[EM] Condorcet for public proposals

[Anthony Duff]

I am replying to:
http://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg01542.html
From: "MIKE OSSIPOFF" 
Subject: [EM] Condorcet for public proposals 
Date: Tue, 23 Dec 2003 09:47:47 +0000 
      
Mike wrote, in part,
 
 
>... SSD, RP, and PC are 
>the Condorcet versions to propose for public elections.
>
>That's because those Condorcet versions are the ones with natural
and 
>obvious motivation and justification. Obviously, of those 3, PC
isn't as 
>good as the other 2.

As I understand: SSD and RP are excellent methods, they are identical
in virtually every reasonable election result, and it is too
difficult to definitively decide which is better.  PC is a very good
method, with the merit of being straightforward and brief to explain.

Mike implies(?), something that I think is very important.  If you
are going to make a serious public proposal, you have to be certain
about your proposal.  If you are hesitating over the details, then
you will not inspire confidence.  When it comes to a public proposal,
with a public that has little patience for details, you must have
precisely one, well defined proposal.

>Sometimes we underestimate how resistant people might be to anything
whose 
>definition is longer than a line or two. Sure, anyone who is
willilng to 
>read the definitions of SSD and MAM will like them. But what about
all 
>those 
>people who will reject them without being willing to read the
definition, 
>because they consider a short paragraph to be too long? For them,
maybe 
>Condorcet is a better idea.
>
>Sure SSD & MAM are better, but if people insist on something more 
>briefly-defined, them  Plain Condorcet (PC) is the thing:

I agree with Mike’s thrust, that simplicity could be the deciding
factor between condorcet getting off the ground, or not.

I’d express things a little differently though.  People won’t “insist
on something more briefly-defined” so much as they will fail to have
their attention held and try and get away from you, politely at
first.

The problem with SSD & RP/MAM is not just that there are extra words
in definitions and explanation of the method, but people will also
want to know why the extra details are required.  Explaining the
“whys” could get particularly convoluted given that an otherwise
uninterested person may only give you a minute or two before they
decide that you are a nuisance.  

I note that PC is not the simplest condorcet method.  PC means
PC(winning votes).  PC(margins) would be simpler and more intuitive. 
Margins are intuitive.  The pairwise contests are decided by margins.
 The newcomer to condorcet will want to know why defeats should be
used instead of margins.  This is the point where I fear that the
explanation of condorcet will become bogged down for too many people.
 You have already startled this unsuspecting person with the news
that the community might express an apparent contradiction
(condorcet’s paradox), and then you try to justify a
counter-intuitive method to choose a winner.

I wonder if, rather than explaining everything, an implicit “just
trust me” approach would be better used in the first instance.  
For example: 
“When resolving a circular tie, measuring defeats by margins has been
shown to be vulnerable to strategic manipulation.  By measuring
defeats by winning votes, that vulnerability is significantly
reduced”

Regarding circular ties:
I have been unable to discover a reasonable example for why a
sincerely voting community would produce a circular tie, except for
where ballots are largely random.  Random ballots (voters making
random choices) can produce a circular tie, but if the number of
voters is very large then the relative margins involved in the ties
will be exceedingly small, and in such a case, non-random votes will
very likely dominate the result.

Sure, it is easy to contrive of multiple complex philosophies with
matching candidates that would produce a circular tie.  However, in
such attempts as I have made, I have not found any good reason why
just as many other people might not have opposing correlations of
philosophies.  The whole thing seems to be verging on randomness. Has
anyone got an argument for why a particular community might produce a
sincere, circular tie?  Does anyone have evidence of one actually
exisiting?

On the other hand, it is easy to see why a narrowly loosing faction
may vote strategically for the specific purpose of creating a
circular tie so as to rob victory from a sincere condorcet winner.

Therefore, I suspect that should a circular tie ever eventuate, that
it would very likely be due to strategic voting.  If this is true,
then admit it upfront. 

Mike defines PC: 

>If anyone is undefeated they win. Otherwise drop the weakest defeat.

>Repeat 
>till someone is undefeated. They win.
>
>[end of PC definition]

My criticism of this is that, by default, it is expected that there
will not be a condorcet winner.  In general, when I read descriptions
of condorcet, the content is overwhelmingly concerned with the
resolution of circular ties.  The main feature of condorcet is that a
full pairwise analysis is done, unlike in IRV.  This should be a
selling point of condorcet, but unfortunately it is buried beneath
the detail.

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.

>Sure, PC violates Condorcet Loser. But it would happen only rarely.
It 
>would 
>be a peculiarly popular Condorcet loser who has fewer people
preferring 
>anyone else to him than anyone else does.
>
>If a Condorcet Loser wins it would be an embarrassment. But the
likely 
>"badness" of that winner is reduced by the fact that he has the
fewest 
>people preferring anyone else to him.
>
>Condorcet Loser could also be used against PC in campaigns, and that

>objection would have to be answered. For one thing, Condorcet Loser
can't 
>be 
>used to oppose replacing Plurality with PC, because Plurality
violates it 
>too, probably more often.

I do not think the condorcet loser criterion is really that
important.  The condorcet winner criterion is very important, and I
might even rank it as paramount.  I think the symmetric relationship
between these two criteria has artificially raised the status of the
condorcet loser criterion.
I think the condorcet loser criterion is less important than an 
overruled majority.
The prime example of PC electing a condorcet loser is:
20 ABCD
20 BCAD
20 CABD
13 DABC
13 DBCA
13 DCAB
D wins despite being ranked last by 60% and despite being beaten by
every other candidate.
My justification of the win by D is this:  No other single candidate
can stand up, in court or in public, and complain that they should be
the winner because they beat D 60 to 39.  Should A, for example, do
this, D can immediately counter by pointing out that A suffered a
worse defeat of 66 to 33.  Therefore, A’s case is worse than D’s.
Condorcet is a pairwise method.  Let the justifications and
complaints be made in a pairwise manner.  I think this would be
convincing in a public forum.

The condorcet loser criterion is, however, emotive.  To have lost
against *everyone* is a pretty bad thing.  If someone wants to obsess
about this, then I would argue that in a large public election, the
result is implausible, as there will have been some other minor
candidate E, and suddenly, D is no longer a condorcet looser.

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.

Someone might suggest that the 39 D voters perverted the result by
deliberately creating a cycle.  Clearly this is not the case, as the
cycle exists among the 60 voters who rank D last, and without a
strong cycle among those 60, the cycle among the D voters would be
ineffective.

Someone might suggest that A, B & C are effective clones, that they
represent a similar position with respect to D.  This is an advanced
argument.  However, a problem with it is that the extreme strength of
the cycle suggests that there are some very strong feelings
differentiating A from B from C.  If they were clones, then why
didn’t nearly as many vote CBA as ABC?


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?


Anthony


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