BY E. L. PIESSE, B.SC, LL.B. 55 



the instance just given, the Droop quota (601 votes) has 

 more votes than each of six other candidates can obtain, 

 and therefore he has sufi&cient votes to entitle him to elec- 

 tion. Even if the Hare quota is used, any candidate who 

 obtains the Droop quota must be elected, and a candidate 

 who obtains the Hare quota receives an excess of votes 

 which are not really required by him, and which are there- 

 fore wasted. Hence it is clear that considering an election 

 as a contest between candidates the Droop quota is to be 

 preferred to the Hare quota. (^^) 



(") See Douglas, Piesse, and Birchall, (10), p. 4, where the following 

 passage is quoted fi-om Propurtional Reprcsrnfation in Large Con- 

 stituencies by Walter Baily (London, Ridgway, 1872) : — 



" We have still to consider what is the sufficient number of votes to be 

 retained for each candidate. The rule in use in Denmark (and adopted by 

 Mr. Hare, for finding this num^ier, which is called the quota), is to divide 

 the number of votes by the number of members to be elected. This is 

 simple, but still it is wrong. For example, if we ap])ly Mr, Hare's plan to 

 an election of two members, in which lUO votes are given — 70 for A first, 

 and then B, and 30 for r*— we should obtain the quota by dividing 100 by 

 2 ; and then retaining this quota of 50 votes for A^ we should hand over 

 20 votes to B \ and the votes would then stand, ^1 50, C 30, B 20, and 

 therefore we should have A and /^'elected. And yet it is clear that, as 70 

 ia more than twice 30. A and B should have been the candidates elected. 



**The number of votes to be retained for a candidate must be enough to 

 make his election certain, whatever combination may be made of the other 

 votes given in the election. The smallest number which will suffice for 

 this is the true quota ; all votf^s retained beyond this number are wasted. 

 There is no difficulty in finding this number. Suppose that two members 

 ha"e to be elected, we must retain for a candidate votes enough to insure 

 his being one of the first two, and this we shall do if we retain for him just 

 over a third of the whole niimber of votes given. It is impossible for three 

 persons each to have mf»re than one-third of the votes, so that any candi- 

 date who has more than one-third by ever so little is certain to be one of 

 the first two, in whatever way the rest of the votes may be distributed. 

 In the same way, we see that if five members have to be elected, a candi- 

 date who has more than one-sixth of the votes will certainly be one of the 

 first five, and therefore elected ; and so for any other number of members. 

 The rule, then, for finding the true quota is this : Divide the number of 

 votes by the number just above that of the members to be elected, and take 

 as a quota the number just above the quotient. 



" In the example given above, the true quota just exceeds one-third of 

 100. It is therefore 34. The 70 votes given to A^ B, will then be divided 

 into 34 for A, 34 for B, and 2 over. C has only 30 votes ; and the result 

 is that A and B are elected, and it is clear they should be. 



'* It will be obsei'ved that some votes are wasted. This must needs be, 

 whatever mode of election is adopted. It a constituency has only one 

 member, a candidate who gets a bare majority will be elected, and it will 

 be of no moment whether the remaining votes ace for him or against him. 

 All except tlie bare majority can have no effisct upon the deletion, and may 

 be consideied as wasted. I3ut as the number of members is increased, the 

 unavoidable waste is diminished. With five members the effective votes 

 for each will just exceed one-sixth, and therefore the waste votes will just 

 fall short of the remaining sixth ; in fact, the unavoidable waste will always 

 just fall short of the true quota." 



