374) CONDORCET. 



that W'^ and W"^ are equal toTf/ ultimately; and on this assump- 

 tion we have the required results at once without the five lines 

 which Condorcet gives after the sentence we have just quoted. 



690. In the course of his eleventh Hypothesis Condorcet 

 examines the propriety of the ordinary mode of electing a person 

 by votes out of three or more candidates. Take the^ following 

 example ; see his page LViil. 



Suppose A, B, C are the candidates ; and that out of 60 votes 

 23 are given for A, 19 for B, and 18 for C. Then A is elected 

 according to ordinary method. 



But Condorcet says that this is not necessarily satisfactory. For 

 suppose that the 23 who voted for A would all consider C better 

 than B ; and suppose that the 19 who voted for B would all con- 

 eider (7 better than A ; and suppose that of the 18 who voted for 

 C, 16 would prefer B to A, and 2 would prefer A to B. Then on 

 the whole Condorcet gets the following result. 



The two propositions in favour of C are C is better than A, 

 C is better than B. 



The first of these has a majority of 87 to 23, and the second 

 a majority of 41 to 19. 



The two propositions in favour of B are B is better than A, 

 B is better than G. 



The first of these has a majority of 35 to 25, the second is 

 in a minority of 19 to 41. 



The two propositions in favour of A are A is better than B, 

 A is better than C. 



The first of these is in a minority of 25 to 35, and the second 

 in a minority of 23 to 37. 



Hence Condorcet concludes that G who was lowest on the 

 poll in the ordinary way, really has the greatest testimony in his 

 favour ; and that A who was highest on the poll in the ordinary 

 way, really has the least. 



Condorcet himself shews that his own method, which has just 

 been illustrated, will lead to difficulties sometimes. Suppose, for 

 example, that there are 23 voters for A, 19 for B, and 18 for G. 

 Suppose moreover that ah the 23 who voted for A would have 

 preferred B to G; and that of the 19 who voted for By there 



