[EM] Condorcet//Approval

[Greg Nisbet]

I just had an idea for a combination of these methods.
There is still an approval portion and a ranked portion and a pairwise
matrix is still generated, this is followed by an RP procedure, but
with the following difference:
the priority of X vs Y is either
X.wv+X.approval_score-Y.approval_score or just X.wv+X.approval_score
(I haven't decided yet)

Then just RP this. Use the absolute approval scores as a tiebreaker.

I'll use the example from Rob LeGrand's calculator.
http://userfs.cec.wustl.edu/~rhl1/rbvote/calc.html
98:   Abby > Cora | Erin > Dave > Brad
64:  Brad > Abby | Erin > Cora > Dave
12:  Brad | Abby > Erin > Dave > Cora
98:  Brad > Erin | Abby > Cora > Dave
13:  Brad > Erin > Abby | Dave > Cora
125: Brad | Erin > Dave > Abby > Cora
124: Cora | Abby > Erin > Dave > Brad
76:  Cora > Erin | Abby > Dave > Brad
21:  Dave > Abby | Brad > Erin > Cora
30:  Dave | Brad > Abby > Erin > Cora
98:  Dave | Brad > Erin > Cora > Abby
139: Dave > Cora | Abby > Brad > Erin
23:  Dave > Cora | Brad > Abby > Erin

Approval Scores:

Abby - 196
Brad - 312
Cora - 362
Erin - 187
Dave - 311

The tiebreaking ballot: Cora > Brad > Dave > Abby > Erin
what other methods chose:

winner method(s)
Abby Baldwin
Abby Black
Abby Borda
Abby Coombs
Abby Copeland*
Abby Raynaud
Abby Schulze
Brad Nanson
Brad Small
Brad Tideman*
Cora Dodgson
Cora Simpson
Cora Approval
Dave Carey
Dave Hare
Erin Bucklin


Pairwise Matrix:

The pairwise matrix:


          Abby Brad Cora Dave Erin
Abby           458   461  485   511
Brad   463            461  312   623
Cora   460    460          460   460
Dave   436   609   461           311
Erin    410    298  461   610

X.wv+X.approval_score

	654	657	681	707
775		773	624	935
822	822		822	822
623	796	648		498
721	609	772	921	

X.wv+X.approval_score-Y.approval_score

	342	295	494	396
579		411	437	624
626	510		635	511
427	484	286		187
525	297	410	734	

Ok so first with X.wv+X.approval_score

Brad > Erin 935
Erin > Dave 921
Cora > Everyone Else 822

Cora wins.

Next with X.wv+X.approval_score-Y.approval_score

Cora wins again as the winner of this Condorcet matrix with approval.

Cora did have a 50 voter lead in the approval section, that is what
won the election.

There might be a few bugs with this. I haven't tested it thoroughly yet.