[EM] Re: Definite Majority Choice

[Russ Paielli]

Araucaria Araucana araucaria.araucana-at-gmail.com |EMlist| wrote:

> I happen to think that DMC is the simplest-to-grasp version of all
> three methods.  Here is one way to find the winner:
> 
>       Eliminate any candidate defeated by another candidate with
>       higher total approval.
> 
>       Among the remaining candidates, the candidate with the lowest
>       approval defeats all others and is the DMC winner.

I was just thinking about this procedure some more, and I came up with a 
simple way to visualize the procedure (for simple-minded folks like me). 
Order the pairwise matrix with Approval scores decreasing (or 
non-increasing) on the diagonal, as usual. Then color the winning cells 
of the pairwise matrix black and the losing cells white. The winner is 
then the candidate who has a solid black row all the way from the left 
column to the diagonal. If I am not mistaken, no more than one candidate 
can have that, barring ties. If no candidate has it, then the Approval 
winner is also the CW and takes the enchilada.

The RAV procedure can be visualized exactly the same way, thus 
demonstrating that DMC and RAV are equivalent, if I am not mistaken.

--Russ