The method that you described is Schwartz PC.
Ah, okay. After experimenting with all these advanced proposals, I end up "rediscovering" Plain Condorcet. :-)
http://lists.debian.org/debian-vote/2000/debian-vote-200002/ msg00014.html
Of course Plain Condorcet could be reworded to say: "The winner is the candidate whose greatest defeat is the least."
So, I guess I need to re-learn how these methods differ from each other.
On Jan 9, 2004, at 6:53 AM, MIKE OSSIPOFF wrote:
Here's how it differs from SSD:
You sequentially drop weakest defeats from the _initial_ Schwartz set. SSD sequentially drops weakst defeats from the _current_ Schwartz set. Dropping defeats removes candidates from the Schwartz set, because a candidate can't be in the Schwartz set merely by tying one of its members.
In public elections the initial Schwartz & Smith sets are identical, because there are no pairwise ties.
Okay, let me see if I understand. If there are no pairwise ties:
- The Schwartz & Smith sets are identical
- PC, Smith PC, and Schwartz PC all give the same result
- SD, SSD, CSSD (Beatpath) are identical to each other, but may differ from * PC
- Tideman still differs from *SD and *PC [is that true?]
If there are pairwise ties:
- The Smith set (beat all outside) is larger than the Schwartz (smallest unbeaten set)
- PC, Smith PC, and Schwartz PC can give different results
That is, the Plain Condorcet winner - with the least greatest defeat - may NOT be in the Schwartz or Smith set
So, back to the algorithm I proposed earlier:
- count the number of pairwise contests each candidate wins (Nwins[candidate])
- identify the candidate(s) with the greatest number of wins
- pick the candidate that beats the other candidates with the same number of wins (LB)
if cyclic tie, pick one at random
Is that in fact sure to pick a member of the Schwartz set? And of the Smith set?
Similarly, if this algorithm gives the Schwartz set: - choose all the candidates which beat LB, directly or indirectly
Then, does this algorithm give the Smith set: - choose all the candidates which beat OR TIE LB, directly or indirectly
Thanks for your help.
-- Ernie P.
The Smith set is more briefly defined, and so I prefer Smith PC to Schwartz PC as a public proiposal.
I haven't dropped Smith PC as a public proposal. It has criterion advantages over PC, mostly cosmetic criterion differences, but they could matter in a campaign. It all depends on what people are found to like. I'd start by offering SSD & MAM, then SD, Smith PC, then PC.
Mike Ossipoff
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