34 QUOTA IN PROPORTIONAL REPRESENTATION, II., 



R.S. TAS. 



Then we have 



51 43 ,. 



. X -4- ?/ = 4/ 



IdO KJO 



and 



49 57 



100 100^ 



whence 2x — 14: y = 600. 



Also X + y = 100. 



From these equations we find x = y = 50 ; i.e., the repre- 

 sentation of the parties is equal, and there is a deadlock 

 in the House, in spite of the 6 % majority which L haa 

 over S in the country. 



If I — s > 2a, we can see from (4) that x > 50, i.e., 

 the smaller party gets a majority of the seats. 



Thus, if the average strength of S in the districts in 

 which it has a majority is 51 %, and the average 

 strength of L in the districts in which it has 

 a majority is just over 57 %, S, the smaller party, will 

 get more seats than L, the larger party, and so the smaller 

 party will have a majority over the larger in the House, 

 although the larger has a majority of over 6 % above 

 the smaller in the country. 



75. J. R. Commons ("^) gives the following illustration 

 of a distribution of votes which would give the smaller 

 party the majority of seats. A country is divided into 

 40 districts, and in each of these 5500 electors vote. In 

 25 districts the smaller party obtains 2800 votes, and the 

 larger 2700 votes ; in 15 districts, the smaller party obtains 

 2000 votes and the larger 3000 votes. The votes polled 

 are, then : 



Smaller Party. 



2800 in 25 districts 70,000 



2000 in 15 districts 30,000 



100,000 



Larger Party. 



2700 in 25 districts 67,500 



3500 in 15 districts 52,500 



120,000 



(Vi^ Proporfioual Rrvi'cxi'ufatlon, 2n(l edition (New Yoi-k. 1011), pp. 

 48-49. 



