Proportional Representation: A Study in Methods of Election Part 38

B. The member votes--

(_a_) By placing the figure "1" opposite the name of the candidate he likes best.

He is also invited to place

(_b_) The figure "2" opposite the name of his second choice.

(_c_) The figure "3" opposite the name of his third choice, and so on, numbering as many candidates as he pleases in order of his preference.

The number of preferences is not necessarily restricted to the number of vacancies.

_N.B._--The vote will be spoilt if the figure "1" is placed opposite the name of more than one candidate.

[A number is printed on the back of the ballot paper corresponding with that on the counterfoil.]

ANNEXURE C

ILl.u.s.tRATIVE ELECTION

_Example of an Election conducted on the system of the single transferable vote in accordance with the preceding regulations_

_Reg. IX._

a.s.suming that there are eight members to be elected, sixteen candidates, and eighty-four electors.

The valid ballot papers are arranged in separate parcels according to the first preference recorded for each candidate, and the papers in each parcel counted. Let it be a.s.sumed that the result is as follows:--

A 3 J 4 B 13 K 4 C 4 L 3 D 2 M 4 E 19 N 4 F 5 O 3 G 5 P 2 H 3 -- I 6 84

_Reg. X._

Each valid ballot paper is deemed to be of the value of one hundred, and the values of the votes obtained by the respective candidates are as shown in the first column of the result sheet.

_Reg. XI._

The value of all the papers are added together and the total, 8400, is divided by nine (_i.e._ the number which exceeds by one the number of vacancies to be filled), and 934 (_i.e._ the quotient, 933, increased by one) is the number sufficient to secure the return of a member, and is called the quota. The operation may be shown thus:-- Quota = 8400/9 + 1 = 933 + 1 = 934.

_Reg. XIII_. (1).]

The candidates B and E, the values of whose votes exceed the quota, are declared elected.

_Reg. XIII_. (3). _Transfer of surplus_.]

As the values of the papers in the parcels of B and E exceed the quota, the surplus of each candidate must be transferred. B's surplus is 366 (_i.e._ 1300 less 934), and E's surplus is 966 (_i.e._ 1900 less 934).

_Reg. XIV_. (2).]

The largest surplus, that of E, is dealt with first.

_Reg. XIV_. (4)(_a_).]

The surplus arises from original votes, and therefore the whole of E's papers are divided into sub-parcels according to the next preferences recorded thereon, a separate parcel of the exhausted papers being also made. Let it be a.s.sumed that the result is as follows:

G is marked as next available preference on 10 papers.

H " " 5 "

L " " 3 "

-- Total of unexhausted papers 18 No. of exhausted papers 1 -- Total of papers 19

_Reg. XIV_. (4)(_b_).]

The values of the papers in the sub-parcels are as follows:--

G 1,000 H 500 L 300 ----- Total value of unexhausted papers 1,800 Value of exhausted papers 100 ----- Total value 1,900

_Reg. XIV_. (4)(_d_).]

The value of the unexhausted papers is 1800, and is greater than the surplus. This surplus is therefore transferred as follows:--All the papers unexhausted are transferred, but at a reduced value, which is ascertained by dividing the surplus by the number of unexhausted papers.

The reduced value of all the unexhausted papers, when added together, with the addition of any value lost as the result of the neglect of fractions, equals the surplus. In this case the new value of each paper transferred is 966 (the surplus)/ 18 (the number of unexhausted papers) = 53, the residue of the value, 47, being required by E for the purpose of const.i.tuting his quota.

The values of the sub-parcels transferred are:--

G = 530 (_i.e._ 10 papers at the value of 53) H = 265 (_i.e._ 5 " " ) L = 159 (_i.e._ 3 " " )

These operations can be shown on a transfer sheet as follows:

TRANSFER SHEET

Value of surplus (E's) to be transferred 966 No. of papers in E's parcel 19 Value of each paper in parcel 100 No. of unexhausted papers 18 Value of unexhausted papers 1,800

New value of each paper transferred =

Surplus 966 / No. of unexhausted papers 18 = 53

Names of Candidates marked as the No. of Papers Value of Sub-parcel next available Preference. to be to be Transferred Transferred G 10 530 H 5 265 L 3 159

Totals 18 954

No. of exhausted papers 1 --- Loss of value owing to neglect of fractions -- 12

Totals 19 966

The values of the sub-parcels are added to the values of the votes already credited to the candidates G, H, L. This operation is shown on the result sheet.

As a result of this operation G's total is brought above the quota, and he is declared elected.

_Reg. XIV_. (2).]