Using first the 600 A votes, we are left with 5400 to make up out of the remaining heaps.

1. Suppose B and C have received the quota. The 5400 can be taken from their heaps exclusively, for in their two heaps are 7200 votes; the proportion to be taken from each heap is therefore 5400 out of 7200, which is three quarters. Thus we make up A's number thus:--

A votes 600 Three-quarters of 2,700 AB " 2,025 Three-quarters of 4,500 AC " 3,375 ----- 6,000

And transfer the remainder (the AB and AC votes transferred being those stamped with the lowest numbers).

2. Suppose B and X have received the quota. Their two heaps amount to 2750 votes. Using these up, there remain 2650 votes to be made up out of the AC, AY, and AZ heaps. These three heaps together contain 5300 votes; and the proportion to be taken from each heap is 2650 out of 5300, or half. Thus A's number is made up as follows:--

A votes 600 AB " 2,700 AX " 50 Half of 4,500 AC " 2,250 Half of 200 AY " 100 Half of 600 AZ " 300 ----- 6,000

And the remaining votes of each of the three last cla.s.ses--being those stamped with the lowest numbers--will be transferred.

It will be observed that the element of chance is not wholly excluded, since the question, which papers out of the AC heap are transferred, is left to depend upon the order of drawing. To exclude chance wholly, these would have to be sorted into heaps according to the third name upon them, and an equal proportion taken from each heap. The figures in the first half of this paper are sufficient to show that such trouble would be wholly superfluous.

[Footnote 1: This Memorandum is published by permission of the Rt. Hon.

J. Parker Smith. Although written in 1884, the arguments still apply.

The method described in the second part of the paper has been adopted in the Munic.i.p.al Representation Bill (see Appendix VII.), but the method of application differs in detail.]

[Footnote 2: Quoted by Mr. (afterwards Earl) Lytton in his _Report on the Election of Representatives for the Rigsraad_.--House of Commons papers, 1864, vol. 61, p. 24 of No. 7.]

APPENDIX VII

THE SINGLE TRANSFERABLE VOTE

SCHEDULE TO MUNIc.i.p.aL REPRESENTATION BILL, 1910

THE FIRST SCHEDULE[1]

RULES FOB THE TRANSFER OF VOTES AND FOR ASCERTAINING THE RESULT OF THE POLL

_Arrangement of ballot papers._

1. After the ballot papers have been mixed, in accordance with the rules contained in the First Schedule to the Ballot Act, 1872, the returning officer shall draw out all ballot papers which he does not reject as invalid, and file in a separate parcel those on which the figure 1 is set opposite the name of the same candidate. The returning officer shall then count the number of papers in each parcel.

_Ascertainment of quota._

2. The returning officer shall then add together the numbers of the papers in all the parcels and divide the total by a number exceeding by one the number of vacancies to be filled, and the result increased by one, disregarding any fractional remainder, shall be the number of votes sufficient to secure the return of a candidate, herein called the "quota."

_Candidates with quota elected._

3. Any candidate whose parcel contains a number of papers equal to or greater than the quota shall be declared elected.

_Transfer of surplus votes_.] 4.--(1) If the number of candidates elected under the last rule shall not equal the number of vacancies, the returning officer shall as far as possible transfer from each elected candidate the votes (if any) in excess of the quota (herein called surplus votes) to the candidates indicated on the ballot papers as next in order of the voters' preference, excluding candidates already declared elected. The votes of the candidate having the largest number of votes shall first be dealt with, and the particular votes to be transferred shall be determined in accordance with the following regulations:--

(a) The returning officer shall arrange all the ballot papers in the parcel of the elected candidate on which votes capable of transfer are given by filing in a separate sub-parcel those on which a next preference is indicated for some one continuing candidate.

(b) The returning officer shall also make a separate sub-parcel of the ballot papers in the parcel on which the votes given are not capable of transfer.

(c) The returning officer shall count the ballot papers in each sub-parcel, and also the total of all the ballot papers containing votes capable of transfer.

(d) If the total number of votes capable of transfer is equal to or less than the surplus votes, the returning officer shall transfer all the votes capable of transfer.

(e) If the total number of votes capable of transfer is greater than the surplus votes, the returning officer shall transfer from each sub-parcel of votes capable of transfer the number of votes which bears the same proportion to the total of the sub-parcel as the number of surplus votes bears to the total of all the votes capable of transfer.

