Condorcet.org
Condorcet is perhaps best known for his work on election methods. I am going to give a brief overview of some of his work, and some ideas that can be accurately attributed to him.
Condorcet favoured rank ballots, which were already in use when he wrote.
In general, therefore, we should replace this method [traditional plurality] with one in which each voter simultaneously shows his preferences among all the candidates by placing them in order of merit. (p 123, "An Essay on the Application of Probability Theory to Plurality Decision-Making" 1785)
Note that when Condorcet says "Plurality Decision-Making" he means majority decision making. He uses the terms "plurality" and "majority" interchangeably, but favouring the latter in his later work. This appears to reflect a change in the language.
Clearly, once the list of candidates in order of merit has been submitted, we can extract from it each voter's judgement on the relative merits of any two candidates. (p 111, "On Ballot Votes", 1784)
Condorcet noticed that these decisions might come into conflict. Condorcet believed that where practical, a contradiction should be taken as giving no decision. (p 128, "An Essay...", 1785) But he thought a lot about what might be done when a contradiction had to be resolved. He makes an analogy to how an individual might solve such a conflict.
When a man compares two individuals and prefers the second to the first, and then, on comparing the second with a third, prefers the latter, it would be self-contradictory if he did not also prefer the third to the first. If, however, on making a direct comparison of the first and the third, he found reasons for preferring the first, he would then have to examine this judgement, balance the reasons behind it with those behind his other judgements (which cannot exist alongside this new one) and sacrifice the one he considers least probable. (p236, "On Elections", 1793)
He related support for a proposition to probability using the following formula, based on a classic formula of probability. (p 35)
v=chance of truth -- note that v doesn't stand for votes, it stands
for verite
e=chance of error 1-v
h=votes for majority
k=votes against majority
p = vh-k / [vh-k + eh-k]
Of course, no one knows v, the chance that a voter will be on the right side of any two-choice proposition. Condorcet was confident that it would be above 0.5. That is, that voter choices would be better than random. This formula assumes that voters act independently, which is hard position to defend. It is an interesting starting point for discussion, however, and it is possible to come up with more plausible assumptions for similar formula. For example, by assuming fewer independent actors. For Condorcet's purposes, it is only necessary that there be a positive relationship between margin of support of a proposition and probability of being correct, so his argument can progress without accepting this precise formula. Condorcet, illustrates the use of his formula with an example.
We must now look at the case in which a decision is made with the smallest possible plurality. If we suppose each vote to have a probability of 9/10 of being correct, then for 10 candidates, we only require a plurality [he means h-k] of four votes to have, even in the worst possible case, a probability of 99/100 [approximately] of having made a good choice. (p134, "An Essay...", 1785)
As previously mentioned, the rank ballot allows us to determine the public's expressed opinion on any two-way (or pairwise) comparison of candidates. So, if we find that a majority prefer B to A, Condorcet would argue that based on that information alone, B is probably a better candidate than A. But perhaps other majority backed propositions, if they contradict this one, might make a different result more probable. But in the simplest case, majority backed propositions do not come into conflict. For example, if majorities prefer C to B, C to A, and B to A,
1. Candidate A clearly does not have the preference, because there is a plurality of votes against him whether he is compared to B or to C (and this is always the case in such situations). The choice is therefore between B and C. As the proposition `B is better than C' has only minority support, we must conclude that it is C who has plurality support. (p126, "An Essay...",1785)
Condorcet implies both a Condorcet winner, and a Condorcet loser criterion. That is, if a candidate is majority preferred to each other candidate, it should win, but if each other candidate is majority preferred to it, it should lose. In fact, Condorcet clearly believes that a Condorcet loser should not even affect the result.
Condorcet only considers examples involving three candidates, but he suggests a procedure that does not have this limit.
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. (p 238, "On Elections", 1793)
Unfortunately, there is a problem with this procedure. In my opinion, Condorcet believes that it will always be possible to eliminate some number of the smallest majorities, and form a complete and consistent ranking out of the larger ones. But it is possible to design examples that do not fit this assumption. For example, A over B with a margin of 6, B over C 5, C over A 4, A over D 3, B over D 2, C over D 1. The conflict is not gone until you reject all the majorities up to 4. But now, you have rejected all the majorities that compare D with the other candidates, giving no result.
Why would Condorcet make such an error? In his writing, he never specifically considers an example with more than three candidates, so he probably never ran into this problem. It has caused a great deal of confusion for later writers, however. Because his words above do not describe a working method, I recommend reserving the term "Condorcet's method" for the procedure of selecting the Condorcet winner, where one exists. Anyone who is using a method that meets the Condorcet criterion is using Condorcet's method (although perhaps implicitly).
I think that Ranked Pairs follows naturally from the principles suggested by Condorcet. He wants to reject smaller majorities in favour of larger, in order to find a complete ranking of the candidates. He seems to assume that the majorities he is rejecting would otherwise form contradictions with higher majorities that he is not rejecting, or that he can safely drop them because they are made redundant by higher majorities. If he did not make this assumption, he might very well have made it an explicit part of his rule for which majorities should be rejected. That is, that majorities should only be rejected if they would otherwise form a contradiction with higher majorities that are not being rejected. Of course, that is Ranked Pairs.
Reference
All quotes are from the following translation of Condorcet's work. Page numbers refer to the translation. The years refer to the original.
Iain Mclean, Fiona Hewitt, 1994
"Condorcet: Foundations of Social Choice and Political Theory"
Edward Elgar Publishing Limited