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Proportional Representation by John H. Humphreys

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_Instructions to Members_

[_Printed below the List of Candidates on the Ballot Paper shown on
opposite page_

A. Each member has one vote, and one vote only.

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

_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.]



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

_Reg. IX._

Assuming 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 assumed 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 assumed 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 constituting 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:


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).]

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. Assume 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.

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

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

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.

(_a_) The quota becomes too large if calculated in the ordinary way.
Assume that 27 electors are to elect 8 candidates. Then the quota is
27/(8+1) + 1 = 4. But 8 x 4 = 32.

There are not enough quotas to go round and difficulties would arise.
The addition of 1 in the case of so small a number makes the quota
disproportionately big. For this reason it is advisable to treat each
paper as of the value of one hundred. In the case of the Transvaal the
quota instead of being 84/(8+1) + 1 = 10 will be 8400/(8+1) + 1 = 934.

(_b_) The disregard of fractions in the case of small numbers may mean
the waste of several votes. Take the following example:--

Seat to be filled, 8
Electors 25
Quota = 25/(8+1) + 1 = 3

First Count
A 10
B 3
C 3
E 2
F 1
G 1
H 1
I 1
J 1

A having 10 has a surplus of 7, which has to be distributed. According
to the usual rule A's 10 votes are examined and the surplus is
distributed in proportion to the next preferences. The preferences are
as follows:--

For B....... 5
" C....... 2
" F....... 1
" G....... 1
" H....... 1

Each of these numbers must be multiplied by 7/10, _i.e._ the surplus
over the number of unexhausted votes, and the following votes are

To B.......3-1/2
" C.......1-2/5
" F.......7/10
" G.......7/10
" H.......7/10

The fractions which are ignored amount to 3 votes, which are
consequently wasted. This difficulty is overcome by increasing the value
of the papers to one hundred, or in other words by working out the
results to two places of decimals.

(c) In a small election at the several stages there may be two or more
candidates at the bottom with an equal number of votes. Resort has to be
had to lot to decide which is to be eliminated. If the papers are raised
to the value of one hundred this difficulty is much less likely to occur
after the first count.]



The _Commission du Suffrage Universel_, a committee of the Chamber of
Deputies, made a careful comparison of the various Bills which had been
submitted to the Chamber for the purpose of securing the proportional
representation of the electors. The Commission in their report,[1] which
was issued in March 1907, recommended the adoption of the Bill, of which
a free translation is given below.

The essential features of this measure, which has received the support
of the leading advocates of proportional representation, are: (1) The
allotment of seats to lists in accordance with the d'Hondt, or Belgian
rule (Art. 8); (2) the use of the cumulative vote in determining the
relative position of candidates (Art. 6). The elector is given as many
votes as there are members to be elected, which he may cumulate upon any
one or distribute among several candidates. The elector is not
restricted in his choice of candidates to any one list.

_Text of the Bill_

(1) Members of the Chamber of Deputies shall be elected on the list
system (_scrutin de liste_) in accordance with the scheme of
proportional representation hereinafter stated. There shall be no
second ballot.

(2) Each department shall elect one deputy for every 75,000
inhabitants. A remainder of 25,000, or more, inhabitants shall be
reckoned as 75,000.

(3) A department shall form a single constituency, provided that where a
department would elect more than ten deputies, it shall be divided into
two or more constituencies, as determined by law hereafter.

(4) A "list" is constituted by a group of candidates who (after making
the declaration prescribed by Article 2 of the Law of 17 July 1889)
jointly appeal for the support of the electors.

A list shall not include a larger number of names than there are
deputies to be elected in the constituency, but it may contain a smaller
number. An independent candidate shall be reckoned as a distinct list.

(5) Each list shall be delivered at the prefecture at any time after the
commencement of the electoral period, and at the latest ten clear days
before polling day. It shall be registered and numbered at the
prefecture, and a receipt for it shall be given to each candidate.

The name of a candidate shall not be registered unless he has signed the
list. A list with more candidates than there are deputies to be elected
shall not be accepted for registration.

A candidate whose name appears on one list shall not be entered on
another unless he has notified the prefecture by writing under his hand,
duly attested, that he retires from the former list, in which case his
name shall be at once removed from the former list.

Twenty-four hours before the opening of the poll the prefect shall cause
each registered list with the number thereto given to be posted on the
doors of the polling station.

