662 METHODS FOR COUNTING IN ELECTIONS. 



{d) That any section of voters large enough to give Hare's 

 quota of votes can secure a representative, so that the 

 elected representative body faithfully and exactly 

 represents all the voters. 



5. The Quota. — The quota with a majority system of 

 counting must be such a number (that all the members can 

 obtain, and such that, when they do so, the remainder is less than 

 a quota. We have seen that Droop's quota is the smallest 



N 

 possible. Hare's quota — is the largest possible (juota that can 



u N 



be used, for if vou add but one unit to — you get such a mmi- 



ber that n members cannot each receive. If there are 10,000 

 voters, and ten members, Hare's quota is 1,000. If you add a 

 single unit to it you get 1,001, a number which iten members 

 cannot each get from 10,000 voters. The advantages of using 

 it Hare secured, by giving the voters the privilege of marking 

 on their ballot papers in the order of their preference, as many 

 of the candidates as they chose. Hare gave the voter thus not only 

 a second choice at another election, as the second ballot does, but 

 as many choices as he chooses to mark. So that, if the candi- 

 date marked i cannot be elected by his vote, there is a chance 

 given that it may help the election of the candidate marked 2, 

 and so on successively. In this way every single vote can become 

 effective, in securing representation. 



The vote is equal h' effective for election and for 

 representation whether it is used as a first choice vote 

 or a second choice vote, and so on. but we must re- 

 member that the degree of preference it expresses is greater 

 if it is used as a first choice vote than if it is used as a second 

 choice vote, and still greater than if it is used as a third choice 

 vote or one of lower grade. 



6. Necessity of Counting as r.rany First Choices as Possible, 

 and Treating alike each Grade of Choice on all Ballot Papers. — 

 Hence, when a voter has expressed these grades of preference, 

 we can only carry out his wishes if we use as many first choices 

 as we possibly can, and so with each successive grade ; this we 

 can do, of course, better by the use of the largest possible quota, 

 which we have seen is Hare's quota. Droop's quota, admir- 

 able for counting votes in all cases, is able in elections by the 

 single non-transferable vote, to point out the members most pre- 

 ferred by the voters. But it entirely fails to do so where votes 

 can be transferred and where dift'erent degrees of preference are 

 expressed by different grades of votes, as is the case with the 

 transferable vote. 



Mr. Humphreys* points out the necessity of using as many 

 first choices as possible, and refers to this as " the principle 

 adhered to throughout the regulations of giving effect to the 



* Report on the Municipal Elections held at Pretoria and Johannesburg; 

 on 27th October, 1909, page 17, paragrapli 52. 



