Proportional Representation. 



39 



diminishing the quota every time a sufficient number of 

 papers are lost, would have to be repeated until either there 

 remain no more candidates than vacancies, or until some one 

 obtains more than the quota. 



If there is only one vacancy to be filled, the whole pro- 

 cess of the election falls under this case. The quota for any 

 count is an absolute majority of the useful votes left. 



It is also to be noticed that if at any stage a candidate 

 has a number of votes greater than the sum of the votes of 

 all the candidates who have less than he has, then all such 

 candidates may be at once excluded ; in particular, if any 

 candidate has an absolute majority on the first count he is 

 elected. 



Next, let us suppose that at least one candidate has more 

 than the quota. Let A, B, C, &c, denote the candidates 

 who have a quota or more, and let P, Q, R, S, &c, denote 

 the candidates who have less than the quota. The first 

 thing to be done is to examine the heaps of A, B, C, &c, so 

 as to arrive at the information shown in the following 

 table : 



Table I. 



A 



B 



C 



Here Al denotes the number of papers on which A is 

 marked 1 and on which no other names, if any, are marked, 

 save those of the elected candidates, B, C, &c, and so for Bl, 

 &c. AP denotes the number of papers on which A is 

 marked 1,' and on which P is marked as the prior choice of 

 the elector amongst the unelected candidates, P, Q, R, S, 

 &c; and so for AQ, and BP, &c. The heaps of A, B, C, &c, 

 are broken up into corresponding parcels. 



For convenience, the numbers A, B, &c, are written at 

 the ends of the rows, and P, Q, R, &c, at the heads of the 

 columns, each set being written down in the order of 

 priority of the candidates on the first count. The number 

 by which the number of votes of an elected candidate 



