50 Proportional Representation. 



vacancies are filled, or there remain no more candidates than 

 vacancies. Any scrutiny except the last will involve either 

 a transference, or distribution, or distribution by selection 

 from at least one heap to other heaps, or a withdrawal of 

 at least one heap of exhausted papers. 



At the end of each scrutiny the papers will be left 

 arranged in heaps for the next scrutiny. Each scrutiny 

 will be made according to the following rules : 



At the commencement of each scrutiny the quota for that 

 scrutiny is to be determined by the following rule : 



From the number of votes polled subtract a number 

 equal to the sum of the number of exhausted and lost votes, 

 and divide, to the exclusion of fractions, the difference by a 

 number equal to the number of vacancies to be filled, 

 increased by one and decreased by the number of candidates 

 withdrawn from the election on exhausted heaps of papers. 

 The quotient so obtained, increased by one, shall be the 

 quota. 



After determining the quota two cases arise, first, the 

 case where there is a surplus ; second, the case where there 

 is no surplus. In the first case, an exhaustive division of the 

 candidates, combined with a series of distributions, is to be 

 made, as follows: 



First divide the candidates into two sets, Class and Not- 

 Class O ; Class consisting of those who have less than the 

 quota (hitherto called not-elected). Next divide Not-Class 

 O into two sets, Class I and Not-Class I; Class I consisting 

 of those whose parcels of papers which are not transferable 

 to Class are respectively less than the quota ; then make 

 distributions from Not-Class I to Class O. Next divide Not- 

 Class I into two sets, Class II and Not-Class II ; Class II 

 consisting of those whose parcels of papers which are not 

 transferable to Class I are respectively less than the quota ; 

 then make distributions from Not-Class II to Class I. This 

 process is to be continued as far as possible, the general rule 

 being that after distribution from the set Not-Class r to 

 Class (r — 1), the set Not-Class r is divided into two sets, 

 Class (r + 1) and Not-Class (r+1); Class (r + 1) consisting 

 of those whose parcels of papers which are not transferable 

 to Class r are respectively less than the quota ; then distri- 

 butions are made from Not-Class (r+1) to Class r. 



After the last division and distribution, if the candidates 

 all fall into the set Not-Class n, they are to be withdrawn 

 from the election, and their heaps set on one side as 