(6) An elector has as many votes as there are deputies to be elected in
his constituency.

He may give all or any of his votes to the same candidate.

The reports of the local returning officer at each polling station shall
state the number of votes obtained by each candidate. (7) A Central
Board (_Commission de recensement_) shall collect the reports of the
local returning officers, and ascertain the electoral total of each
list, and allot the seats among the lists in proportion thereto.

The electoral total of a list is the sum of the votes given to the
candidates whose names appear thereon.

(8) For the purpose of allotting the seats, each electoral total shall
be divided by the figures 1, 2, 3, 4, and so on up to the number of
vacancies, and as many of the resulting quotients as there are vacancies
shall be arranged in order of size, beginning with the largest. The
smallest of these quotients so arranged, corresponding to the last seat
to be filled, shall be used as the common divisor, and to every list
shall be allotted a number of deputies equal to the number of times
which its electoral total contains the common divisor.

(9) Within each list the seats shall be assigned to the candidates who
have the largest numbers of votes; in case of an equality of votes, the
eldest candidate shall be elected.

(10) If two or more lists have an equal right to a seat, it shall be
allotted as between the competing candidates to that one who has
received the greater number of votes, and if those votes are equal the
eldest candidate shall be elected.

(11) The unelected candidates of each list with the greatest number of
votes shall be classed as first, second, and third substitutes
(suppléants), and so on.

If any vacancy shall occur by death, resignation, or otherwise, the
substitutes shall be summoned in their classified order to fill the
places of the elected members of the list to which they are attached,
provided that at the time of summons they are in the enjoyment of their
political rights.

(12) If more than six months before the end of a Parliament, the
representation of a constituency is diminished by one-fourth and there
is no substitute who can be declared elected, bye-elections to fill the
vacant seats shall be held in that constituency. (13) The present law
shall extend to Algeria. Nothing in this law shall affect the
representation of the Colonies.

NOTE.--Since the introduction of this Bill several other proposals have
been considered by the _Commission du Suffrage Universel._ The draft
Bill proposed in the last report (March 1911) is not based so strictly
upon proportional principles as the measure given above.

The points of difference may be summarised as follows:--

(_a_) The use of the cumulative vote is retained (Art. 6), but there is
a change in the method of allotting seats to various lists (Art. 8). The
new method of allotment is as follows: an "electoral quotient" is found
by dividing the number of voters by the number of vacancies, and as many
seats are allotted to each list as the number of voters supporting a
list contains this quotient. Since each voter has as many votes as there
are seats to be filled, the number of voters supporting a list is
determined arbitrarily by dividing the total number of votes cast for
the list by the number of vacancies.

If there are any seats not allotted by this distribution they are
awarded to any list which obtains an absolute majority of the votes.
Should no party obtain an absolute majority, the remaining seats are
allotted to the various lists in accordance with the method described in
the succeeding Appendix. This method leads to the same distribution of
seats as the d'Hondt rule.

(b) The Bill recognises an important new principle in permitting
_apparentement des listes_. Parties may unite for the purpose of
presenting lists in combination, and the lists so presented are treated
for the purpose of the allotment of seats as if they emanated from one
party. This is an elastic form of the Belgian "cartel," allowing parties
to act together without loss of individuality. The seats won by any such
cartel are allotted to the various lists composing the cartel in
accordance with the second of the methods described in the previous

[Footnote 1: _Chambre des Deputés, Neuvième Legislature:_ 1907, No. 883.
See note as to further report, March 1911, at end of Bill.]



The special features of the following law are as follows:--

(1) The partial use of the cumulative vote in determining the relative
position of candidates (sec. 9).

(2) The allotment of seats to lists in accordance with the rule
formulated by Professor Hagenbach-Bischoff (sec. 13).

The provisions for bye-elections are contained in sections 17 to 20.

(1) The elector is supplied three days before the election with copies
of the various party lists; he is given as many votes as there are
members to be elected; he may strike out any names and insert others in
any of the lists supplied to him, or compose his own list; he may repeat
the name of the same candidate three times, but no more; but in no case
may the total number of names exceed the number of members to
be elected.