(f) The number of votes to be transferred from each sub-parcel under the preceding regulation shall be ascertained by multiplying the total of the sub-parcel by the number of surplus votes and dividing the result by the total number of votes capable of transfer. Fractional remainders shall be disregarded.

(g) The particular votes transferred from each sub-parcel shall be those last filed in the sub-parcel.

(2) The transfer of surplus votes shall be effected by making new sub-parcels of the ballot papers on which those votes are given, and adding those sub-parcels to the parcels (if any) of the candidates to whom the transfers are made, or, where any such candidate has as yet no parcel, a new parcel shall be formed for him from the papers transferred.

(3) All ballot papers in a parcel of an elected candidate not transferred under this rule shall be set aside as finally dealt with, and the votes given thereon shall thenceforth not be taken into account.

(4) If two or more parcels of elected candidates are equal in size, the returning officer shall decide which parcel he will first deal with under this rule.

(5) A transfer of votes under this rule shall not be made unless the surplus votes of the elected candidate, together with any other surplus votes not transferred, exceed the difference between the totals of the votes of the two continuing candidates lowest on the poll.

(6) This rule shall take effect subject to the provisions for filling the last vacancy herein-after contained, and if at any time it shall be possible to fill the last vacancy under those provisions, no further transfer under this rule shall be made.

_Result of transfer._

5. After the transfer of the surplus votes of an elected candidate, any candidate who shall, as a result of the transfer, obtain the quota of votes, shall be declared elected.

_Further transfer of surplus votes._

6.--(1) Unless and until the last vacancy shall have been filled under the provisions herein-after contained, if, after the transfers directed by Rule 4, there shall still remain a vacancy, and the votes of any elected candidate to whom a transfer has been made are in excess of the quota, the returning officer shall, as far as possible, take from the sub-parcel last transferred to that candidate a number of votes equal to the surplus.

(2) The particular votes to be taken shall be determined in accordance with the regulations given in Rule 4 hereof, in the same manner as if the votes included in the sub-parcel last transferred had been the only votes given to the candidate; the ballot papers so taken shall be added in separate sub-parcels to the parcels of the continuing candidates (if any) indicated thereon as next in order of the voters' preference, and the votes given thereon shall be transferred to those candidates accordingly. Where any such candidate has as yet no parcel, a new parcel shall be formed for him from the papers transferred.

(3) The remaining ballot papers in the parcel of the elected candidate (including the ballot papers taken from the parcel under Sub-Rule (1) on which the votes given are not capable of transfer) shall be set aside as finally dealt with, and the votes given thereon shall thenceforth not be taken into account.

(4) After any transfer of votes under this rule, any candidate who shall, as a result of the transfer, obtain the quota of votes shall be declared elected.

(5) The process directed by this rule shall be repeated until the last vacancy is filled, or until no candidate has any surplus votes, whichever shall first happen.

(6) If two or more parcels shall be equal in size, regard shall be had to the number of votes counted to each candidate under Rule 1, and the parcel of the candidate highest on that count shall first be dealt with, but if the numbers of votes on that count were equal, the returning officer shall decide which parcel he will first deal with under this rule.

(7) A transfer of votes under this rule shall not be made unless the surplus votes of the elected candidate, together with any other surplus votes not transferred, exceed the difference between the totals of the votes of the two continuing candidates lowest on the poll.

_Distribution of votes of lowest candidate_.

7.--(1) Unless and until the last vacancy shall have been filled under the provisions herein-after contained, if, after the transfers under the preceding rules, there shall still remain one or more vacancies, or, if no candidate shall have been declared elected under Rule 3, the returning officer shall exclude from the poll the candidate having the lowest number of votes, and shall distribute the votes capable of transfer on the ballot papers in his parcel among the continuing candidates next in order of the voters' preference. Any ballot papers in the parcel, on which votes not capable of transfer are given, shall be set aside as finally dealt with, and the votes given thereon shall thenceforth not be taken into account.

(2) If in any case the total of the votes of the two or more candidates lowest on the poll together with any surplus votes not transferred is less than the votes of the next highest candidate, the returning officer may in one operation exclude those candidates from the poll and distribute their votes in accordance with the foregoing provisions.

(3) After the distribution under this rule of votes capable of transfer, any candidate who has received the quota shall be declared elected.