[EM] Method definitions (remainder of reply)

[MIKE OSSIPOFF]

>
>MIKE OSSIPOFF wrote:
> > > > I don't know of a MinMax or Condorcet definition in an academic
> > > > article that says anything about incomplete rankings.
> > >
> > >That's what I thought.  My point is, that if they aren't considering 
>the
> > >issue of incomplete rankings, they might say one of:
> > >
> > >1.  Find the candidate who has the fewest votes against it in any 
>pairwise
> > >contest.
> > >2.  Find the candidate who has the fewest votes against it in its 
>greatest
> > >loss.
> > >3.  Find the candidate who has the smallest margin of defeat in its
> > >greatest
> > >loss.
> > >
> > >Knowing that all three are equivalent for their purposes.  If you take
> > >their
> > >words out of that context, and instead apply them to incomplete 
>rankings,
> > >you
> > >have them arguing for a method that they likely never even considered, 
>let
> > >alone advocated.

But don't mathematicians scrupulously state their assumptions?

And if, assuming complete rankings, there's no difference between
the different defeat-magnitude measures, doesn't an author's
choice among those measures say something about which one he
likes? Condorcet chose to word it in terms of dropping the
defeat that thas the smallest majority. Even if he assumed that
all rankings would be complete, his choice of that wording tells
us that he likes that measure best, or strongly suggests it.

> >
> > Brams & Fishburn, whom I'll quote in this letter, speak of
> > MaxMin votes-for. It seems to me that the Simpson-Kramer definition
> > in the _Journal of Economic Perspective_ is written that way too.
> > So it isn't usually necessary to guess what they meant. And if
> > someone _were_ completely vague about it, then they could mean
> > votes-against or votes-for, and that would mean it would make a
> > difference whether we look at all of a candidate's pairwise
> > comparisons or just at his defeats.
>
>You haven't addressed my point.  If Simpson and Kramer describe a
>method without considering partial rankings, and you take their words
>out of context, and apply them to ballots with partial rankings, you
>are not doing what they intended.  For all we know, Simpson and Kramer
>would be surprised and horrified to have their names attached to their
>method as you describe it.

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.

>
>It isn't that they were vague.  It is that by your own admission,
>they never considered the issue of partial rankings.  So, how can they
>be taken as advocating a specific way of handling them?

I used to say that, probably because others said it. I no
longer believe that we can assume that they didn't consider
partial rankings. 1. From what they said, there's no reason
to believe that they assumed complete rankings; 2. Even if
they did, the fact that they expressed the defeat-measure as
they did suggests that they like that measure. (Votes-for,
in the case of Brams & Fishburn & Simpson & Kramer, and
votes-against in the case of Condorcet).

>
> > >
> > >As well, I dislike the term "Plain Condorcet" for the following 
>reasons:
> > >
> > >1.  It is unknown off this list.
> >
> > True, but so seem the interpretations of Condorcet's method
> > that are discussed on this list, except for Tideman.
>
>Yes, but there is a difference between finding a new name for a new
>concept, like "Schulze's method" and finding a new name for a well
>known method.

What old name is good? MinMax(pairloss,wv) is ok, but it isn't
an old name. And I don't know how well-known the method is, if
Brams & Fishburn's definition is the prevailing academic definition
of Condorcet's method.


>My understanding is that Condorcet only seriously considered the
>situation of three candidates and complete rankings.  If so, we have
>the same problem as before.  His words have been taken out of context
>to appear to advocate Minmax(winning-votes) when in the context he was
>using, margins was equal to winning-votes, and Tideman, Schulze and
>many others are equivalent to Minmax.

Markus's quote & translation shows that Condorcet wasn't limiting
his proposal to 3 candidates.

>
>He also mused briefly about extending his principles to more than
>three candidates.  He suggested that they could be solved the same way
>as the 3 candidate example, by keeping the higher majorities and
>losing the weaker ones.  It is clear he assumed that the higher
>majorities would be consistent.  Since this is not the case, his
>attempts to extend the method from beyond three candidate do not work.

He may have said those things too, but he still wrote the
2 proposals that Markus quoted, and they're stated in a general
way that isn't about only 3 candidates. Whatever else he said,
he made those proposals, even if elsewhere he speculated about
other possible ways of dealing with many-candidate elections.


> > As nearly as I can remember, this is what Condorcet is translated
> > as saying:
> >
> > If those propositions [pairwise defeats] cannot all exist
> > together [because of a cycle], then ignore the proposition having
> > the smallest majority. Proceed in that way till there's
> > an unbeaten candidate.
>
>If that was the phrasing, I don't see it as obvious that he is
>"literally" specifying margins.  My dictionary gives as one definition
>of a majority, "The number of votes cast for a particular candidate,
>bill, etc., over and above the total number of remaining votes."

