PROCEEDINGS OF SECTION G. 495 



in the quota itself. The results of an investigation carried out 

 on lines suggested by Mr. Piesse, of Tasmania, were as follows: — 

 Suppose there is a two-party contest for the representation of 

 a constituency returning m members: the number of members 

 being reduced to i?i + 1. 



(a) With the Hare quota disproportionate representation 

 may occur through a percentage range of H [m - ^^ + ^ 

 + 1 + . + ^L_ )] where H = li" , i.e., the Hare 



quota. 

 (6) With the Droop quota disproportionate representation 

 must occur within a percentage range of ^^^ if m is 

 even, or '" if m is odd. 



Party List. 



Having now considered the ' ' transferable vote ' ' method of 

 proportional representation, attention must be directed to the other 

 method, i.e., the " party list." The distinctive feature of this 

 system is that it applies the proportional principle to parties, and 

 not to candidates. This system has had its greatest practical appli- 

 cations in countries like Belgium and Switzerland, where there are 

 large numbers of parties. But there is no reason why it should be 

 so restricted in its application. Its best features could easily be 

 utilized in a contest between two parties only, provided it was 

 operated in a constituency returning several members. 



Party-list System. 

 In operating the party-list system, the problem which has to be 

 solved is that of allotting a certain number of seats between differ- 

 ent parties, as nearly as possible in the proportion of the votes 

 polled. A number is taken which we will call the " unit of repre- 

 sentation," and divided into the several votes polled, and the 

 quotient gives the number of members to which the party is 

 entitled. When (as nearly always happens) the sum of the 

 quotients does not exactly equal the number of representatives, the 

 seats to be still allotted are awarded to the parties with the largest 

 remainders. Some injustice is done to the parties with smaller 

 remainders, but this seems the fairest arrangement that can be 

 devised in practice, and one to which no reasonable person could 

 take exception. This in essence is what is known as the " rule of 

 three " method. 



Suppose that in a constituency where A votes have been polled, 

 there are 7?i members to be elected . The ' ' unit of representation ' ' 

 may be either taken as ^- (the Hare quota) or -^^ + 1 (the 

 Droop quota). 



