238 Methods of Election. 



'Hence we see that 



(i.) If the same number of candidates be bracketed for 

 each place, the plan is accurate. 



(ii.) If m x be greater than each of the numbers m 2 , m 3 , 

 &c, that is, if more candidates are bracketed for the first 

 place than for any other place — then the errors will be all 

 positive, and the effect will be to give the elector more 

 negative votes than he is entitled to, and, consequently, to 

 increase unduly the chances of the candidates bracketed for 

 the first place. 



(iii.) If mi be less than each of the numbers m 2 , m 3 , &c. — 

 that is, if fewer candidates are bracketed for the first place 

 than for any other place — then the errors will be all negative, 

 and the effect will be to give the elector fewer negative 

 votes than he is entitled to, and, consequently, to decrease 

 unduly the chances of the candidates placed at the top end 

 of the elector's list. 



(iv.) If mi be equal to the mean of the numbers m 2 , m 3 , 

 &c, the elector will have just as many votes as he ought to 

 have, but he will give more negative votes to some 

 candidates and less to others than they ought to have. 



(v.) If m x be not equal to the mean, then the elector will 

 have more or less votes than he is entitled tq, according as 

 mj is greater or less than the mean. 



The results just given apply to each scrutiny ; but the 

 numbers m b m 2 , m 3 , &c, will generally be altered at each 

 scrutiny. Thus it is in general impossible to tell at the 

 commencement of an election what will be the effect of 

 different modes of bracketing. Sometimes the elector will 

 get too many votes, sometimes too few. At some scrutinies 

 the candidates at the top end of his list will get too many 

 votes, and at others those at the lower end will get too many 

 votes. 



If there be one candidate only in each place except the 

 last, or, in other words, if the only bracket be for the last 

 place, we have the case of incomplete papers discussed 

 above. In this case the plan just described, and the method 

 adopted above, agree ; and the effect is, as has already been 

 pointed out, to give the elector too few votes ; and this 

 would be the case at each scrutiny, until all but one of the 

 candidates in the bracket are rejected. 



If, however, an elector bracket a number of candidates 

 for the first place and arrange all the rest in order of merit, 

 he would get more votes than he is really entitled to and 



