Methods of Election. 211 



consists merely in combining the principle of successive 

 scrutinies with the method of Borcla, and at the same time 

 making use of the preferential voting paper, so that the 

 proposed method belongs to the third class. I propose, first, 

 to describe and discuss the method for the case of three 

 candidates, and then to pass on to the- general case in which 

 there may be any number of candidates. 



Let us suppose, then, that there are three candidates, A, 

 B, C. Each elector writes on his voting paper the names of 

 two candidates in order of preference, it being clearly un- 

 necessary to write down a third name. If we prefer it, the 

 three names may be printed on the voting paper, and the 

 elector may be required to indicate his order of preference 

 by writing the figure 1 opposite the name of the candidate 

 of his first choice, and the figure 2 opposite the name of the 

 candidate of his second choice, it being clearly unnecessary 

 to mark the third name. In order to ascertain the result of 

 the election two scrutinies may be necessary. 



At the first scrutiny two votes are counted for each first 

 place and one vote for each second place, as in the method 

 of Borda. Then if the two candidates who have the smallest 

 number of votes have each not more than one-third of the 

 whole number of votes, the candidate who has most votes is 

 elected, as in Borda's method. But if one only of the candi- 

 dates has notmore than one-third of thevotespolled(and some 

 candidate must have less), then that candidate is rejected, and 

 a second scrutiny is held to decide between the two remain- 

 ing candidates. At the second scrutiny each elector has one 

 vote, which is given to that one of the remaining candidates 

 who stands highest in the elector's order of preference. The 

 candidate who obtains most votes at the second scrutiny is 

 elected. 



The method ma}^ be more briefly described as follows : — 

 Proceed exactly as in Borda's method, but instead of electing 

 the highest candidate, reject all who have not more than the 

 average number of votes polled. If two be thus rejected, 

 the election is finished ; but if one only be rejected, hold a 

 final election between the two remaining candidates on the 

 usual plan. 



In order to show that the proposed method is free from 

 the defects above described, it is necessary and it is sufficient to 

 show that if the electors consider any one candidate, A, say, 

 superior to each of the others, B and C, then A cannot be 

 rejected at the first scrutiny. For if A be not rejected at 



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