100,99,...,1,0]). I think this is
more of a difference in implementation than the method, since the initial
ordering is by total approval.
In the above case, a more graduated cardinal rating (say 100-0) would allow a
voter to approve weaker candidates with a low, but non-zero, rating.
Using fine-grained CR ballots with some range like 0 to 100, or even
-100 to 100, so that there are always
many more possible grades (slots) available than there are candidates
allows at the cost of greater counting
complexity what is in my opinion a big improvement:
(1) Inferring rankings from ratings, eliminate non-members of the
Schwartz set.
(2) If more than one candidate remains, "interpret" each ballot to be
approving those remaining candidates that it
rates higher than the mean of it's ratings of the remaining candidates,
and half-approving those that it rates at exactly
this mean (and of course not approving those it rates below.)
(3) Based on the inferred rankings and the step(2) construed approvals,
use Definite Majority Choice (DMC) to
elect the winner.
The idea is that voters don't need to have any idea of what the chances
of any of the candidates being elected are, and
voters who (in the "manual" version) would approve or not approve all
the candidates except one sure loser are not
unfairly disadvantaged.
A while ago I proposed "Automated-Approval Margins" which is identical
except that in step(3) "Approval Margins"
replaces "DMC". Also possible would be in step (3) to ignore the
rankings and just use (construed) Approval, but at
the time I looked at that and decided it wasn't as good on strategy grounds.
BTW, I think unadorned DMC with an explicit approval cutoff (so that
voters can rank candidates they don't approve)
is an excellent practical proposal for public political elections. I
am opposed to "blindly vote my favourite's ticket" idiot
boxes (which will just give rich parties incentive to sponsor lots of
"fake" candidates), and to the proposed rule
that if some candidate gets more than 66% approval, then the candidate
with
greatest approval wins.
This is an arbitrary complication that would cause the method to fail
Majority Favourite and Irrelevant Ballots.
Chris Benham
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