228 Methods of Election. 



not, on the average, require more than three scrutinies. 

 There can be no doubt, however, that the method would be 

 tedious if the number of electors were very large, unless 

 the number of candidates was very small indeed. In cases 

 where the number of electors is large Ware's method has 

 great practical advantages ; for in that method we only 

 require to count one vote for each paper examined at each, 

 scrutiny, and at every scrutiny except the first the number 

 of papers to be examined is but a small fraction of the 

 whole number of papers. 



Condorcet's Theoretical Method. 



A method of election was described by Condorcet in 1785, 

 but on account of its complexity it was never proposed for 

 actual use. On this account, and in order to distinguish it 

 from Condorcet's practical method (which has been already 

 described), I propose to call it Condorcet's theoretical 

 method. This method is described by its author in the 

 following terms : — 



"There exists but one rigorous method of ascertaining 

 the wish of the majority in an election. It consists in 

 taking a vote on the respective merits of all the candidates 

 compared two and two. This can be deduced from the lists 

 upon which each elector has written their names in order of 

 merit." 



"But, in the first place, this method is very long. If 

 there are only twenty candidates, in order to compare them 

 two and two we must examine the votes given upon one 

 hundred and ninety propositions, and upon seven hundred 

 and eighty propositions if there are forty candidates. Often^ 

 indeed, the result will not be as satisfactory as we could 

 wish, for it may happen that no candidate may be declared 

 by the majority to be superior to all the others ; and then 

 we are obliged to prefer the one who is alone judged 

 superior to a larger number; and amongst those who are 

 judged superior to an equal number of candidates, the one 

 who is either judged superior by a greater majority or 

 inferior by a smaller. But cases present themselves where 

 this preference is difficult to determine. The general rules 

 are complicated and embarrassing in application." (CEuvres 

 de Condorcet, vol. xv., pp. 28, 29.) 



By this method Condorcet showed that the single vote 

 method and the methods of Ware and Borda are erroneous. 

 I do not think however, that any one has hitherto noticed 



