CONDORCET. 385 



where i> (g + 1) - 4> iq) ^ I^TT^ I""'" ^^ ~ "''^'" ~ '"'*' ^^ -^)'' j • 



In this manner Condorcet deduces various formulae similar to 

 equation (2) of Art. 663. 



We may remark that at first Condorcet does not seem to deduce 

 his formulae in the simplest way, namely by applying the results 

 which he has already obtained in his first part ; but he does 

 eventually adopt this plan. Compare his pages 191 and 208. 



706. Condorcet now proceeds to the ai^plication of the problems 

 to the main purposes of his Essay. As he says in the passage we 

 have quoted in Art. 695, there are two questions to be considered. 

 The first question is considered in pages 213 — 223, and the second 

 question in pages 223 — 241. 



707. The first question asks for two results ; Condorcet barely 

 notices the first, but gives all his attention to the second. 



Condorcet proposes two methods of treatment for the first ques- 

 tion ; the premier moyen is in pages 213 — 220, and the seconde 

 methode in pages 220 — 223. Neither method is carried out to a 

 practical application. 



708. We will give a simple illustration of what Condorcet pro- 

 poses in his first method. Suppose we have a tribunal composed 

 of a large number of truly enlightened men, and that this tribunal 

 examines a large number of decisions of an inferior tribunal. Sup- 

 pose too that we have confidence that these truly enlightened men 

 will be absolutely correct in their estimate of the decisions of the 

 inferior tribunal. Then we may accept from their examination 

 the result that on the whole the inferior tribunal has recorded m 

 votes for truth and n votes for error. We are now ready to apjDly 

 the problem in Art. 704, and thus determine the probability that 

 out of the next 2q + l votes given by members of the inferior tri- 

 bunal there will be a majority in favour of the truth. 



This must be taken however only as a very simple case of the 

 method proposed by Condorcet ; he himself introduces circum- 

 stances which render the method much more complex. For in- 

 stance he has not complete confidence even in his truly enlightened 



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