[EM] Re: Definite Majority Choice

[Russ Paielli]

Araucaria Araucana araucaria.araucana-at-gmail.com |EMlist| wrote:
> On  5 Apr 2005 at 23:51 UTC-0700, Russ Paielli wrote:
> 
>>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.
> 
> 
> Sorry, you are mistaken -- that is not a unique characteristic.

Whoops! I should have known better.

> 
>>If no candidate has it, then the Approval winner is also the CW and
>>takes the enchilada.
> 
> 
> Color the diagonal as a winning cell and you don't have to have a
> special case rule.

Good point.

> 
>>The RAV procedure can be visualized exactly the same way, thus
>>demonstrating that DMC and RAV are equivalent, if I am not mistaken.
>>
> 
> 
> That's what I said!  They are equivalent since they find the same

I know that's what you said. I was agreeing with you.

> winner.  But the CW concept is a big leap.  The procedure can be
> automatic without mentioning the Smith set or Condorcet winner.

I like the fact that the Smith set need not be defined or determined, 
but I really think you want to define the CW anyway even if the method 
doesn't need the definition explicitly. It's just too fundamental to 
keep from the public.

> If you will allow to modify the visualization slightly:
> 
>  - Reorder the pairwise array as you specify above.
> 
>  - Instead of black and white, I'd suggest highlighting winning (and
>    approval!) scores, rather than blacking them out and obscuring
>    their values!  With a yellow highlighter pen, you look for a solid
>    yellow row up to (and including) the diagonal.
> 
> Here is the crucial difference:
> 
>  - You need to start checking left-side to diagonal cells starting
>    with the last (least-approved) candidate, and work up the diagonal
>    until you find the first candidate with a solid row of wins to the
>    left of the diagonal.
> 
> For DMC, I would first travel down the diagonal from the upper left,
> looking for defeats to the right of the diagonal.  Then I would draw
> lines (strike out) through the rows and columns of those
> correspondingly defeated candidates to indicate that they have been
> eliminated, and move to the next diagonal cell (even if it has been
> eliminated).  You can stop once there are no more non-eliminated
> candidates with lower approval.  Once all lower-approved candidates
> have been eliminated, move back up the diagonal again until you find
> the lowest-approved non-eliminated candidate.

Well, not to beat it to death, but I still think my explanation is 
simpler. Color the winning cells black, then, starting at the bottom, 
simply look for the first row to have a solid black bar all the way from 
the left column to the diagonal. Once the coloring is done, the answer 
will be staring you right in the face! No explicit elimination is even 
necessary.

> The higher-approved remaining candidates are the other members of the
> definite majority set.  Each of them will also have a solid row of
> wins from the diagonal to the left side.
> 
> Re your other message about the name: Ranked Approval Voting is fairly
> descriptive and probably as good as any other choice, but it is just
> as fuzzy as IRV's "Ranked Choice Ballot" -- it describes the ballot

I've never heard of IRV being called by that name, which seems to me 
more of a general name for any ranked ballot rather than a name for a 
particular election method that uses ranked ballots.

> method and only hints at how they're tallied.  It also implies that
> Approval Voting is the primary characteristic of the method and that
> the ranking is a slight modification, when what we're doing is
> actually the opposite.

You have a point. On the other hand, RAV is a generalization of 
Approval. According to Kevin Venzke, RAV (hence, DMC too) would be 
equivalent to Approval if all approved candidates must be ranked equally.

In the interest of full disclosure, I may impartial to the acronym RAV 
because my initials are RAP. 8^)

--Russ