(2) The Hagenbach-Bischoff rule, like the d'Hondt rule, aims at finding
an electoral quotient which will allow all the seats to be allotted to
the different parties without remainder. In the former rule this is
found by trial. The following example explains its mechanism:--

Suppose, in an election for sixteen seats, five lists have obtained
votes as follows:--

List. Votes.
A 5,537
B 9,507
C 3,885
D 4,769
E 377
Total 24,075

The first quota is ascertained as prescribed in section 11. The number
of votes is divided by one more than the number of vacancies, and the
result is increased by one, thus:--

24075/(16+1) + 1 = 1417

It will be observed that this quota is identical with the Droop quota of
the single transferable vote system. The totals obtained by each list
are divided by this quota, as many representatives being allotted to
each list as the list contains the quota. Remainders are ignored.

Lists. Votes. Quota. Representatives.
A 5,537 ÷ 1,417 3
B 9,507 ÷ 1,417 6
C 3,885 ÷ 1,417 2
D 4,769 ÷ 1,417 3
E 377 ÷ 1,417 0
Total 14

Only fourteen out of sixteen seats have been allotted in this operation.
It is obvious that the quota is too large, and a smaller quota is
ascertained in the following way. The number of votes for each list is
divided by one more than the number of members already assigned to such
list, and the first seat still to be disposed of is allotted to that
list which has the largest quotient. The following table shows the

Lists. Votes. Quotient. Representatives.
A 5,537 ÷ 4 1,384 4
B 9,507 ÷ 7 1,358 6
C 3,885 ÷ 3 1,295 2
D 4,769 ÷ 4 1,192 3
E 377 ÷ 1 377 0
Total 15

The largest quotient is 1384, and this figure, which is taken as the new
quota, allows of the allotment of fifteen seats. There still remains one
seat to be disposed of, and the process just described is again
repeated, as shown in the following table:--

Lists. Votes. Quotient. Representatives.
A 5,537 ÷ 5 1,107 4
B 9,507 ÷ 7 1,358 7
C 3,885 ÷ 3 1,295 2
D 4,769 ÷ 4 1,192 3
E 377 ÷ 1 377 0

On this occasion all sixteen seats are allotted, the final quota being

The results obtained by the Hagenbach-Bischoff method are identical with
those obtained by the d'Hondt rule. The operations required in the
preceding example for the allotment of seats by the latter rule are as

List totals
divided by A B C D E
1 5,537 9,507 3,885 4,769 377
2 2,768 4,753 1,942 2,384 --
3 1,845 3,169 1,295 1,589 --
4 1,384 2,376 971 1,192 --
5 1,107 1,901 -- -- --
6 -- 1,684 -- -- --
7 -- 1,358 -- -- --

The sixteen highest quotients arranged in order of magnitude are:--

9,507 (List B) 2,376 (List B)
5,537 (List A) 1,942 (List C)
4,769 (List D) 1,901 (List B)
4,753 (List B) 1,845 (List A)
3,885 (List C) 1,589 (List D)
3,169 (List B) 1,584 (List B)
2,768 (List A) 1,384 (List A)
2,384 (List D) 1,358 (List B)

The lowest of these sixteen figures, viz. 1358, is the electoral
quotient, and agrees with the final quota furnished by the
Hagenbach-Bischoff rule. _Law for Elections to the Grand Council, on
the principle of Proportional Representation, 26 January 1905_

1. Nomination papers for the various electoral districts must be handed
in to the police department not later than three weeks before the day
fixed for the re-election of the Grand Council.

They may contain the names of one or more persons eligible for election,
provided that the total number of names in any nomination paper is not
greater than the number of members which the electoral district in
question is entitled to elect; any name may appear more than once, but
not more than three times.

2. Nomination papers for town districts must be signed by at least ten
qualified electors; those for country districts by at least three. An
elector may sign one, and only one, nomination paper, on each occasion,
in each electoral district.

When handing in the nomination paper the signatories thereto must
designate one of their number to attend to any necessary formalities
with the police department in connexion therewith.

3. The police department shall at once communicate with the candidates
nominated, and call upon them to declare within two days whether they
accept the candidature or not.

If the person nominated declines to stand for election his nomination
shall be cancelled.

4. No candidate may appear on more than one nomination paper. If
therefore any candidate be nominated in different electoral districts,
or on several nomination papers in the same district, the police
department shall, in informing him of the nominations, call upon him to
declare, within two days, under which nomination he wishes to stand, and
on receipt of his declaration shall strike his name off the other
nomination papers.

