The system may be more fully understood from some details of the
election of 1907 in the Nyland division. In this division, the largest
in Finland, returning twenty-three members, no less than seventy-two
schedules were presented, or which all except five were combined into
compacts. The five remained isolated. Of the combined schedules
seventeen were included in the compact of the Swedish party, but the
individual candidates in these seventeen schedules numbered only
twenty-three, the legal limit, the same names being repeated in several
schedules. The old Finnish compact contained thirteen schedules, the
Young Finns seventeen, the Social Democrats eight, the "Christian"
compact seven, the "Free Christian" compact three, and the Radicals two.
As already stated, the voter's task is not difficult. He, or she, simply
marks the schedule of his, or her, choice. The voter can also, if he
wishes, alter the order of the names in a schedule. The effect of doing
this will be apparent in a moment. That the task is simple is
conclusively shown by the fact that the percentage of spoilt votes was
in the Nyland division only 0.58 per cent. For the whole country the
percentage was only 0.93, and this with universal adult suffrage and a
poll of 899,347, or 70.7 per cent, of the electorate.
_The returning officer's task_.
The task of the returning officer is twofold. He has to ascertain (1)
the relative positions of candidates within each compact (or independent
schedule), and (2) their position relatively to the candidates of other
compacts in the final allotment of seats. He proceeds as follows. He
first counts the votes on each schedule, reckoning a full vote to the
first name, a half vote to the second, and a third of a vote to the
third (the effect of an alteration of the order of names in a schedule
by the voter is now apparent). Thus if schedule No. 1 (in the specimen
ballot paper on page 323), containing the names Schybergson, Neovius,
and Soderholm, receives the support of 6000 voters in all, of whom 3000
have placed Schybergson as No. 1, 2000 as No. 2, and 1000 as No. 3,
Schybergson will have a total of 3000 + 2000/2 + 1000/3 = 4333.
Similarly, if Neovius obtains the support of 2000 as No. 1, 2000 as No.
2, and 2000 as No. 3, his total will be 2000 + 2000/2 + 2000/3 = 3666;
Soderholm, the third candidate, would receive 1000 votes as No. 1, 2000
as No. 2, and 3000 as No. 3, and his total would be 1000 + 2000/2 +
3000/3 = 3000. But these individual totals of 4333, 3666, and 3000 are
used merely to determine the order of the candidates within the schedule
itself, and having performed that function, they are not taken further
into account. In the example given (as would usually be the case in
practice) the order within the schedule has not been disturbed, and the
candidates are credited, the first (Schybergson) with the full number of
the voters who supported the schedule--6000; the second (Neovius) with
one-half that number--3000; the third (Soderholm) with one-third of that
number--2000. These last figures are called "numbers of comparison," a
phrase intended to throw light upon their function. The same process is
gone through with all the other schedules in the same compact. The
returning officer then adds up all the numbers of comparison which each
candidate has obtained in all the schedules within the compact where his
name appears, and arranges candidates within the compact in the order of
these totals. Thus, in the actual election of 1907, in the Nyland
division, Schybergson headed the Swedish party compact with 9192 as the
total of his "numbers of comparison," Soderholm coming next with 6837.
_The allotment of seats_.
When the candidates in each compact have thus been arranged in order
(and the votes given in writing by independent voters have also been
counted), the returning officer proceeds to the second stage of his
duties--the determination of the position of candidates with reference
to their competitors in other compacts; and it is on this position that
the actual allotment of seats depends. For this purpose he primarily
takes into account, not the "numbers of comparison" of individual
candidates, but the total number of voters who have supported each
compact; he credits this total to the candidate who has the highest
"number of comparison" within the compact; credits the next candidate
with one-half this total, the third candidate with one-third, and so on,
finally arranging the whole of the candidates in order. Thus far this
stage of the process is identical in substance with the Belgian method,
though the appearance is different. For, obviously, if List (or compact)
A, of which the candidates are G, H, I, in that order receives 12,000
votes, while List B, with candidates P, Q, R, receives 10,000, and List
C, with candidates X, Y, Z, receives 8000, it is all one whether the
returning officer applies the d'Hondt rule and assigns two seats to List
A (thus seating G and H), two seats to List B (thus seating P and Q),
and one seat to List C (thus seating X), or whether he tabulates the
result of the polling thus:
G 12,000 \
P 10,000 |
X 8,000 > Elected.
H 12,000/2 i.e. 6,000 |
Q 10,000/2 i.e. 5,000 /
Y 8,000/2 i.e. 4,000 Not elected, and so on.
But at this point a characteristic feature of the Finnish system comes
into play. Candidates' names may occur in more than one compact, and may
be found in isolated schedules, or on the written papers of independent
voters as well. Consequently their final order cannot be determined by
this simple application of the Belgian method. The returning officer
must[1] add to the number of votes credited to a candidate of any one
compact such additional votes as he may have obtained either as a member
of another compact or from independent voters. Thus, in the Nyland
elections, Miss Sohlberg, whose name will be found at the head of
Schedule 48 within the Swedish compact, obtained the eleventh place
within that compact. The total number of voters supporting this compact
was 44,544, and Miss Sohlberg was therefore credited with an eleventh of
this total, or 4049 votes. But Miss Sohlberg's name also occurred in
Schedules 62 and 63 in the "Free Christian" compact and Schedule 21 in
the "Christian" compact, and as her share of the votes of these compacts
she received 153 and 325 respectively. She also received four votes in
writing. Thus her final total was 4049 + 153 + 325 + 4, or 4531 in all,
and it was this number which determined her position on the poll.
