[EM] Condorcet for public proposals - IMV

[Ernest Prabhakar]

Hi Anthony,

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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