Proportional Representation: A Study in Methods of Election Part 39

The next largest surplus, that of B, viz. 366, is then transferred, the operations being similar to those described in the transfer of E's surplus. a.s.sume that there are no unexhausted papers. The new value is therefore 366 / 13 or 28. The surplus is distributed according to next preferences, as follows:

A = (7 x 28) = 196 C = (6 x 28) = 168 Value lost owing to neglect of fractions 2 ---- Total ... 366

_Reg XIV. (5)._

G's surplus has now to be transferred, only the sub-parcel last transferred being re-examined. The details are as follows:--

Value of G's surplus 96 No. of papers in sub-parcel 10 Value of each paper therein 53 No. of unexhausted papers 10 Value of unexhausted papers 530

New value of each paper transferred = 96/10 = 9

The result of the distribution is shown on the result sheet, five papers of the value of nine each being transferred to A, and five of the same value to O.

_Reg. XV. (1)._

There being no further surplus, the candidate lowest on the poll has now to be excluded. D and P both have 200.

_Reg. XIX._

The returning officer casts lots, and P is chosen to be excluded.

_Reg. XV. (1)._

Being original votes the two papers are transferred at the value of 100 each, as shown in the result sheet, 100 going to L and 100 to N. D, now being lowest, is then excluded in the same way, 100 going to H and 100 to J, all transfers being made to the next preference as marked by the elector.

O now being lowest with 345, is next excluded.

_Reg. XV. (2)._

300 being the value of original votes, the three corresponding papers are transferred at the value of 100 each to K.

_Reg. XV. (3)._

45 being the value of transferred votes, the five corresponding papers are transferred at the value of 9 each to N.

M is then excluded; his papers represent original votes and are transferred to F. J is then excluded; of the 500 credited to him, 400 come from original and 100 from transferred papers, but the value of the latter being 100, all five papers are transferred at that value, 300 going to I and 200 to H.

A is then excluded, the value of his votes being as follows:--

Original 300 Transferred 196 " 45

The 300 original go to L.

The 196 transferred representing 7 papers of the value of 28 each, and the 45 representing 5 papers of the value of 9 each, all go to N.

C is then excluded, the value of his votes being as follows:--

Original 400 Transferred 168

The original go 300 to K and 100 to I, and the transferred go 84 to L and 84 to H.

H, I, K, and L now exceed the quota, and are declared elected. Seven seats are now filled.

_Reg. XIX._

I and K now both have a surplus of 66, which surpluses have to be transferred. I having had 600 from original votes, and K 400, K's surplus is first distributed.

_Reg. XIV. (5)._

The last sub-parcel of the value of 300 is dealt with, and the whole surplus 66 goes to F, he being the next preference on all three papers.

F then has the quota and is declared elected. The election is now completed, the full details being shown on the accompanying result sheet.

RESULT SHEET Number of Votes 84 Number of Members to Elect 8 8,400 Value of Votes 8,400 Quota ----- + 1 = 934 9

Column headings: 1: Names of Candidates 2: Value of Votes at 1st Count.

3: Distribution of E's Surplus.

4: Result.

5: Distribution of B's Surplus.

6: Result.

7: Distribution of G's Surplus.

8: Result.

9: Distribution of P's and D's Votes.

10: Result.

11: Distribution of O's and M's Votes.

12: Result.

13: Distribution of J's and A's Votes.

14: Result.

15: Distribution of C's Votes.

16: Result.

17: Distribution of K's Surplus.

18: Result. (E: Elected, NE: Not elected)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 A 300 300+196=496+45=451 541 541-541 -- -- -- B 1,300 1,300-366=934 934 934 934 934 934 934 E C 400 400+168=568 568 568 568 568-568 -- -- D 200 200 200 200-200 -- -- -- -- -- E 1,900-966=934 934 934 934 934 934 934 934 E F 500 500 500 500 500+400=900 900 900+66=966 E G 500+530=1,030 1,030-96=934 934 934 934 934 934 E H 300+265= 565 565 565+100=665 665+200=865 +84= 949 949 E I 600 600 600 600 600 600+300=900+100=1,000 1,000 E J 400 400 400 400+100=500 500-500 -- -- - K 400 400 400 400 400+300=700 700+300=1,000-66=934 E L 300+159= 459 459 459+100=559 -- 559+300=859 +84= 943 934 E M 400 400 400 400 400 400-400 -- -- -- N 400 400 400 400+100=500 +45=545+241=786 786 786NE O 300 300 300+45=345 345-345 -- -- -- -- P 200 200 200 200-200 -- -- -- -- -- Value of exhausted papers

Loss of value owing to neglect of fractions +12 = 12 +2= 14 +6= 20 -- 20 - 20 -- 20 -- 20 -- 20

Totals 8,400 8,400 8,400 8,400 8,400 8,400 8,400 8,400 8,400

[Footnote 1: The fact that a voter has not marked every preference correctly does not invalidate the whole of his preferences. His paper is only treated as exhausted when the wrongly marked preference is reached.

The following are examples:--

{ A 1 { A 1 { B 2 { B 2 (1) { C 3 (2) { C 3 { D 3 { D 5 { E 4 { E 6 { F -

In case (1) the preferences for A and B would be valid. If the third preference were reached the paper would be treated as exhausted, as it would be impossible to say for which candidate the voter really intended to give his third preference. In case (2) the preferences for A, B and C would be valid, but not the later ones, whether D had been elected or excluded or was still a continuing candidate. It is possible that the voter meant to give a fourth preference for some other candidate, _e.g._ F, but omitted to do so. It would not be possible to treat 5 as being meant to be 4.]

[Footnote 2: In small elections certain difficulties arise which are not present in the case of large elections.