Some more specific comments
At 01:28 PM 1/6/2013, Jameson Quinn wrote:
I worked out a new, simpler way to explain CMJ based on a
Bucklin-like process. To accord better with this improved
explanation, I'm renaming the system to GMJ, or Graduated Majority
Judgment. Here's the explanation:
===Ballot===
The ballot will ask you to grade each candidate on a scale from A
(excellent) to F (unacceptable). You may give two candidates the
same grade if you wish. Any candidate whom you do not explicitly
grade will get an F from you.
It should be 0 (worst) to 4 (best). If grades are going to be used,
those should be the descriptions.
C is generally considered a minimally passing grade. So if this is
going to be used in a runoff system, 2 or C should be "minimally acceptable."
===Counting===
To find the winner, first the "A" votes for each candidate are
counted. If no candidate gets over 50% of the voters, the "B" votes
are added to the count, then "C" votes, etc. The first candidate to
get over 50% is the winner. If two candidates would reach 50% at the
same grade, each candidate's votes for that grade are added
gradually, and the winner is the one who needs the smallest portion
of those votes to reach 50%.
This gradual process can be stated as a "graduated score" for each
candidate. If a candidate reaches 50% using 8/10 of their "C" votes
(along with all their A and B votes), then their graduated score
would be 1.7 (a C-). Another candidate who needed only 2/10 of their
"C" votes to reach 50% would have a graduated score of 2.3 (a C+),
so between those two candidates the second would be the winner.
The "graduated score" mentioned above is exactly the same as the old
CMJ score, and the old formula can be used.
As you can see, this conception of gradually adding the votes in
cases of ties is very natural. In fact, I now feel that this is
clearly the most natural extension of Bucklin to the
fully-evaluative (graded/cardinal/equal and skipped rankings) domain.
The explanation for the "graduated score" will be confusing. The
basis for graduated score is the half-point below the grade. The
percentage of the C votes needed in the examples given is added to 1.5.
Under this is an assumption of C grades arising out of a spectrum of
grades, evenly distributed, between 1.5 and 2.5, that have all been
rounded to C, 2.0.
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