Art. XIX. — Methods of Election. 

 By Professor E. J. Nanson. 



[Read 12th October, 1882.] 



If there be several candidates for an office of any kind, 

 and the appointment rests in the hands of several persons, 

 an election is held to decide who is to receive the appoint- 

 ment. The object of such an election is to select, if possible, 

 some candidate who shall, in the opinion of a majority 

 of the electors, be most fit for the post. Accordingly, 

 the fundamental condition which must be attended to in 

 choosing a method of election is that the method adopted 

 must not be capable of bringing about a result which is 

 contrary to the wishes of the majority. There are several 

 methods in use, and none of them satisfy this condition. 

 The object of this paper is to prove this statement, and 

 to suggest a method of election which satisfies the above 

 condition. 



Let us suppose, then, that several persons have to select 

 one out of three or more candidates for an office. The 

 methods which are in use, or have been put forward at 

 various times, may be divided into three classes. 



The first class includes those methods in which the 

 result of an election is arrived at by means of a single 

 scrutiny. 



The second class includes those in which the electors 

 have to vote more than once. 



The third class includes those in which more, than one 

 scrutiny may be necessary, but in which the electors have 

 only to vote once. 



In describing these methods, the number of candidates 

 will in some cases be supposed to be any whatever, but 

 in other cases it will be assumed, for the sake of 

 simplicity, that there are only three candidates. The case 

 in which there are only three candidates is the simplest, and 

 it is of frequent occurrence. I propose, therefore, to 

 examine, for the case of three candidates, the results of 

 the methods which have been proposed, and to show that 



