[EM] Does this method already have a name?

[Forest W Simmons]

Here's an example that might clear up some questions:

Suppose that the original ballot is

A=B>C=D>E=F|G=H>I=J>K=L

where "|" is the voter's marked approval cutoff.

Then in calculating reactive approvals relative to C we move the 
approval cutoff adjacent to but not past the position shared by C and D:

A=B>C=D|E=F>G=H>I=J>K=L

Note that this ballot gives A, B, C, and D reactive approval relative 
to C.  The reactive approvals relative to D are exactly the same.

Going in the other direction, let's see which candidates receive 
reactive approval relative to either I or J.  Starting at the original 
approval position and moving to (but not past) the position shared by I 
and J we get


A=B>C=D>E=F>G=H|I=J>K=L

All of the candidates except I, J, K , and L get reactive approval 
relative to I or J from this ballot.

Note that in every case, the reactive approval of candidate X relative 
to candidate X is just its original approval, since the cutoff does not 
move past X.

Furthermore, if a voter wants all of the reactive approvals to be the 
same as his original approvals, all he has to do is rank all of his 
approved candidates equal top and truncate the rest.

Here's the nitty gritty of deciding an election by this method:

Form a square array in which the number in row i and column j is the 
total reactive approval of i relative to j.

To the right of each row in the array write the smallest number in that 
row.  Then circle the largest of these row minima.  The winner is the 
candidate whose row is to the left of the circled number.

Note that I have started using "reactive" instead of "reactionary" 
because of the negative political connotation of the latter term (which 
I used formerly).

Forest