[EM] Method definitions

[MIKE OSSIPOFF]

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.

>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),
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".

Mike Ossipoff




>
>Markus Schulze
>schulze at sol.physik.tu-berlin.de
>schulze at math.tu-berlin.de
>markusschulze at planet-interkom.de
>

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