[EM] Method definitions

[Blake Cretney]

Here's my latest response to the what did various people mean by various methods controversy.  First, dealing with Simpon-Kramer, Mike said,

> Maybe they'd be chagrinned if the literal interpretation of
> their proposal isn't something that they like. If they meant
> for their definition to apply only if all rankings are complete,
> then they should have said so. In any case, as with Condorcet,
> the fact that they worded their defeat-measure as they did
> suggests that they like that measure best. Even if they
> assumed that rankings would be complete. But it's only a guess
> that they assumed rankings would be complete. All we know is
> what they said.

Presumably you could tell by their definition of a ballot.  If anyone has easy access to this paper, please quote how they define a ballot.

------------

On Wed, 1 Mar 2000, "Norman Petry" wrote:

> >  There is no justification for deciding that Condorcet favoured
> >>winning-votes, however.
> >
> >Except for the way "plurality" is used now in reference to voting.
> >Maybe it was used differently in Condorcet's time & country, but
> >until we have word from a scholar of that time & place, what
> >we have to go on is how "plurality" is used now. Conceivably
> >Condorcet could have meant either. I claim that votes-against
> >seems more likely, as a guess, based on current usage.
> 
> I'm no scholar, but I do have access to a good dictionary :-)

Norman Petry goes on to provide dictionary references to a winning-votes type definition of plurality.  That's pretty compelling, but surely Condorcet must have at some time mentioned what the plurality was for some given example.  
 
> Blake has suggested that Condorcet did not consider the question of
> truncated ballots, and in the absence of truncation, absolute votes and
> margins are equivalent, so that a marginal variant would be an equally valid
> interpretation of Condorcet's method.  However, I disagree with this
> reasoning.  Abstention is equivalent to truncation, and was probably a
> common practice, so it seems presumptuous to assume that Condorcet did not
> consider the possible effect of abstention on his voting method.  Had
> Condorcet assumed that there would be no abstentions, he might have easily
> used the term "pluralité absolue" or "majorité" rather than simply
> "pluralité" when describing his method (since all pluralities would be
> majorities) but clearly did not do so.

These would be more recent terms, with which either he or his intended audience may have been less familiar.  Unlike today, when majority is a better known concept than plurality, and therefore the more natural one to use, when equivalent.

>  In my recollection, his writings do
> not even suggest the use of the ranked ballot -- I think he assumed voters
> would consider each pair of candidates in separate votes.  

I recently read that it was Hare who first suggested the rank ballot, so I have to agree with you on that.

> If this is done,
> one would expect abstentions between certain pairs of candidates to be quite
> common, unless it was prohibited by the rules of the assembly.  Unless there
> is evidence for this, I am inclined to regard his use of the term
> "pluralité" as a *deliberate* choice.

Although it would be surprising if Condorcet had the same kind of concerns that Mike does, and yet never expressed this.

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On Tue, 7 Mar 2000, Markus Schulze wrote:
> Dear Blake,
> 
> in his paper "Sur la Forme des Elections" (1789),
> Condorcet proposes a Copeland method. He writes:
> 
--snip--
> My own translation:
> 
> > If there are only 20 competitors then -to get the result
> > of their head to head comparisons- it is necessary to
> > evaluate the votes for 190 propositions, and for 780
> > propositions if there are 40 competitors. Very often
> > even this result isn't as satisfying as you might
> > want it to be; it can happen that no competitor is
> > declared superior to all the others by the plurality,
> > and thus you have to prefer that one who is considered
> > superior to the largest number; and amongst those
> > who are considered superior to an equal number of
> > competitors, that one who is considered superior by
> > the largest plurality or inferior by the smallest. But
> > there are situations where this preference is difficult
> > to determine and where the general rules can be
> > complicated and embarrassing. Therefore this election
> > method can only be used for distinguishable choices
> > or for situations where you can appeal to new
> > voters immediately whenever the question couldn't
> > be answered. And even if this appeal cannot
> > guarantee a success, it makes it more probable.
> 
> To my opinion, this quotation demonstrates that Condorcet
> rather promotes a family of election methods than one
> single election method.

That seems a reasonable conclusion.  He certainly seems uncertain about the method that he is rather vaguely defining above.

--------------

On Tue, 7 MaOn Tue, 7 Mar 2000, "MIKE OSSIPOFF" wrote:
> Markus wrote:
> 
> 
> >in his paper "Sur la Forme des Elections" (1789),
> >Condorcet proposes a Copeland method. He writes:
> 
> > > If there are only 20 competitors then -to get the result
> > > of their head to head comparisons- it is necessary to
> > > evaluate the votes for 190 propositions, and for 780
> > > propositions if there are 40 competitors. Very often
> > > even this result isn't as satisfying as you might
> > > want it to be; it can happen that no competitor is
> > > declared superior to all the others by the plurality,
> > > and thus you have to prefer that one who is considered
> > > superior to the largest number; and amongst those
> > > who are considered superior to an equal number of
> > > competitors, that one who is considered superior by
> > > the largest plurality or inferior by the smallest. But
> 
> Considered superior by the largest plurality or inferior by
> the smallest. If the tie-member considered superior by the
> largest plurality isn't the same one who is considered inferior
> by the smallest plurality then there must be truncation or
> pairwise abstention. That passage shows that Condorcet didn't
> assume that those wouldn't occur.

You can read this, as you did, that Condorcet is proposing two different ways (winning-votes and losing-votes) to decide, and doesn't much care which.  You could also read this as suggesting that these are equivalent.  I don't see how either backs up an interpretation of Condorcet as a strong winning-votes advocate.  At best, he doesn't appear to care.

> >To my opinion, this quotation demonstrates that Condorcet
> >rather promotes a family of election methods than one
> >single election method.
> 
> By stating his Condorcet criterion he could be said to have defined
> a more general class of methods, the Condorcet Criterion methods.
> But since he specifically defined the above-quoted method, and
> 2 methods that drop weakest defeats (Tideman can be worded that way),

He may have, in one instance, suggested dropping weakest defeats, and it may be that Tideman can be worded to drop weakest defeats, but that is a far cry from saying he advocated Tideman.  Not that that would be a bad thing, if he had.

> and since he defined a few other voting procedures too, the
> term "Condorcet's method" seems to properly refer to one of those
> relatively specific proposals. The method quoted above seems to
> come under the meaning of Copeland's method, and so it makes sense
> to use "Condorcet's method" to refer to his other class of pairwise-
> count methods, the ones that sequentially drop defeats that
> are the weakest among some set of defeats. Though someone could also
> apply his name to his less-well-known proposals too, it seems
> reasonable to apply it to the one that has some advocacy now.
> Also, the academic use of "Condorcet's method" is used by them
> to designate something that, however inaccurately, appears derived
> from Condorcet's bottom-up, weak-defeat-dropping proposal.
> 
> So it seems to me to be justified to keep calling that class of
> methods "Condorcet's method".

At least you do not say that Minmax has some special claim to this name.  My preference is to refer to "Condorcet's Method" as the method that chooses the candidate that pairwise beats every other candidate, the Condorcet winner.  Just as plurality is the method that picks the plurality winner.  A cursory look at web sites from colleges and teaching institutions suggests that this is the definition that is being taught academically.  

http://www.colorado.edu/education/DMP/voting_b.html
This page is from our good friend, Saari.
http://www.everydaylearning.com/Pages/mathlink/s99/elections99.html
http://smg.ulb.ac.be/Preprints/Marchant99_22.html

Of course, presumably, if the word is used enough with a different meaning, its meaning may change.

---
Blake Cretney