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. ---- Election-Methods mailing list - see http://electorama.com/em for list info
