Methods of Election. 199 



C were the only candidates C would win ; thus B and C can 

 each beat A, and yet neither of them wins. A wins simply 

 because he is opposed by two men, each better than himself. . 



Thus the single vote method does not satisfy the 

 fundamental condition. It appears also not only that the 

 best man may not be elected, but also that we are not even 

 sure of getting in the second best man. It is clear that if 

 any candidate obtain an absolute majority of the votes 

 polled this error cannot occur. All we can say, then, about 

 the single vote method is that if any candidate obtain an 

 absolute majority the method is correct, but if no one 

 obtains such a majority the result may be quite erroneous. 



These results are well known, and consequently in 

 elections under this plan great efforts are generally made 

 to reduce the number of candidates as much as possible 

 before the polling day, in order to avoid the return of a 

 candidate who is acceptable to a small section only of the 

 electors. This reduction can, in practice, be made only by 

 a small number of the electors, so that the choice of a 

 candidate is taken out of the hands of the electors them- 

 selves, who are merely permitted to say which of two or 

 more selected candidates is least objectionable to them. 



The Double Yote Method. 



In this method each elector votes for two candidates, and 

 the candidate who obtains the largest number of votes is 

 elected. This method is erroneous, for it may lead to the 

 rejection of a candidate who has an absolute majority of 

 votes in his favour, as against all comers. For suppose that 

 there are twelve electors, and that the votes polled are, 

 for A, nine ; for B, eight ; for C, seven, then A is elected. 

 Now, in order to show that this result may be erroneous it 

 is merely necessary to observe that it is possible that each 

 of the seven electors who voted for C may consider C better 

 than A and B ; that is to say, an absolute majority of the 

 electors may consider C to be the best man, and yet the 

 mode of election is such that not only does C fail to win, but 

 in addition he is at the bottom of the poll. This is an 

 important result ; we shall see presently the effect it has on 

 other methods of election. 



In the case in which there are only three candidates this 

 method is, in fact, equivalent to requiring each elector to 

 vote against one candidate, and then electing the candidate 

 who has the smallest number of votes recorded ao-ainst him. 



