BY E. L. PIESSE, B.SC, LL.B. 59 



the ends of two vertical broken lines are joined by a con- 

 tinuous line the broken line coincides with the continuous 

 line ; and for the strengths corresponding to these coinciding 

 lines, each quota gives the correct representation of the 

 parties. Where there is a horizontal broken line there 

 may be disproportionate representation. 



12. As an example consider, in the six-member constitu- 

 ency, the case of party A having 14 %, party B 86 %, of 

 the votes. Party A should have one member, party B 

 five members. If the Droop quota (14^%) is used, party 

 A will not obtain a member, and party B will get all six 

 members. If the Hare quota (16|%) is used, six candi- 

 dates of party B may each obtain more than 14 % of the 

 votes, and the one candidate (or the last unexcluded 

 candidate) of party .4 having only 14 % must be excluded, 

 and the six candidates of party B will be elected. 



13. As another example consider, again in the six-mem- 

 ber constituency, the case of party .4 having 40 %, party 

 B 60 %, of the votes. Using the Hare quota, suppose 

 that three candidates of party B have been elected (thus 

 absorbing 50 % of the votes), and that four candidates 

 are left, one of party B with 10 %, and three of party A, 

 each with more than 10 % (and having 40 % between 

 them). The remaining B candidate must be excluded, 

 and the three A candidates elected; so that A, with only 

 40 % of the votes will obtain half the members, instead 

 of two, the number to which it is entitled. With strengths 

 of 40 % and 60 % this is not possible if the Droop quota 

 is used; although the graph shows that with A 42 %, 

 the Droop quota would give only two members, instead 

 of the three to which .4 is entitled. 



14. It is to be noted that with the Hare quota the dis- 

 proportionate representation is due to the possibility of one 

 or more candidates being elected with less than the quota. 

 The occurrence of disproportionate representation depends, 

 therefore, on the distribution of votes among the unex- 

 cluded candidates when the last ssat is filled ; and the dis- 

 tribution may be such that no error can occur. With the 

 Droop quota, on the other hand, no candidate (on the-, 

 assumptions made) can be elected with less than the quota,, 

 and the error is due to the quota itself; and when the 

 parties have the appropriate strengths (for instance, 14 % 

 and 86 % in the example in § 12), it is certain that there 

 will be an error. 



15. Considering the matter in symbols, let m be the 

 number of members to be elected ; and assume that thQ 



