Jobst Heitzig heitzig-j at web.de
Wed Mar 14 17:44:49 PDT 2007


when proposing DAMC, I also wrote:
> What I'm not sure about so far is ... what would happen
> when we used the "resorting" or the "definitively defaeted" version
> of DMC with absolute majority size defeats only.

Here's a "resorting" version which seems to be equivalent to DAMC(River) 
but which is, however, a bit more complicated to describe:

1. Sort the options from top to bottom by descending approval score and 
draw for each absolute majority defeat an arrow from the defeated to 
the defeating option.

2. Remove all arrows for which a second, upward arrow exists with the 
same source and a higher target.

3. If no more downward arrows exist, elect the topmost option.

4. Otherwise, pick a downward arrow from those with the topmost target 
option. If this arrow builds a cycle with some upward arrows, remove 
it. Otherwise move its source option from its current position to just 
below the current position of its target option (thereby turning the 
downward arrow into an upward arrow).

5. Go to step 2.

When leaving out step 2, we get another "resorting" method which 
probably is equivalent to DAMC(Ranked Pairs).

Yours, Jobst
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