72 



QUOTA IN PROPORTIONAL REPRESENTATION, 



ideal when the deviation from equality in this respect is 

 as small as possible for each vote ; a condition expressible in 

 the form that 



s« (f _ ^ + -y + ^ v 



P p -j- g + ry 



or 



(p'-py 



(11) 



shall be a minimum. 



As in the second method, the analysis gives us for the 

 zero value of (11) the ideal point; and for values greater 

 than zero an ellipsoid gradually expanding from the ideal 

 point. As before, we project from the ideal point to 

 obtain a circle, and the shape of the projected triangle is 

 given by — 



.^=S^-_^ 



P P 



p 



V 



c 



P 



9 



V 



> 



(12) 



The properties of this triangle can be investigated in 

 much the same way as before, and will be found to be 

 similar to those of the triangle of the second method. 



Fig. 5. 



Fig 5 is drawn for the case of 5\, = 5J, y^ = IJ, Zq = 3J. 

 Comparing this with Fig. 4, which represents this case 

 according to the second method, we see that the result is 

 much the same, but that the range for which |3 -y can be 



less than half the electoral unit, without the largest party 

 getting the seat, is rather less than with the second method. 



