Proportional Representation. 



41 



that as small an alteration as possible is made in the order 

 in which the unelected candidates stand. When the surplus 

 of a candidate is distributed all the unelected candidates 

 next indicated on his papers are helped forward, and each, 

 as far as possible, to the same extent. Thus, indirectly, 

 greater weight is given to the first choice of each elector. 



In order to show the mode of carrying out this principle, 

 the following table is constructed. 



Table II. 

 Q R 



S 



B 



C 



p 



Q 



E 



S 





ap 



aq 



ar 



as 



a 



bp 



bq 



br 



bs 



b 



cp 



cq 



cr 



cs 



c 



The names at the ends of the rows and columns are the 

 same as in Table I. a denotes A's surplus, ap denotes the 

 number of papers which are to be transferred from A to P, 

 and so on. The letters P, Q, fcc, in the first row of the 

 table, denote the numbers of papers in the heaps of P, Q, 

 &c. The sum of the numbers ap, aq, ar, &c, is equal to a, 

 or to the sum of the numbers A P, A Q, A R, &c, whichever 

 is the smallest. No one of the numbers ap, aq, &c, can be 

 greater than the corresponding number in Table I.; those 

 which are less are all equal to one another, or differ by unity 

 at the most. The method of finding these numbers- is as 

 follows. Suppose papers taken one by one from the parcels 

 A P, A Q, &dg. } in this order, and let the process be continued 

 and repeated until either the number of papers so taken is 

 equal to A's surplus, or all the heaps, A P, A Q, &c, are 

 exhausted. Then ap denotes the number of papers taken 

 from the parcel A P, and so on. 



This merely shows how the numbers ap, aq, &c, are 

 arrived at ; it does not show us what papers are to be taken 

 from the parcel A P and transferred from A to P. Before 

 considering the rule by which we are to select the ap papers 

 from the parcel A P, it is as well to notice one or two 



