[EM] Condorcet for public proposals - Tounament

[Dave Ketchum]

I like what Ernest writes, though I see a bit of room for improvement and 
suggest "tournament" as a less foreign-sounding title (even though its 
ancestry is also French).

On Tue, 27 Jan 2004 09:10:36 -0800 Ernest Prabhakar wrote, per subject:

    Re: [EM] Condorcet for public proposals - IMV


> 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.


Cycles are possible, so they better get attended to, however rarely they 
may be expected (one general rule to be remembered is that whatever is 
possible, but not prepared for, WILL happen - regardless of theoretical odds).

But they should not get in the way of explaining the heart of the basic 
method.

> 
>> ..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.
> 

Looking back to what Anthony wrote - his voters AGREED that D was a lemon 
- any method that declares such a lemon to be sweet had better start 
defending or revising.

> 
> 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:
> 

Ahead of much that I have seen, but I suggest tournament as even easier to 
visualize from.  My definition will follow yours.


IMV:

> 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'
> 
Tournament:
0. Voters simply rank as many of the candidates as they choose, starting with 
their most-preferred.
1. Each rank-ordered ballot is interpreted as a series of matches among all 

candidates in the election:
     That is, ranking A > B > C, and D and E not ranked by this voter, 

implies each ranked candidate winning over each candidate ranked later, and 

over each unranked candidate.

      Thus unranked candidates do not get counted as ranked over each other.

     Note that "A>B" is counted separately from "B>A" (i.e., winning votes).
2. Tally up the number of wins for each ordered pair of candidates in an 

N*N array (with an empty diagonal, for candidates do not play against 
themselves).

3. If one candidate wins when compared with each other candidate, that's 

the absolute winner.
4. If no absolute winner, we have a 'rock-paper-scissors' near tie such as 

(A >= B, B >= C, C >= A), and the tiebreaking winner is the candidate from 

that group with the 'least greatest defeat'.


NOTE:  I consider 'least greatest defeat' unacceptably opaque for this 
purpose, and ask for help in providing simpler words.

BTW:  Debatable whether voters should be permitted to rank candidates as 
equal.  If so then, for each pair of equal candidates, count 1/2 win for 
each (thus if two voters rank A=B=C then A>B, B>A, A>C, C>A, B>C, and C>B 
each get credited one full win).

> 
> 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.

-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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