[EM] "one-line" definition of ASM/AM/AWP

[Araucaria Araucana]

Hi all,

I've revised the Definite Majority Choice page a bit.  See if you like
it (you may need to empty cache and refresh page to see latest
changes):

        http://wiki.electorama.com/wiki/Definite_Majority_Choice

As I was going through my revised definition, I thought of a simple
refinement that might be expanded on:

,----[ from http://wiki.electorama.com/wiki/Definite_Majority_Choice ]
| We call a candidate definitively defeated when that candidate is
| defeated in a head-to-head contest against any other candidate with
| higher Approval score. This kind of defeat is also called an
| Approval-consistent defeat.
| 
| To find the DMC winner, the candidates are divided into two groups:
| 
|    1. Definitively defeated candidates.
|    2. Candidates that pairwise defeat all higher-approved
|       candidates. We call this group the definite majority set.
| 
| The least-approved candidate in the definite majority set pairwise
| defeats all higher-approved candidates, including all other members
| of the definite majority set, and is the DMC winner.
`----

James Green-Armytage is currently discussing strategy questions with
both Mike Ossipoff and Chris Benham.

I like the idea of getting better strategy resistance, but not at the
expense of simplicity.  So I've been attempting to think of some
sieve-like approach to these ideas that is analogous to DMC.

I think the main idea of ASM/AM/AWP is to exclude the DMC winner in
some circumstances, and give more favor to approval.  What might those
circumstances be?

Let's consider refining the definite majority set (Forest's P set) a
little further.

Say that you have some additional metric of defeat strength: Approval
Margins, AWP's strong preference, what have you.  With Approval
Margins, the smaller the margin, the stronger the defeat.

The P set is ordered pairwise from least-approved to highest-approved.
Define the upward strength of a P-set candidate as the strength of its
victory over the next-higher-approved P-set candidate.

Then eliminate any P-set candidate whose upward strength is weaker
than its defeat from below by a definitively-defeated candidate.

Whatever metric you use, you have pruned away alternatives that can't
escape their pursuers.  You're left with a stronger set of candidates
that are well separated in strength from the rest, and have strong
beatpaths (approval + extra metric) to any other candidate that
defeats them directly.

Ted
-- 
araucaria dot araucana at gmail dot com