[Fwd: [EM] Approval/Condorcet]

[Russ Paielli]

Forest Simmons wrote:

> I agree with Russ that Kevin's Approval Runoff method (eliminate lowest 
> approval candidates until there is a CW) is a decent public proposal.

I'm glad to hear that.

Let me suggest a nifty way to think about this method. It may be obvious 
to some, but so be it.

Let the approval scores fill in the diagonal elements of the pairwise 
matrix. Then reorder the matrix so the diagonal elements are 
nonincreasing (starting from the upper left and going down). If no CW 
exists, the procedure is to simply eliminate the last row and column 
until a CW emerges.

In the case of Approval ties, the ordering should probably be based on 
the pairwise result. If that's a tie too, then all the tied candidates 
should be removed simulataneously (assuming they aren't at the top, of 
course).

> It would be interesting to compare that method with what I call TACF, 
> Total Approval Chain Filling:
> 
> Proceeding from the highest approval candidate to the lowest approval 
> candidate, fit as many as possible into a chain totally ordered by 
> pairwise defeat.  The candidate that beats all of the others in this 
> chain wins the election.

I'd be interested in an example (or pseudocode) of this procedure if you 
have time to provide one. Or have you already done so?

> The two methods always agree when there are only three candidates, since 
> they both pick the CW when there is one, and both eliminate the lowest 
> approval candidate when there is no CW.

That's encouraging.

> TACF always picks a member of the Banks set. It seems improbable that 
> Kevin's version of Approval Runoff always picks from Banks.

What is the Banks set?

> Both methods are monotone and clone proof.

That's encouraging too.

--Russ