37G CONDORCET. 



2°. II faiit de plus que les Yotans soient eclaires, et d'autant plus 

 eclaires, que les questions qu'ils decident sont plus compliquees ; sans 

 cela on trouvera bien ime forme de decision qui preservera de la crainte 

 d'une decision fausse, mais qui en meme temps rendant toute decision 

 presque impossible, ne sera qu'un moyen de perpetuer les abus et les 

 mauvaises loix. Page lxix. 



692. We now come to Condorcet's second part, which occupies 

 his pcages 137 — 175. In the first part the following three elements 

 were always supposed known, the number of voters, the hypothesis 

 of plurality, and the probability of the correctness of each voter's 

 vote. From these three elements various results were deduced, 

 the i^rincipal results being the probability that the decision will 

 be correct, and the probability that it will not be incorrect ; these 

 probabilities were denoted by (j> {q) and 1— 'v/r(^) in Art. 669. 

 Now in his second part Condorcet supposes that we know only huo 

 of the three elements, and that we know one of the two results ; 

 from these known quantities he deduces the remaining element 

 and the other result; this statement applies to all the cases 

 discussed in the second part, except to two. In those two cases 

 we are supposed to know the probability of the correctness of a 

 decision which we know has been given with the least admissible 

 plurality ; and in one of these cases we know also the probability 

 of the correctness of each voter s vote, and in the other case the 

 hypothesis of plurality. 



Condorcet himself has given three statements as to the con- 

 tents of his second part ; namely on pages xxil, 2, and 187; of 

 these only the first is accurate. 



693. Before proceeding to the main design of his second part 

 Condorcet adverts to two subjects. 



First he notices and condemns Buffon's doctrine of moral cer- 

 tainty ; see Condorcet's pages LXXi and 138. One of his objections 

 is thus stated on page 138 : 



Cette opinion est inexacte en elle-meme, en ce qu'elle tend a con- 

 fondre deux clioses de nature essentiellement differente, la probabilite et 

 la certitude : c'est precisement comme si on confondoit I'asymptote 

 d'une courbe avec ime tangente menee a un point fort eloigne ; de telles 

 suppositions ne pourroient etre admises dans les Sciences exactes sans en 

 detruire toute la precision. 



