Methods of Election. 237 



can be greater than the corresponding one of the numbers 

 (1), that when no bracketing occurs the two sets (1), (2), are 

 the same, and that the two sets agree until the first bracket 

 is reached. Now observe that the numbers entered in the 

 poll-book are in reality negative votes, and we see at once 

 that the moment an elector begins to bracket, he diminishes 

 the influence of his own vote on the result of the election, 

 and also decreases the chances of success of all candidates 

 who on his own list are placed higher than the bracket. 

 Each additional bracket will have precisely the same effects. 

 Thus it is clear that the effect of the proposed method will 

 be to discourage the practice of bracketing. If we do not 

 wish to discourage this practice we must resort to the 

 accurate method, and use the numbers (1) instead of (2). 

 This is not very difficult to do, but as it introduces a new 

 method for the bracketed votes, it would give considerable 

 extra trouble to the officers who make up the poll-books. 

 The most convenient way of stating the accurate method 

 would be as follows: — For each first place count one nega- 

 tive vote, for each second place count in addition J (mi + m 2 ) 

 negative votes, for each third place count in addition to the 

 last J (m a + m 3 ) negative votes, for each fourth place count 

 in addition to the last J (m 3 + m 4 ) negative votes, and so 

 on. As before remarked, the numbers for the successive 

 places would be the natural numbers 1, 2, 3, 4, &c, until a 

 bracket was arrived at. When brackets do occur we shall 

 in general have to deal with half-votes, but no smaller 

 fraction could occur. 



Another Method for Cases of Bracketing. 



Another plan might also be adopted for dealing with 

 cases of bracketing. It is as follows. For each candidate 

 in the first place count one vote; for each candidate in the 

 second place count m x + 1 votes ; for each candidate in the 

 third place count mi + m 2 + 1 votes ; for each candidate 

 in the fourth place count m x + m 2 + ??i 3 + 1 votes; and so on. 

 The plan now under consideration comes to the same thing 

 as counting for the successive places the numbers 0, m u m x + 

 m 2 , .... mj + m 2 + . . . -{- wi r -\, & c - instead 

 of the proper numbers (1). Thus the errors for the suc- 

 cessive places are 



m 1 — m 2 m x — m 3 m y — m r 



