Condorcet Tiebreak; que veut dire "=?iso-8859-1?Q?pluralit=E9?="?

[Hugh Tobin]

DEMOREP1 at aol.com wrote:
> 
> Yet another Condorcet circular tie with 15 voters--
> 
> 3 AC
> 4 AB
> 
> 5 BC
> 
> 2 CA
> 1 C
> 
> A v. B-- 9 to 5
> B v. C-- 9 to 6
> C v. A-- 8 to 7
> 
> According to Mr. Ossipoff, A should win by having the fewest votes against A
> in his/her worst (and only) defeat (8).  Note that all of the B and C voters
> combined thus could not defeat A (even if, horror of horrors, B and C were
> "progressives" against a "reactionary" A)
> 

I do not understand this claim.  If all the C voters voted for B second,
then surely B would win.  But if two C voters prefer A to B, as
indicated, why shouldn't A win?  I have my doubts about the [EM]
tiebreak for Condorcet, but not because of an example like this one.

>If each vote is an approval vote, then there is-- 
>A 9, B 9, C 11.

One cannot infer from the rankings you give that C would get the most
"approval" votes if that feature were added, so what is the point of
this statement? For example, some of the BC voters might "approve" all
candidates, or AC voters might "approve" only A.

[snip]
> [Condorcet's comments translated (by Prof. Young ?) from his Essai sur
> l'application de l'analyse a la probabilite des decisions rendues a la
> probabilite des voix (1785), pp. 125-126 ]
> [snip]
> 3. One forms an opinion from those n(n-1)/2 propositions that agree with the
> most voices. If this opinion is among the n(n-1)... 2 possible opinions, one
> regards as elected the subject to whom this opinion accords the preference.
> If this opinion is among the 2 (to the exponent n(n-1)/2) minus n(n-1) .....
> 2 impossible opinions, then one successively deletes from that impossible
> opinion the propositions that have the least plurality, and one adopts the
> opinion from those that remain.
> -----
> [snip]
> 
> My comments----In view of Condorcet's definition of a "proposition" (i.e. a x
> versus y pairing), if there is a cycle (i.e. tie- such as the above a>b, b>c,
> c>a), then did Condorcet mean to drop the pairing(s) in the cycle with the
> least pluralities (the one or more lowest x minus y, if x>y) to produce a
> result without a tie ?   Note Condorcet's use of *successively deletes* and
> *the least plurality*.
> 
[snip]

Why do you read "plurality" as "margin" or "difference"?  May we assume
it is "pluralité" in the original French?  The English term today can
mean either the winner's total or the winning margin, but my 1968 Petit
Larousse defines "pluralité" as "le plus grand nombre." This would seem
to imply using the least total votes for x where x > y, as in Ossipoff's
method, not the margin.  (Does someone have a better or older French
dictionary?)  The OED attributes the usage of "plurality" to mean
"excess of votes" to U.S. politics and indicates it arose in the 19th
century (though the citations are unclear as to whether the margin or
absolute number is meant).  The pre-1823 meaning, from the French, was
"the greater number or part; more than half of the whole;  = MAJORITY
3," per the OED (where 3 is the OED definition of MAJORITY as the total
number, not the margin of victory).  Had he intended the margin,
Condorcet could have used "excès,"  defined in the Larousse as "quantité
qui se trouve en plus" (roughly, "quantity that is in addition"); also
"différence" is a perfectly good word in French arithmetic.  I doubt
that Young would have translated either as "plurality," though I admit I
have not seen the French text or the translation.  

I am not convinced that total votes against is the best tiebreak method,
and I am not sure it is very important what Condorcet intended if he did
not expressly recognize the possibility of incomplete rankings and did
not articulate a theoretical basis for his tiebreaker, but if Condorcet
said "le moindre pluralité," the above sources suggest this bears
Ossipoff's reading better than yours.

-- Hugh Tobin