62 QUOTA IN PROPORTIONAL REPRESENTATION, 



18. It is to be noted that when the Droop quota gives 

 disproportionate representation, it is the larger party that 

 is over-represented; with the Hare quota it is equally 

 likely that the larger party will be under-represented as 

 that it will be over-represented. 



19. From (3) and (4) we get the following results: — 

 In a six-member constituency, disproportionate repre- 

 sentation may occur with the Hare quota for a range of 

 46 % of all the possible strengths of a party ; with the 

 Droop quota it is certain to occur with a range of 21 %. 



In a seven-member constituency, disproportionate repre- 

 sentation may occur with the Hare quota for a range of 

 52 % ; with the Droop quota it is certain to occur with a 

 range of 19 %. 



20. From Fig. 1 we can see what will be the representa- 

 tion for the important cases of the larger party between 

 50 % and 60 %. 



In the six-member district, the larger party is not 

 entitled to four members until its strength exceeds 58J % ; 

 although, in the interests of party government, it might 

 be justifiable to say that the larger party shall have four 

 members even if its strength is only just over 50 %. The 

 figure shows that the Hare quota may give the larger party 

 four members if its strength exceeds 53^ % ; also that the 

 Hare quota may fail to give more than three members even 

 if the strength exceeds 58^ %. The Droop quota is certain 

 to give four members if the strength of the larger party 

 lies between 57^% and 58J%; otherwise no anomalies 

 are possible with this quota. {^^') 



In the seven-member district, the larger party is entitled 

 to four members as soon as its strength exceeds 50 %. 

 The figure shows that the Hare quota may give only 

 three members if the strength lies between 50 % and 54# %, 

 and that it may give five members if the strength exceeds 

 59J %. No anomalies are possible with the Droop quota. 



21. On the whole, then, the Droop quota seems to be pre- 

 ferable in a two-party contest; but neither the Hare nor 

 the Droop quota is quite S9,tisfactory. In fact a single 

 transferable-vote system subordinates the party to the 

 candidates, and in essence is not a system of proportional 

 representation at all ; as contrasted with list systems which 

 subordinate the candidate to the party and have for their 



('*•) This would have occurred in the district of Franklin at the General 

 Election of 30th April, 1912, if the Liberal party had held during the 

 transfers of the scrutiny the first choices which its candidates obtained. 

 The strength of the Liberal party, based on the first choices, was 57'3°/o, 

 and the strength of the Labour party was 42"7°/o. 



