[EM] Re: More thoughts on approval margins

[Araucaria Araucana]

On 15 Apr 2005 at 16:03 UTC-0700, Monkey Puzzle wrote:
> I think I'm getting the sieve idea into better focus now.  Is the
> following method is equivalent to Approval Sorted Margins?
>
> Ranked ballots with approval cutoff.
>
> Strong defeat = pairwise defeat by higher-approved candidate
>
> Strong losers = set of all strongly defeated candidates
>
> Provisional set = set of non-strongly-defeated candidates
>    Each provisional winner defeats all higher-approved members of the set.
>    This is Forest's "P" set.  Convenient that Provisional starts with
> P, isn't it? ;-)

New definition:

Clear upward defeat of X by Y:
   Y has lower approval than X, but pairwise defeats X and is not
   defeated by any other candidate with approval in between theirs.

>
> Marginal defeat: Pairwise defeat of provisional candidate X by strong
> loser Y under these conditions:
>     (1)    Z = the least-approved provisional winner who strongly defeats Y.
>     (2)   Approval(X) - Approval(Y) < Approval(Z) - Approval(X)
>     TODO:  Need a more succinct description of this.

Revised definition of marginal defeat:

   (1) Y has a clear upward defeat over X
   (2) Z defeats Y and is the least-approved candidate with greater
       approval than X.
   (3) Approval(X)-Approval(Y) < Approval(Z)-Approval(X)

The last part of the definition is the definition of secondary defeat
strength.  Here I use approval margin, but any measure, such as
winning votes, AWP's strong preference votes, etc., could be used.

>
> Marginal losers = set of all marginally defeated candidates
>
> Strong set = set of candidates neither strongly nor marginally defeated.
>
> The least-approved member of the strong set defeats all
> higher-approved strong candidates and wins the election.
>
> The approval winner and the highest-approved member of the Smith set
> are always strong candidates.
>
> I think a good name for this method would be Marginal Ranked Approval
> Voting (MRAV).
>
> I've created a page for it here:
>    http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting 
>
> One interpretation of the marginal defeat is that a marginal loser
> doesn't have enough approval "buoyancy" to rise above the
> strong-defeated candidates, and is peeled off of the edge of the
> provisional set.
>
> Strategy should be similar to Approval Margins and identical in
> 3-candidate cases.
>
> The MRAV strong set could be used for a DFC-like random ballot method.
>
> Suggestions?  Discussion?

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