[EM] Condorcet's words

Markus Schulze markus.schulze at alumni.tu-berlin.de
Sun Jan 4 10:28:03 PST 2004


Condorcet discusses the 3-candidate case in great detail.
However, I am aware of only 4 instances where Condorcet
discusses the general case.

Condorcet wrote ("Essai sur l'application de l'analyse
a la probabilite des decisions rendues a la pluralite
des voix," Imprimerie Royale, Paris, p. LXVIII of the
introduction, 1785):

> From the considerations we have just made we get the
> general rule that whenever we have to choose we have
> to take successively those propositions that have a
> plurality -- beginning with those that have the largest
> -- and to pronounce the result as soon as these first
> propositions create one.

Condorcet wrote ("Essai sur l'application de l'analyse
a la probabilite des decisions rendues a la pluralite
des voix," Imprimerie Royale, Paris, p. 126, 1785):

> Create an opinion of those n*(n-1)/2 propositions that
> win most of the votes. If this opinion is one of the
> n! possible then consider as elected that subject to
> which this opinion agrees with its preference. If this
> opinion is one of the (2^(n*(n-1)/2))-(n!) impossible
> opinions then eliminate of this impossible opinion
> successively those propositions that have a smaller
> plurality and accept the resulting opinion of the
> remaining propositions.

Condorcet wrote ("Sur la Forme des Elections," 1789):

> To compare just 20 candidates two by two, we must examine
> the votes on 190 propositions, and for 40 candidates,
> on 780 propositons. Besides, this will often give us an
> unsatisfactory result; it may be that no candidate is
> considered by the plurality to be better than all the
> others, and then we would have to prefer the candidate
> who is just considered better than a larger number; and
> when several were considered better than the same number
> of candidates, we would have to choose the candidate who
> was either considered better by the greatest plurality,
> or worst by the smallest plurality.

Condorcet wrote ("Sur les Elections," Journal
d'Instruction Sociale, vol. 1, p. 25-32, 1793):

> A table of majority judgements between the candidates
> taken two by two would then be formed and the result
> -- the order of merit in which they are placed by the
> majority -- extracted from it. If these judgements
> could not all exist together, then those with the
> smallest majority would be rejected.


I am aware of only one instance where Condorcet mentions
that he doesn't presume that each voter votes a complete
ranking of all candidates.

Condorcet wrote ("Sur les Elections," Journal
d'Instruction Sociale, vol. 1, p. 25-32, 1793):

>    It is not necessary for everyone to compare all the
> candidates or to form a complete list. A voter may for
> various reasons regard a certain number of candidates
> as equal to one another, either after considering their
> attributes or because he does not know the candidates and
> is therefore unable, or unwilling, to judge them.
>    This condition in no way restricts the voters' freedom,
> since it simply requires everyone to decide which candidates
> he wishes to choose between. The list of all those put
> forward in this way would then present each voter with the
> names of all the candidates between whom the other voters
> wanted the election to be conducted, and he would then
> have complete freedom to decide how he could share in this
> judgement: which candidates he wanted to rank in order of
> merit and which to reject entirely by placing them after
> all the others.
>    Any election method in which the votes given are
> incomplete will produce results which contradict the will
> which the majority would have had if complete votes had
> been collected.
>    The results of these incomplete votes will of course have
> some degree of probability of being correct, but it would be
> similar to that of a proposition which has been only half
> examined. In fact, we should support a probable proposition
> only when we have discovered the impossibility of
> incorporating new information, and as long as this
> impossibility lasts.
>    However, we would be just as far from fulfilling our aim
> if we forced each voter to express, not the complete vote
> which he actually forms, but a complete vote in an absolute
> sense; that is, if we forced him to establish an order of
> preference between all the candidates, including those he
> does not know. Clearly, he would then rank the latter at
> random and his vote could result in the election of a
> candidate who would not otherwise have had sufficient
> support. In the first case, we are neglecting judgements
> which should have been assessed, and in the second, we are
> assessing judgements which have not been given. In the first
> case, we are acting as if we had randomly excluded a certain
> number of voters, and in the second as if we were randomly
> giving some of them double the number of votes.
>    In theory, therefore an election procedure should be as
> follows: after having determined the list of acceptable
> candidates, each voter should express his complete will,
> whether of preference or indifference.

Markus Schulze

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