If the candidate makes no declaration within the time fixed, the police
department shall decide by lot under which nomination he shall stand.

5. The police department shall inform the representatives of the
nominators of the cancellings due to the refusal of the nominees to
accept nomination, or to the latter having been nominated more than
once, and shall allow the former a period of two days in which to make
further nominations. To these further nominations the declaration in
writing of the person nominated, accepting the candidature, must
be attached.

If this declaration is not attached, or if the proposed candidate
already appears on another nomination, the supplementary nomination
shall be rejected.

6. The final (definitive) nomination papers thus obtained shall be
called lists, and no further alterations may be made in them. The lists
shall each be printed on a separate sheet with the names of the
candidates in the order in which they appear on the nomination papers.
The lists shall also be provided with a number (in rotation) for each
electoral district, and if the proposers have given them any titles
these shall likewise be printed.

If more than one list have the same title the police department shall
require the representatives of the nominators to make some distinction
between them. If this is not done within two days, these lists shall be
distinguished by further special numbers (in rotation).

The different lists shall be printed on paper of the same size and the
same colour.

7. At least three days before the election these lists shall be
delivered to each elector in an envelope, which shall at the same time
serve as a voucher of the elector's right to vote. In addition to the
printed lists, each voter shall receive a blank list containing no
names, but as many numbered lines as there are members to be elected
(free lists).

The voucher shall take the place of the present admittance card.

8. Electors must present themselves in person at the polling booth and
deliver the voucher to the polling officers.

The latter shall retain the voucher, and in return give the elector an
official stamp.

9. Each elector shall have as many votes as there are members of the
Grand Council to be elected in his district, and shall for that purpose
choose _one_ of the lists supplied to him. If he makes use of a printed
list he may strike out any names and insert any others. Every vote is
valid where the name of an eligible candidate is clearly given, and the
only restrictions are that the same name may not appear more than three
times, and that the total number of names may not exceed the number of
members to be elected.

The voter may make the alterations he desires in the printed list
selected by him, or fill in the free list either at the polling booth or
before reaching it.

The voter shall affix the official stamp supplied to him to the list he
has selected, and place the latter in the ballot box.

10. At the close of the poll the presiding officer shall open the ballot
box and compare the number of voting papers therein with the number of
vouchers received and the number of official stamps issued.

Only the official voting papers with stamps attached shall be valid.

11. The polling officers shall then examine the valid voting papers and
ascertain by entering the votes on counting sheets how many votes each
name has received.

If a voting paper contain more names than there are Councillors to be
elected for the electoral district, then the votes in excess at the
bottom of the list shall not be counted.

If a voting paper contain fewer names than there are Councillors to be
elected in the district, then the number of votes not used shall be
ascertained and shall be added (as list votes) to the list chosen by the
elector, provided the latter has made use of a printed list.

The number of votes for each list shall then be ascertained by adding
together the list votes and the vote given for individual candidates
on the list.

If eligible persons not standing on any list receive votes, each of
these names shall be treated as a separate list.

12. If no nominations have been handed in, those persons shall be
elected who receive most votes.

In the event of equality of votes, the returning officer shall at once
decide the matter by casting lots.

13. If one or more lists have been nominated, the vacancies on the Grand
Council shall be divided among the several lists in proportion to the
number of votes each list has received. The procedure shall be as

The total number of the valid votes shall be divided by the number of
vacancies increased by one.

The quotient thus obtained increased by one (but disregarding fractions)
shall be called the quota.

To each list there shall be allotted as many members as the number of
times the quota is contained in the votes it receives. If the total
number of members thus obtained is less than the number to be elected,
the votes for each list shall be divided by one more than the number of
members already assigned to such list, and the first seat still to be
disposed of shall be allotted to that list which has the
largest quotient.

The same procedure shall be repeated as long as any seats remain to be
disposed of.

If two or more lists have the same claim to the last seat to be disposed
of (equality of quotient), that list shall always take precedence in
which the candidate who would be selected under the provisions of Clause
14 has received the largest number of votes. In case of equality of
votes the returning officer (_Wahl-bureau_) shall immediately decide the
question by casting lots.

14. From each list those candidates (to the number allotted to the list)
shall be selected who have received the largest number of votes.
Equality of votes is decided by lot, to be drawn immediately by the
returning officer.

