CONDORCET. 367 



. V 



This is not tnie. In fact Condorcet gives -p for the probability 



when he ought to give -^ — ^ , that is V. 



Condorcet says on the same page, Le cas le plus favorable est 

 celui oil Ton aura d'abord j^ decisions consecutives, sans aucun 

 melange. It would be difficult from the words used by Condorcet 

 to determine what he means ; but by the aid of some s^^mbolical 

 expressions which follow we can restore the meaning. Hitherto 

 he has been estimating the probability before the trial is made ; 

 but he now takes a different position altogether. Suppose we are 

 told that a question has been submitted to a series of tribunals, and 

 that at last p opinions in succession on the same side have been 

 obtained ; we are also told the opinion of every tribunal to which 

 the question was submitted, and we wish to estimate the pro- 

 bability that the decision is correct. Condorcet then means to 

 say that the highest probability will be when the first ^ tribunals 

 all concuiTed in opinion. 



Condorcet continues, S'il y a quelque melange dans le cas de 



jo = 2, il est clair que le cas le plus defavorable sera celui 



de toutes les valeurs paires de r, oil le rapport des probabilites 



. v^ e V ^ ^ • ^1 • 



est -3- . - = - , Let us examine tnis. 

 eve 



Suppose that p = 2. Suppose we are told that a decision has 



been obtained after an odd number of trials ; then we estimate the 



probability of the correctness of the decision at . For sup- 

 pose, for example, that there were five trials. The probabilities of the 

 correctness and of the incorrectness of the decision are proportional 

 respectively to evev^ and veve"^, that is to v and e. On the other 

 hand, suppose we are told that the decision has been obtained after 

 an even number of trials ; then in the same way we shall find that 

 the probabilities of the correctness and of the incorrectness of the 

 decision are proportional respectively to v^ and e^. Thus the 



. . v" . 



probability of the correctness of the decision is -^ ^ ; and this 



V 



is greater than , assuming that v is greater than e. Thus 



