[EM] Approval-Sorted Margins(Ranking) Elimination

[Brian Olson]

I'm trying to understand the details of this procedure.

On Apr 16, 2007, at 12:03 PM, Chris Benham wrote:

> My current favourite plain ranked-ballot method is  "Approval- 
> Sorted Margins(Ranking) Elimination":
>
> 1. Voters rank candidates, truncation and equal-ranking allowed.
>
> 2. Interpreting ranking above bottom or equal-bottom as 'approval',  
> initially order the candidates
> according to their approval scores from the most approved (highest  
> ordered) to the least approved
> (lowest ordered).

I'm a little fuzzy on this step, it sounds like that reverse-IRV  
method of disqualifying the most-last-placed choice.
Does A>B>C>D mean I approve of all but D?
And I'd think A>B>C=D would mean I approve of A and B, but this  
statement seems to imply approval for all of A-D, unless perhaps  
there's E and F left unranked then it would approve A-D and not E,F.

> 3. If any candidate Y pairwise beats the candidate next highest in  
> the order (X) , then modify the order
> by switching  the order of the X>Y  pair  (to Y>X) that are closest  
> in approval score.
> Repeat until all the candidates not ordered top are pairwise beaten  
> by the next highest-ordered candidate.

So, said another way, if the intermediate total order is
A>B>C>D>E>F
as ordered by approval counts, but more ballots rank C>B than B>C,  
and more ballots rank E>D than D>E, then if the approval count of B-C  
is less than D-E, then flop B and C in the intermediate order.
Repeat fixing up the intermediate order, always with the closest  
approval count difference, until no neighbors in the intermediate  
order violate pairwise ranking winner. (This seems to be very much  
like a condorcet process, actually, is it ever different unless  
there's a tie?)

> 4. Eliminate and drop from the ballots the (now) lowest ordered  
> candidate.
>
> 5. Repeat steps 2-4 until one candidate (the winner) remains.