METHODS FOR t"(,)UNTIiN(; IN ELECTIONS. 659 



The rules at present used divide the whole electorate not 

 into n, but into [ii -f- i) smaller sections, and thereby deprive the 

 additional section of any share whatever in the election of the 

 members ; and in the case of very many of the other ballot papers 

 which are used, fail to carry out the other voters' wishes as 

 they have marked them at the poll. They are thus altogether 

 incompatible with Hare's object, which was to make every 

 single vote equally effective, in securing representation. 



This is a very important matter, and I have to ask your 

 close attention while I demonstrate these facts to you by the 

 critical examination of the choices marked and used on the 

 ballot papers in two actual South .\frican elections, which, for- 

 tunately. I am able to show you. 



I. Object — To find I he mciiibrrs iiiosl preferred by all I he 

 voters — Ten General Principles. — In all elections the object is 

 to choose out the members most preferred by all the voters. 



(a) In all elections the getting of Droop's quota, one more 



vote than iV divided by ( ;; + i ) , secures the election 

 of a candidate ; and with the single non-transferable 

 vote the elected candidate is proved to be one of the 

 members most preferred Iw the voters, so far as the 

 expression of one choice shows their preference. 



(b) When votes can be transferred, election no longer 



proves that the elected candidate is one of the members 

 most preferred by tb.e voters. This can only be done, 

 by alloting to each member Hare's quota, .V dixided 

 by ;;. a larger number than that which elects the mem- 

 ber, and in this way onh' can we get Proportional Re- 

 presentation, that is the equal representation of every 

 voter by the member he most prefers. 



(c) When a voter expressed onlv one choice he indicated 



the candidate he most prefers. 



(d) If we give him the opportunity of expressing a second 



choice, that second choice may become equally effec- 

 tive as a vote, but it indicates a lower grade of pve- 

 ference than his first clioice did. 



(e) Each voter's vote, his Ijallot paper, is alike, and is 



entitled to similar treatment and to e(|ual considera- 

 tion, and the same i> true of each grade of choice; 

 Ijut a first choice must be used, if possible, before a 

 second choice, and so on grade by grade. 



(/) This is the case with votes and choices for the same 

 candidate, and also with those inr different candidates. 



(g) But where the voters have given expression to their 

 preferences for different candidates, we can find out 

 which are the candidates they most prefer only by 

 giving effect to their first choices to the greatest 

 possible extent before we make use of their second 

 choices, and so on downwards, grade by grade. 



(/;) All elections are over as soon as the member Avith the 

 fewest votes gets more than all the outstanding votes. 



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