[EM] Re: suggestion for MMPO/Approval hybrid

[Araucaria Araucana]

On 27 May 2005 at 00:02 UTC-0700, Russ Paielli wrote:
> I have been amusing myself trying to think of a way to combine MMPO
> with Approval. Here's what I've come up with.
>
> Start with ranked ballots and Approval cutoffs as usual. Then
> arrange the pairwise matrix so the Approval scores are decreasing
> (or non-increasing) along the main diagonal, as in DMC. Now select
> two candidates as follows for a pairwise "runoff." The first
> candidate is the Approval winner. The second candidate is selected
> using the following variation of the MMPO procedure. In finding the
> candidate with the minimum number of maximum votes against, only
> consider the other candidates who are more approved than the
> candidate in question. In other words, consider only the
> upper-triangular portion of the pairwise matrix. That means the
> least-approved candidate has the most (n-1) other candidates over
> which to find the maximum votes against (hence his max votes against
> are more likely to be higher as a "penalty" for being least
> approved).
>

I like the idea ;-).

Let's call the approval winner AW and your alternate winner
Minimum-opposition-from-higher-approved, or MOFHA.

How might this fail Later-no-harm?  

 - A voter ranks her favorite X over MOFHA and approves both.

 - X ends up with less approval than MOFHA.

 - MOFHA's globally maximum opposition is greater than X's but comes
   from a candidate Y with even lower approval than X and is thus not
   counted.

So this fails later-no-harm with respect to approval cutoff, in the
same way as DMC/RAV.  If the voter had not approved MOFHA, X might be
approval-ranked above MOFHA and might have been a contender in the
runoff.

If I'm wrong, somebody please correct me.

Q
-- 
araucaria dot araucana at gmail dot com
http://www.metafilter.com/user/23101
http://wiki.electorama.com/wiki/User:Araucaria
Q = Qoph = "monkey/knot" -- see http://www.ship.edu/~cgboeree/alphabet.html