On Jan 27, 2004, at 5:26 AM, Anthony Duff wrote:
I suggest that a definition of the condorcet election method being publicly proposed should be explicit about the full pairwise analysis, and that the possibility of a circular tie, and the resolution of such a circular tie should be treated like a footnote.
I tend to agree with you.
..Is the problem that D is not in the smith set? The general public is not going to make this complaint. With PC, such a set is never mentioned.
Actually, I"m leaning towards Smith PC (Plain Condorcet within the Smith Set of tied winners) as perhaps the optimal tradeoff between rigor and clarity for public elections. As you point out, in public elections circular ties are rather unlikely to come up. But I think the concept of a tiebreaker round actually helps in the understanding, and using PC (least greatest defeat) as a tie breaker is far simpler to calculate and explain than any of the alternatives I've seen.
Another thought: “condorcet” is an unfortunate name. It is an unfamiliar French name. People probably won’t even agree on how it is to be pronounced. As for the abbreviation “PC” – it has already been used, as in “personal computer”, and in “politically correct”. Are there any thoughts for a better name?
Yeah, my friends (on the radical centrist list) are unanimous that the term Condorcet has to go. :-)
I have been proposing the term 'Instant Matchup Voting', or IMV, by analogy with Instant Runoff Voting. I compare it to a round-robin tournament, which most people have direct experience with. I think this leads to a simple, easy to visualize definition:
1. Each rank-ordered ballot is interpreted as a series of "Instant Matchups"
That is A > B > C, implies one point each for the three pairwise Matchups A > B, B > C, and A > C
Note that "A>B" is counted separately from "B>A" (i.e., winning votes)
2. Tally up the N * (N-1) Matchups, for each ordered pair of candidates
3. If one candidate beats everyone, that's the absolute winner
4. If there is a 'rock-paper-scissors' tie (A >= B, B >= C, C >= A),
the tiebreaking winner is the candidate from that group with the 'least greatest defeat'
I actually think the Smith tiebreaking round makes it easier to understand and defend than straight PC. Terms like Smith sets, cycles, and even circular ties can be confusing. However, using the round-robin analogy, everyone I've talked to quickly grasps the rock-paper-scissors concept. We could even recurse it to give a complete ordering (which is important to many people).
While Smith PC is not quite perfect, to me this seems the simplest possible definition that would make sense to people. I have something close to this implemented, though I've been planning to also implement Ranked Pairs, Beatpath, and perhaps SD so that the experts can easily compare alternative calculations. And of course I've been distracted by my Auto-Districting program (which was written a week ago, but I've just started debugging).
Does anyone think Smith PC is likely to cause any severe pathologies in a public election? Are there open questions that we could work to resolve, if people agree it is a good idea?
-- Ernie P.
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