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

[Abd ul-Rahman Lomax]

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.