[EM] Method definitions (partial reply)

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Feb 29 21:11:59 PST 2000

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> > The translations of Condorcet's own words for his bottom-up
> > iteration proposal have Plain Condorcet as their literal
> > interpretation. Yes some of us, including me, believe that
> > Mr. Condorcet meant more than Plain Condorcet, but what I
> > call Plain Condorcet is the literal, simplest interpretation
> > of that proposal, the name seems reasonable, to distinguish
> > it from the more refined interpretations, that I call
> > Cycle Condorcet interpretations, because, though they solve
> > circular ties by dropping defeats, they won't drop a defeat
> > unless it's the weakest defeat in some cycle. I fit Schulze
> > into that category since Schulze, SSD, & SD are equivalent when
> > there are no pairwise ties or equal defeats.
>
>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.

Here's a translation:

on page LXVIII of his "Essai sur l'application de l'analyse a la
probabilite des decisions rendues a la pluralite des voix"
(Imprimerie Royale, Paris, 1785), Condorcet writes due to my own
translation:
>From the considerations, we have just made, we get the general
>rule, that in all those situations, in which we have to choose,
>we have to take successively all those propositions that have
>a plurality, beginning with those that have the largest,
>& to pronounce the result, that is created by those first
>propositions, as soon as they create one, without considering
>the following less probable propositions.

On page 126, he writes due to my own translation:
>Create an opinion of those n*(n-1)/2 propositions, which win
>most of the votes. If this opinion is one of the n*(n-1)*...*2
>possible, then consider as elected that subject, with which this
>opinion agrees with its preference. If this opinion is one of the
>(2^(n*(n-1)/2))-n*(n-1)*...*2 impossible opinions, then eliminate
>of this impossible opinion successively those propositions, that
>have a smaller plurality, & accept the resulting opinion of the
>remaining propositions.

This makes it clear that, in Condorcet's top-down proposal,
and in his bottom-up proposal, he _isn't_ limiting his proposal
to 3 candidates.

As for assuming that he thinks everyone will rank all the
candidates, does he actually say that? If not then we can't
assume it. If he doesn't say one way or another, then we must
assume that his proposals apply whether or not there's truncation.
We can't read his mind, so we must go only by what he said.

Mike

(more tomorrow)

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