# [EM] Condorcet for public proposals - IMV

Ernest Prabhakar drernie at mac.com
Tue Jan 27 09:33:02 PST 2004

```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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