366 THE ALTERNATE VOTE. 



an absolute majority is declared elected, and the scrutinies are 

 continued till one applicant has an absolute majority ; if no appli- 

 cant has that, the one with fewest votes is thrown out, and his 

 alternate votes distributed. Here, as in the Single Vote at the 

 first count, the best man may be thrown out. 



19. The Venetian Method. — At the first scrutiny each selector 

 has two votes, which are given i to each of the two candidates he 

 most prefers, as in the double vote system. The candidate with 

 fewest votes is rejected. We saw under the double vote that an 

 applicant whom an absolute majority of the voters preferred mav 

 be thus rejected at the first count. 



If there are 2n voters, and the candidate with the fewest votes 

 at the first count has less than n votes, we saw before [Section 9) 

 that he could not possibly be the best man, nor compete with the 

 best man successfully, and that his rejection left the best man in ; 

 and in this case the Venetian Method answers, the best man is 

 elected. 



20. Condorcel's Practiced Method. — At the first count one 

 vote is counted for each first place. If any candidate obtains an 

 absolute majority he is elected. If not, a second scrutiny is 

 made, one vote is counted for each first place and one vote for 

 each second place as in the Venetian Method, and the Double 

 Method ; and the highest applicant is selected. Suppose 16 voters 

 vote as follows : 5 AB, 5 CB, 2 AC, 2 BA, and 2 CA. Then 

 counting first votes only, we get A, B, C, with 7, 2, 7 votes, 

 respectively on the first scrutiny, giving no absolute majority. 

 The second scrutiny will give for A, B, C, counting first and 

 second votes, 11, 12, and 9, respectively; thus B is elected. 



Yet A gets a majority of two votes against B ; for he gets 

 5 AB, 2 AC, 2 CA against 5 CB and 2 BA ; that is 9 against 7 

 say A is better than B ; and the same majority of two votes, 

 namely 5 CB, 2 AC, and 2 CA against 5 AB and 2 BA, say C 

 is better than B. 



Having thus shown that the seven methods may be fallacious, 

 we now come to the only effective method, Nanson's, which com- 

 bines the principle of successive scrutinies with Borda's Method 

 of giving a preferential value to the vote, or first preference, over 

 the second preference or alternate vote (16), and makes use of the 

 preferential voting paper, and excludes the lowest man. 



21. Nanson's Method. — In the case of three candidates each 

 elector marks the numerals i and 2 opposite the names of his 

 first and second choice. At the first scrutiny two votes are 

 counted for each first place, and one vote for each second, as in 

 Borda's Method (16). 



If the two candidates, who have the smallest numbers of votes, 

 have each less than one-third of the votes, both are thrown out, 

 and the third candidate, who has most votes, is elected (10). 



But if only one candidate has less than one-third of the votes, 

 he is rejected ; his alternate votes are distributed to the two 

 continuing candidates, and a second scrutiny is made to see who 

 now has most first votes, and that candidate is elected. This is 

 Borda's Method ; hut in place of electing the highest, as Borda 