15. If to one or several lists are allotted more seats than there are
names contained, all their candidates shall in the first place stand
elected. The surplus seats shall be divided among the remaining lists by
continuance of the procedure prescribed in Clause 13.

16. After ascertaining the result of the election, the electoral office
shall draw up a report stating the number of the voting vouchers
received, of the official stamps issued, and of the voting papers handed
in, the number of the votes received for each name and for each list,
arranged according to the lists, particulars of the allotment of seats
and the names of the elected members.

Mention shall also be made of any irregularities which have occurred.

These reports shall be signed by all the electoral officers, and shall
then be forwarded, together with the voting vouchers received, the
unused official stamps, the voting papers and the unissued papers, to
the Government Council.

The result of the election shall be affixed conspicuously outside the
Chief Polling Booth.

The Polling Officers shall notify each elected candidate of his election
in writing.

17. An elected candidate who did not appear on any of the nominations
put in may refuse to accept his election within one week by giving
written notice to the Government Council.

The Government Council shall then immediately order a bye-election.

18. Those elected candidates whose election is rendered void owing to
their simultaneously having been elected as members of the Government
Council shall be immediately replaced by the Government Council by the
non-elected candidates on the same list who have received most votes.

If there are none, the vacant seats on the Great Council shall
immediately be filled by supplementary elections, which shall also serve
to fill any seats, if any rendered vacant under Clause 17.

19. Members retiring from the Great Council during their period of
office shall be replaced immediately by the Government Council by the
non-elected candidates on the same list who have received most votes.
If there are none, supplementary elections shall take place in the first
half of the next following month of May.

20. The same regulations shall serve for supplementary elections as for
general elections.

21. The provisions of this law shall come into operation for the first
time in the general election for the Grand Council which takes place in
the year 1905.

The provisions of earlier laws and resolutions of the Grand Council
referring to elections to the Grand Council are hereby repealed, in so
far as they are contrary to this law.


(The letter _f_ after a number signifies 'and page following.' The
letter _n_ signifies "note.")

Accuracy of proportional systems,
Acton, Lord,
Education (1867),
Port of London (1908),
Queensland Electoral (1905),
Redistribution (1885),
South Africa (1909),
Tasmanian Electoral (1896),
Tasmanian Electoral (1907),
Transvaal Municipal (1909),
Advantages of proportional representation,
Advantages of single transferable vote.
_See_ Single transferable vote
Aldermen, election of,
Allotment of seats to parties,
Alternative vote,
Andrae, M.,
Anson, Sir William R., Bart.,
Asquith, Rt. Hon. H. H.,
Avebury, Rt. Hon. Lord,

Balfour, Rt. Hon. A. J.,
Ballot papers, copies of,
Ballots, second,
Battersea Borough Council,
Beale, Mr. W. Phipson,
Belgian, or d'Hondt system,
Bernstein, Dr. Ed.,
Alternative Vote (1908, 1910),
Electoral Reform (1867),
Electoral Reform (1884),
Electoral Reform (France),
Irish Council (1907),
Municipal Representation
Parliamentary Representation (1854),
Plural Voting (1907),
Redistribution (1905),
Reform (1832),
Representation of the People (1867),
Birrell, Rt. Hon. Augustine,
Blind, Karl,
Block vote,
Borough Councils,
Boundaries, importance of,
Bright, John,
Brown, Prof. Jethro,
Burke, Edmund,

Cairns, Lord,
Campbell-Bannerman, Sir Henry,
Cape Colony Legislative Council,
Carlskrona election,
_Case de tête_,
Cecil, Lord Hugh,
Cecil, Lord Robert,
Chance, effect of,
Churchill, Rt. Hon. Winston S.,
Clark, Justice,
Commons, Prof. J. R.,
_Commission du Suffrage Universel_,
Constituencies, size of,
Constitutional reform,
Corbett, Mr. J. Rooke,
Cost of elections,
Courtney of Penwith, Rt. Hon. Lord,
Criticisms of single transferable vote,
Cross voting,
Cumulative vote,

d'Alviella, Count Goblet,
Deakin, Mr. Alfred,
Defects of majority systems,
d'Hondt system,
Dicey, Prof. A. V.,
Dilke, Sir Charles,
Dobbs, Mr. Archibald E.,
Droop, H. R.,

