236 Methods of Election. 



voting paper into a column of the poll-book, taking care to 

 write in two 3's in the two blank spaces opposite the names 

 C, G. After copying the numbers from each ballot-paper 

 into the poll-book and filling up all the vacant spaces, we 

 should add up the different rows and proceed exactly as 

 before to ascertain the result of the election. Thus it is 

 clear that the method of dealing with the papers is exactly 

 the same no matter how many or how few names be marked, 

 nor how many are bracketed in the various brackets, and 

 that there is very little risk of error in the process. 



If this system of bracketing be permitted we at once get 

 rid of the objection that the proposed method could only be 

 used in a highly educated constituency, because it is only 

 highly educated electors who can possibly arrange the can- 

 didates in order of merit. The method can easily be used 

 by the most ill-informed electors. In fact, an elector, if he 

 so pleased, could vote in exactly the same manner as in 

 elections under the common "majority" system of voting in 

 cases where there are several candidates — that is, the elector 

 may simply cross out the names of all the candidates he 

 objects to and leave uncancelled as many names as he 

 pleases. In such a case the uncancelled names would all be 

 considered bracketed for the first place, and the cancelled 

 ones as bracketed for the second or last place. 



Exactly as in the case of incomplete papers previously 

 discussed, it is easy to see that the method just given is not 

 strictly accurate, that the strictly accurate method would be 

 too complicated for practical purposes, and that the error 

 has the effect of decreasing the chances of success of the 

 favourite candidates of the elector Who resorts to bracketing. 

 In fact it may be shown that the numbers which ought 

 strictly to be entered in the poll-book for the candidates in 

 the successive brackets are 



n m, m m, m» 



°,-i+T' T +«,+ £.... (i) 



— -f m. 2 + m 3 + . . . + m r _ x + y, £c. 



Now the plan just described comes to the same thing in the 

 end as entering instead of these the numbers 



0, 1, 2, ... . (r— l),&c. (2) 



and as no one of the numbers m^ w 2 , m z , &c, can be less 

 than unity, it is easy to see that no one of the numbers (2) 



