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
---- Election-Methods mailing list - see http://electorama.com/em for list info