The dictionaries that I've checked give both definitions of
a majority. The bigger half, or the difference. Conceivably
the translators who used "majority" could have meant the
difference, and conceivably Condorcet could have meant that
by "pluralite".

I don't know French, and I suppose that few people who know
French know what "pluralite" meant in Condorcet's day.
It seems to me a little unlikely that "pluralite" would have
the same double meaning that "majority" now has, though it
of course could. Now, "plurality", like "majority", can have
either meaning. But nowadays, when we hear "plurality", in
a voting context, it nearly always means the largest group,
not the difference. So I'd suggest that therefore that's
the best guess for what it meant elsewhere, elsewhen.
Unless we hear from someone who knows late 18th century French
for political applications.

Maybe I have to admit that Margins has to be admitted to
the Condorcet interpretations, while emphasizing that when
I say Condorcet's method I'm talking about the votes-against
interpretations.


>As well, I note that in your recollection, Condorcet, like me,
>assumes that all pairwise victories are in a sense a majority.  What
>do you read into that?

The larger of the two groups: The group voting for the defeat
and the group voting against it. Whichever is larger. A majority
of those voting between candidate X & candidate Y.

>
>Of course, I am just playing the same game of taking Condorcet's
>words out of context.  In context, none of this mattered because
>Condorcet was only considering full rankings.

We don't know that either, unless he said so.
In any case, his wording shows which measure he liked best.
(to the extent that we can guess what "pluralite" meant then
in France).

> > That's true, but I hate to give up the name "Condorcet's method",
> > because it carries the prestige of the founder of voting theory.
>
>Why not call it Abraham Lincoln's method?  He is even better known.
>Of course, he didn't invent Minmax either.  The fact that it is
>frequently called Simpson-Kramer suggests to me that they are credited
>with its invention.

Are you sure that Simpson-Kramer is MinMax? It seems to me
that their wording is MaxMin, though I could be mistaken.
In any case, their proposal doesn't resemble Condorcet's because
they aren't looking only at a candidate's defeats, but are
looking at all his pair-comparisons.

Why not call it Abraham Lincoln's method? How about because
Lincoln didn't found voting theory, and didn't write anything
that literally means MinMax(pairloss,wv), or MinMax(pairloss,m),
with the former being more likely based on how "plurality" is
almost always used now in English, to the extent that that
can inform a guess.

But you're still onto something. Lincoln's method? No, it
wouldn't have really great popular appeal. But howabout
Neil Armstrong's method, or Michael Jackson's method, or
Spice Girls' method. You have my permisson to use the Spice Girls*,
but you can't have Neil Armstrong or Michael Jackson.
(* but get their permission first)


>It is only when you take the definitions out of context, and apply
>them to partial rankings, that this method becomes different than
>Minmax.  But that is clearly not what Brams and Fishburn intended.
>They were just defining the method as efficiently as possible
>considering that it wasn't intended for partial rankings.

I don't notice any efficiency difference in MinMax wording
vs MaxMin wording. Their use of MaxMin therefore indicates
a preference on their part in favor of MaxMin. And, as I said,
they're mathematicans, and mathematicians state their assumptions.
If they didn't state it, then we can't assume they made it.

>
>I note that their definition of "Condorcet's method" when taken out
>of context is not equivalent to the definition of Condorcet's method
>that you get from taking his own definition out of context.

It's true that Brams & Fishburn differ from Condorcet other than
in their choice of MaxMin instead of MinMax. They say to check
all of a candidate's pair-comparison's instead of just his defeats.
But I wouldn't ignore the fact that B&F chose to say MaxMin
& Condorcet chose to say MinMax.

>
>Of course, I would argue, based on the quote above, that Brams and
>Fishburne have committed a similar error in describing "Condorcet's
>procedure".  Condorcet described a procedure for handling three
>candidates that was equivalent to Minmax/Maxmin.  He might have
>extended this procedure to more than three candidates, but he did not.

In the written proposals posed by Markus, Condorcet made it
clear that his methods were for any number of candidates.

>  In fact, his remarks on extending his procedure are very different
>than this procedure.  Either he considered the Minmax/Maxmin procedure
>and rejected it, or he did not think in terms that allowed it as a
>natural extension of his 3 candidate procedure.  I suspect the latter
>is the case.

If he speculated elsewhere on other ways of dealing with more
than 3 candidates, that doesn't change the fact that when he
wrote those 2 actual proposals, he specifically indicated that
the methods were for any number of candidates.

  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.

>
> > Their definition doesn't say anything about whether x beats
> > y or vice-versa.
>
>Yes, because in context, it doesn't matter.

Even with 3 candidates, a candidate's score can differ depending
on whether we consider all his pair-comparisons or just his
pairwise defeats.

Mike Ossipoff

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