[EM] Wow: new, simple Bucklin motivation for CMJ. So renaming to Graduated MJ.

[Jameson Quinn]

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. ===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.
Jameson
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