18 QUOTA IN PEOPORTIONAL REPRESENTATION, II., 



R.S. TAS. 



there are I seats left, these seats will be distributed 

 according to the I smallest of these numbers, or according 

 to the I largest of the numbers — 



X +1.' X ^ 2 r i- i' r + 2 ' z + 1 



If we notice that the numbers — 



f^ i\ ^^ iL. V, (I, i, >% . . /•, 



1 '2 3 • • X 1 2 ' • r 1 z • • ' 



each greater than those that follow in the same series, 

 may be considered as corresponding to the seats already 

 allotted, we are led to the rule of D'Hondt, of which the 

 statement is the same as the rule of least squares, with 

 the substitution of the consecutive integers 1, 2 3, 4 .. as 

 divisors in place of the odd integers 1, 2, 3, ... 



58. If we consider only negative errors {i.e., errors for 

 electors who are under-represented), and limit ourselves to 

 cases in which the parties have at least X, 7, Z ... members, 

 negative errors will occur for such of the lists as do not 

 get any more seats, and we have therefore to choose for 

 the allotment of the remaining seats the smallest of the 

 numbers 



We must choose then the smallest of the numbers —rp/pQ 

 (fee., or the largest of the numbers rp/p, &c., for the 

 remaining seats. This is the rule of the largest fractions. 

 This method, M. Sainte-Lague points out, is not to be 

 confused with the rule of the largest remainders^ in which 

 the remaining seats are allotted according to the largest 

 of the remainders z-^^, /;^ . . . 



59. Finally, the rtde of l^quer results from making as 

 small as possible the difference between the largest positive 

 error and the largest negative error. 



