64 



QUOTA IN PEOPORTIONAL REPRESENTATION, 



electoral unit, that there are two or more remainders; and,, 

 accordingly, in order to complete the apportionment it will 

 be necessary to allot one or more seats to remainders less 

 than the electoral unit. We have then to consider how 

 this allotment of seats to remainders is to be effected so as 

 to give as nearly as may be an equality of representation 

 between the various parties. 



•U. The following example illustrates the problem. 

 Assume that 10 seats are to be allotted among three 

 part^'es. A, B, C, whose strengths are as follows: — 



Party A 16,000 votes 

 Party B 4,000 votes 

 Party C 10,000 votes 



Total votes 30,000 



The electoral unit is obtained by dividing 30,000, the 

 total of all the votes, by 10, the number of seats for the 

 constituency; it is therefore 3000. 



The result of dividing the strength of each party by 

 the electoral unit is — 



Party A 5 electoral units; remainder, 1000. 

 Party B 1 electoral unit; remainder, 1000. 

 Party C 3 electoral units; remainder, 1000. 



Party A, then, must have at least five members; party 

 B, at least one; party C, at least three; but which party is 

 to get the remaining seat ? If party A gets it, each 2666 

 votes polled for that party return a member; each 3333 

 votes polled for party C return a member; but there is 

 only one member for the 4000 votes of party B. If party 

 B gets the remaining seat, the corresponding numbers will 

 be: party A^ 3200 votes to a member; party B, 2000; 

 party C, 3333. If party C gets the remaining seat, the 

 numbers will be: party A, 3200 votes to a member; party 

 B, 4000; party C, 2500. 



Which is the nearer approach ^o electoral equality 

 between the supporters of the various lists ? Probably the 

 first distribution, in which the larger party is favoured 

 in a case of doubt; but it is clear that the apportionment 

 of seats may often present difficulties of which the solu- 

 tion is not at once obvious to common sense. 



25. To examine the matter more accurately, we shall 

 use the following notation : — 



m, the number of members to be elected by the con- 

 stituency. 



