BY E. L. PIESSE, B.SC, LL.B. 57 



of the two parties. Thus, in a contest in a six-member 

 constituency between two parties, one of which polls 

 72 % of the votes, the other 28%, the first party 

 has five Droop quotas, and therefore returns five 

 members; while the second party, having less than two 

 quotas, returns only one member. But the fairest repre- 

 sentation (see § 52) in this case would be four members for 

 the first party, and two for the second. (^^) 



10. The comparison of the merits of the two quotas in 

 a contest between parties therefore involves an examination 

 of the possible number of cases in which each can give 

 disproportionate representation . 



In making this examination it must be assumed that 

 there is no cross-voting, and that each voter votes for all 

 the candidates of his party. 



11. Fig. 1 shows the result of the comparison in a con- 

 test between two parties in a six-member constituency 

 and in a seven-member constituency. 



In each case the continuous sloping line 00' represents 

 the strength of the parties for all values from % 

 to 100 % of the voters. The strength of party A is repre- 

 sented by the distance from OX, and the strength of party 

 B by the distance from O'Y . 



The continuous stepped line shows what is the 

 best possible apportionment of members between the two 

 parties for each strength of each party. This apportion- 

 ment is obtained by dividing the strength of each party by 

 the Hare quota, and, in the case of remainders, giving the 

 last member to the party having the larger remainder 

 (see § 52). Thus, in the case of the six-member constit- 

 uency, if party .4 has just over 8J %, party B just under 

 91| %, of all the votes, on dividing by the Hare quota 

 (which is 16J% of the total votes), A will have the 

 larger remainder, and should therefore have one member. 

 As the strength of A increases, it does not become entitled 

 to two members until its strength reaches 25 %; from 

 25 % to 41§ % it is entitled to two members; and so on. 



The broken lines show the representation which may be 

 produced by the Hare quota and the Droop quota. Where 



<■") Mr. J. W. McCay, in one of a series of articles on Piopf)rtional 

 Voting published some years ago in the Melbourne "Age," gave the fol- 

 lowing instance of the Droop quota as " a successful practical joker " :— 

 In a six-member constituency, let there be 500 voters for party J, 199 for 

 party B ; total 699 voters. The quota is 100, and A gets 5 seats, B 1 

 seat. But let A poll one more vote, making the total of tlio voter* 700. 

 The D.oop quota is now 101, and party A now gets only 4 seats. 



