THE TRANSFERABLE VOTE IN ELECTIONS. IJS 



and "D" their share of votes, that is, the share of actual voting 

 papers, Gregory gives "A" that proportional share of the value 

 of each vote, which will secure him the quota, and distributes all 

 the actual votes "at their diminished value," to the several can- 

 didates marked as next preferences, and on the sub-parcels he 

 marks this diminished value, in our case two-thirds. He gives 

 " A " ^5m o^ three-fifths of the value of each vote, three- 

 fifths of 5,000 votes = 300 votes in value ; "C" gets 3,000 of these A 

 votes in a sub-parcel, marked as containing votes each of the 

 transfer value of two-fifths: — two-fifths of 3,000 votes =1,200 

 votes in value. "D" gets two-fifths of 2,000 votes = 8oo votes in. 

 value in a sub-parcel similarly marked with a transfer value of 

 two-fifths for each vote. "Transfer value" is defined as "that 

 portion of a vote which is unused." 



In the case supposed above (Section 13), where "D's" suu- 

 parcel gave him the quota, and a surplus of fifty votes, the future 

 value of two-fifths in each vote would be modified, as "D" would 

 retain what value he required from every vote he received to give 

 him his quota, and every vote would be passed on with its new 

 fractional value something less than two-fifths. 



Under the Johannesburg rules we suppose that "D" required 

 (Section 13) 750 votes to make up his quota, so he retained them, 

 and only the fifty last filed were taken out for further redistribution. 

 So, under the Gregory method, *' D " retains ^ or i5-i6ths 

 of the value of the votes in his sub-parcel. That value was, v.e 

 saw, two-fifths. "D" retains i5-i6ths of 2-5ths or 30-8oths of 

 each of these 800 votes, and all of "A's" votes that were in "D's" 

 sub-parcel, that is, Soo of them, are now marked with a value of 

 i-i6th of 2-5ths or 2-8oths= i-4oth, and at this value are redis- 

 tributed to the next available preferences. "A" used up 3-5ths 

 of the value of each vote, that is, 48-8oths, "C 'used up 30-8oths ; 

 the transfer value, that is, "the unused portion" of each of these 

 800 votes is now i-40th, and this is marked on each sub-parcel of 

 those that are redistributed. 



20. In the Senatorial elections we ha\e small constituencies 

 electing relatively large numbers of members, and so the quotas 

 are very small ; in the two smaller provinces in future elections 

 42 voters will have to elect eight members with a quota of five. 

 In such cases the loss of votes by the neglect of fractions becomes 

 a very set'iou> matter. To obviate this, provision has been made 

 to treat each voting paper as of the value of 100. Thus, in the 

 Transvaal, where 84 voters had to elect eight senators, instead of 



84 8,400 



the quota being (-1 = 10, we get [-i = 934- This 



8 + 1 84-1 



comes to the same thing as working out the division to two places 

 of decimals. Gregory's fractional system of distributing all sur- 

 pluses is also adopted in these elections. 

 We turn now to the elections. 



21. In the Cape Province Senatorial Election, igio, 132 voters 

 had to elect eight members from over twenty candidates. There 