Education Act (1867),
"Effective voting,"
Elections, General,
_See also_ Statistics
Elections, procedure at,
Elector, freedom of,
Elector's task,
_See also_ Voting
Electoral Reform Bill (1884),
Electoral Reform Bill (1867),
Electoral systems, Royal Commission on.
_See_ Royal Commission
Elimination of lowest candidate,
Executive under proportional representation,

Fairness of proportional systems,
Federal Home Rule,
Freedom of elector,
French Electoral Reform Bill,

Gladstone, W. E.,
Gove method,
Gregory method,
Grey, Earl,
Group formation,
Group representation,
Gulland, Mr. J. W.,
Guyot, M. Yves,

Hagenbach-Bischoff, Prof.,
Hare, Thomas,
Hare-Clark method,
Hayashida, Mr. Kametaro,
Home Rule,
House of Commons,
House of Commons committees,
House of Lords,
House of Lords, Select Committee on its Reform,
House of Lords, Select Committee on Municipal Representation Bill,

Imperial Parliament,
Independents, the fate of,
Irish Council Bill (1907),

Jaurès, M. Jean,
Jenks, Prof. E.,

Labour Councils, Canadian,
Labour Party,
Lachapelle, M. Georges,
Late preferences, effect of,
Limited vote,
List systems,
Localities, representation of,
Lochee of Gowrie, Rt. Hon. Lord,
London Borough Councils,
London County Council,
Lubbock, Sir John (Lord Avebury),

Macdonald, Mr. J. Ramsay,
Majorities, exaggeration of.
_See also_ Statistics,
Majorities, small,
Majorities, under-representation of,
Majority systems,
Marshall, J. Garth,
Mill, John Stuart,
Milner, Lord,
Miners' Association, Northumberland,
Minorities, disfranchisement of,
Minorities, representation of,
Model elections,
Monk, Mr. F. D., 122, 247
Morley of Blackburn, Rt. Hon. Lord,
Muir, Prof. Ramsay,
Municipal elections,
Municipal Representation Bill (1907),

Nanson, Prof. E. J.,
Naville, Ernest,
New Zealand,
Nomination of public bodies,
Northumberland Miners' Association,

Objections to proportional representation,
Orange Free State,
Organisation of elections,

Parliamentary Representation Bill (1854),
Party exclusiveness,
Party government,
Party organisation,
Peers, Scottish Representative,
Plural Voting Bill (1907),
Port of London Act (1908),
Powell, Mr. Ellis T.,
Practicability of single transferable vote,
Praed, Mackworth,
Preferences, comparative efficiency of different,
Present systems, defects of,
Pretoria, Proportional Representation League (France),
Proportional Representation Society,
Provincial Councils, South Africa,

Queensland Electoral Act (1906),
Quota, the,

Redistribution Act (1885),
Redistribution Bill (1905),
Reform Bill (1832),
Representation of the people (1867),
Result sheet,
Returning officer, duty of,
Robertson, Mr. John M.,
Royal Commission on Electoral Systems,
Russell, Lord John,

School Board elections,
Scottish Grand Committee,
_Scrutin de liste_,
Seats, allotment to parties,
Second ballot,
Selection of successful candidate in a list,
South Africa,
Single transferable vote--
_See also_ Advantages of proportional representation
Single vote,
Smith, Rt. Hon. J. Parker,
Social Democratic Party (Germany),
South Africa,
South Africa Act (1909),
Spence, Catherine Helen,
Spoilt ballot papers,
Statistics of elections--
South Africa,
United Kingdom,
Surplus votes, transfer of,
Systems, majority.
_See_ Present systems
Systems, proportional.
_See_ Bâle, Belgium, Finland, France, Japan, Sweden, and
Single transferable vote

Tasmanian Electoral Act (1896),
Tasmanian Electoral Act (1907),
Three-cornered contests,
Trades Unions,
Transfer of surplus votes,
Transfer sheet,
Transvaal Municipal Act (1909),
Two-party system,

United States,

Vandervelde, M.,
Vivian, Mr. Henry,
Voting, modes of,

Wallas, Mr. Graham,
Whips in House of Commons,
_See also_ Party organisation
White, Mr. Dundas,
Williams, Mr. Aneurin,

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