210 Methods of Election. 



scrutiny on the Venetian method, and the candidate who 

 obtains most votes is elected. At first sight we might 

 suppose that this method could not lead to error. Com- 

 paring it with the Venetian method, described above, we see 

 that Condorcet supplies a remedy for the obvious defect of 

 the Venetian method — that is to say, the rejection of a 

 candidate who has an absolute majority is now impossible. 

 A little examination, however, will show, as seems to have 

 been pointed out by Lhuilier,* that the method is not free 

 from error. For, let us suppose that there are sixteen 

 electors, of whom five put A first and B second, five put C 

 first and B second, two put A first and C second, two put B 

 first and A second, and two put C first and A second. Then 

 the result of the first scrutiny will be, for A, B, C, seven, 

 two, seven votes respectively. Thus, no one having an 

 absolute majority, a second scrutiny is necessary. The 

 result of the second scrutiny will be — for A, B, C, eleven, 

 twelve, and nine votes respectively. Thus B, having the 

 largest number of votes, is elected. This result, however, is 

 not in accordance with the views of the majority of the 

 electors. For the proposition, " B is better than A," would 

 be negatived by a majority of two votes, and the proposition, 

 " B is better than C," would also be negatived by a majority 

 of two votes, so that in the opinion of the electors B is 

 worse than A and also worse than C, and, therefore, ought 

 not to be elected. 



Summing up the results we have arrived at, we see that 

 each of the methods which have been described may result 

 in the return of a candidate who is considered by a majority 

 of the electors to be inferior to each of the other can- 

 didates. Some of the methods — viz., the double vote 

 method, the method of Borda, and the Venetian method — 

 may even result in the rejection of a candidate who has an 

 absolute majority of votes in his favour as against all 

 comers. It would, however, be quite impossible for such a 

 result to occur on the single vote method, or the methods of 

 Ware and Condorcet. 



Method Proposed. 



Having pointed out the defects of the methods in common 

 use, it now remains to describe the method proposed for 

 adoption, and to show that it is free from these defects. It 



* See Montucla's Eistoire des Mathematiques, vol. iii., p. 421. 



