[EM] Does this method have a name?

[Forest W Simmons]

The "reactive approval" of candidate X relative to Y as defined below 
is supposed to approximate the approval that X would get given only 
that Y was ahead of all the other candidates in the polls.

In other words, if there were zero info up until someone reveals that Y 
is the front runner, would you approve X or not?

Suppose that under zero info your approval cutoff was below Y.  Given 
the information that Y is the frontrunner, wouldn't it make sense to 
move your cutoff up to just below Y?

On the other hand, suppose that under zero info you disapprove Y.  
Given the info that Y is the frontrunner wouldn't it make sense to move 
your cutoff down to just above Y? 

The move would be in reaction to the given information, hence the term 
"reactive."

So we define the reactive approval of X relative to Y as the number of 
ballots on which X would be approved if the voted approval cutoff were 
moved adjacent to (but not past) Y on each and every ballot.

Let RA be the matrix whose entry in row i and column j is the reactive 
approval of candidate i relative to candidate j.

Let's call this matrix the reactive approval matrix.

Below I suggested one way of using this matrix to determine a winner.  
Here's a more interesting one:

1. Circle the largest number in each column of the RA matrix.

2. Cross out each row that has no circled element.

3. Cross out the columns that correspond to the rows that were crossed 
out. [These rows and columns represent straw men or false alarms, so to 
speak, since any poll indicating that they were ahead would be 
misleading.]

4. Repeat steps 2 and 3 until each remaining row has exactly one 
remaining circled element.

5. The winner is the candidate who has the largest row minimum in the 
remaining matrix.

What do you think?

Forest



>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
>
>
>
>
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>End of election-methods Digest, Vol 35, Issue 8
>***********************************************
>