Methods of Election. 235 



into that column. After doing this add up the figures in 

 each row; then find the mean or average of the sums. 

 Every candidate who has a sum equal to or greater than 

 the average is to be excluded. A little consideration will 

 show that this process will give the same result as the 

 method described above. When the papers have once been 

 copied into the poll-book as just described, all subsequent 

 scrutinies that may be necessary can be conducted without 

 handling the voting papers again. 



Cases of Bracketing. 



Under the head of "Incomplete Yoting Papers" we 

 have considered a case in which an elector does not 

 fully express his preference. There is, however, another 

 way in which an elector may fail to fully express his 

 preference. An elector may have no difficulty in putting 

 a number of candidates at the bottom of his list, and yet 

 he may have considerable difficulty in deciding as to the 

 precise order in which to place the candidates at the top 

 end of his list. In such a case an elector might wish to 

 put two or more candidates equal for the first, second, or 

 some other place on his list. This may be called a case of 

 bracketing. It is now to be shown that this system of 

 bracketing can be permitted without causing any difficulty 

 in the practical working of the system. Let us suppose 

 that an elector brackets 7n 1 candidates for the first 

 place, m 2 for the second place, and so on ; so that 

 mi + m 2 + m 3 + . . . = n, the case in which one candidate 

 only is put in the r th place being provided for by supposing 

 m r = 1. Then in the poll-book already described enter the 

 number one for each of the mi candidates in the first 

 bracket, the number two for each of the m 2 candidates .in 

 the second bracket, the number three for each of the 

 m 3 candidates in third bracket, and so on. Suppose, for 

 example, that there are seven candidates, A, B, C, D, E, F, G, 

 and that an elector wishes to bracket B, E for 

 the first place and A, D, F for the second place, 2A 

 and that he does not care to say anything about IB 

 C, G. Then he would mark his paper as shown C 



in the margin. As nothing is said about C, G, 2D 

 we should consider them as bracketed for the IE 

 third or last place. Now in order to record this 2F 

 vote in the poll-book it is merely necessary, as G 



before, to copy the column of numbers on the 



