•68 QUOTA IN PROPORTIONAL REPRESENTATION, 



through the nearest node of the lattice. The solution is 

 therefore given by the trilinear coordinates of the nearest 

 node. If the sum of the remainders is 1, Z is in a triangle 

 similarly situated to ABC, and the one unallotted seat 

 goes to the largBst remainder ; if the sum of the remainders 

 is 2, 7 is in a triangle not similarly situated to ABC, and 

 the two unallotted seats go to the two largest remainders, 



33. The solution is therefore the same as that given by 

 the rule-of -three method, with the condition, in the case 

 of remainders, that if there is one unallotted seat it goes 

 to the party having the largest remainder, if two they go 

 to the two parties having the largest remainders. Our 

 discussion shows that the rule-of-three method, with this 

 condition, gives the correct result if the apportionment is 

 considered ideal when the differences between p and p , 

 q and q' , r and r' , are as small aa possible. 



34. The following example for a 10-member constitu- 

 ency illustrates the solution : — 



Party A 13,000 votes. 



Party B 10,500 votes. 



Party C 6,500 votes. 



Total votes ... 30,000 



The rule-of-three method gives:- — 



Party A 4 electoral units; remainder, 1000 



Party B 3 electoral units; remainder, 1500 



Party C 2 electoral units; remainder, 500 



With the condition that the unallotted seat goes to the 

 party having the largest remainder, the allotment is : 

 A, 4 members ; -B, 4< ; C, 2. The point J of ¥ig. 3 is the 

 position of the ideal point for this case; and the nearest 

 node is (4, 4 2). 



35. The solution gives no guidance where remainders are 

 equal. In such cases the solution given by the next method 

 shows that the unallotted seat or seats should go to the 

 largest party or parties. 



36. A second method of discussing the problem is to 

 give our attention to the proportion between votes and 

 seats in each party instead of (as in the first discussion) 

 to the differences between the actual and the assumed 

 strengths of the parties. 



Kegarded thus, the allotment may be considered ideal if 

 the number of votes to a member is as nearly as possible 