_Successful candidates in the Nyland election._ This
explanation will perhaps be more comprehensible if the actual result of
the polling in the Nyland division, so far as the first 25 candidates
are concerned, is given in a tabular form:--
Final Names of Party. Number of Additional Final
Order Candidates. Votes resulting Votes. Total.
of from Place of
Poll. Candidates on
Compact.
1 Schybergson Swedish 44,544 2.33 44,546.33
2 Häninan Social Dem. 40,951 6.5 40,957.5
3 Soderholm Swedish 22,272 0.33 22,272.33
4 Sillanpää Social Dem. 20,475.5 8.83 20,484.33
5 Käkikoski Old Finn 20,402 9.33 20,411.33
6 Oljemark Swedish 14,848 -- 14,848
7 Sirén Social Dem. 16,650.33 2.33 16,652.66
8 Rosenquist (G.) Swedish 8,908.8 2,932.83[2] 11,841.63
9 Rosenquist (V.) Swedish 11,136 4.33 11,140.33
10 Helle Social Dem. 10,237.75 3 10,240.75
11 Palmén Old Finn 10,201 8.83 10,209.83
12 Pertillä (E.) Social Dem. 8,190.2 4.67 8,194.87
13 Ahlroos Swedish 7,424 1 7,425
14 Pertillä (V.) Social Dem. 6,725.17 1.5 6,726.67
15 Reima Old Finn 6,800.67 5.67 6,806.34
16 Erkko Young Finn 6,521 6.32 6,527.32
17 Ehrnrooth Swedish 6,363.43 75.83 6,439.26
18 Laine (M.) Social Dem. 5,850.14 4 5,854.14
19 Wasastjerna Swedish 5,568 -- 5,568
20 Ingman Social Dem. 5,118.88 3.5 5,122.38
21 Laine (O.) Old Finn 5,100.5 -- 5,100.5
22 von Alfthan Swedish 4,949.33 -- 4,949.33
23 Johansson Social Dem. 4,550.11 1.33 4,551.44
(All the above were elected.)
24 Sohlberg Swedish 4,049.45 482.45[3] 4,531.9
25 Gustaffsson Swedish 4,454.4 4.5 4,458.9
&c. &c.
_Equitable results._
It will to some extent be gathered from the foregoing table that the
total number of the supporters of the various compacts or parties in the
Nyland division and the number of seats won were as follows:
Seats Seats in
Parties. Votes. Actually Proportion
Won. to Votes.
Swedish 44,544 9 8.7
Social Democrat 40,951 9 8.0
Old Finn 20,402 4 4.0
Young Finn 6,521 1 1.3
"Christian" compact 2,932 - .6
"Free Christian" 458 - .1
Radical 168 - -
Isolated schedules 1,356 - .3
Total 117,332 23 23.0
The result is thus in reasonable correspondence with the demands of a
strictly proportionate allotment of seats; this statement is also true
of the results for the whole of Finland, as the following table
will show:--
Seats Seats in
Parties. Votes. Actually Proportion
Won. to Votes.
Social Democrat 329,946 80 74.1
Old Finn. 243,573 59 54.7
Young Finn 121,604 26 27.3
Swedish 112,267 24 25.2
Agrarian 51,242 9 11.5
Christian Labourer 13,790 2 3.1
Minor groups 18,568 - 4.1
Total 890,990 200 200.0
An exactly mathematical distribution is, of course, not to be expected
from this, any more than from any other method which does not adopt the
system of treating a whole country as a single constituency. As to the
mechanism of the system it only remains to add that the process of
counting was found to be very lengthy. In the Nyland division, where the
results were ascertained sooner than in any other case, the elections
were held on 15 and 16 March, but the result was not announced until
the 2 April. To people accustomed to the greater rapidity of ordinary
electoral methods this will seem a serious drawback. Possibly improved
arrangements may shorten this long interval between the elections and
the announcement of the result.
It would obviously be premature to attempt to estimate the political
effects of the Finnish system as compared with other systems of
proportional representation.
_Elector's freedom of choice._
The Finnish system has been in operation since 1907, and the whole
political circumstances of Finland have undergone so many striking
changes, and so many new factors are at work that to disentangle
particular causes and effects is an impossibility. But plainly the
Finnish machinery gives a greater freedom to the elector than the
Belgian system. The Finnish system in fact encourages the electors to
arrange the candidates of a party in the order preferred by the electors
themselves, and not in the order dictated by the party managers. There
is no "party ticket" for which the elector can vote blindfold. He must
choose the schedule that he prefers; he can even rearrange that
schedule, or, if he chooses, can make one of his own. No doubt the
schedule itself is ready made for him, but it contains three names only,
and is not the equivalent of the Belgian "list." On the other hand, the
elector who chooses to vote for a schedule within a compact adds,
whether he likes it or not, to the total votes of the compact, and so
may help to return not the candidate of his choice, but the candidates
preferred by the majority of the party with which he is in sympathy. An
illustration of this fact may be taken from the Nyland poll. The old
Finnish party were alive to the possibilities of the situation, and
combined their lists with great skill so as to attract votes. They
placed their favourite candidates in nearly every schedule, but not at
the head of the schedule. At the head of the schedule they placed some
man of local popularity, usually a peasant proprietor, whose name was
not repeated in many, if any, other schedules. Thus the local favourite
attracted votes to the schedule, but in the race for the highest numbers
of comparison the candidates whose names appeared on few schedules were
left behind those whose names appeared on many schedules even in the
lower places.
A portion of the official ballot paper showing the compact put forward
by the Swedish People's Party is printed on the opposite page. In one
corner of the ballot paper was a blank schedule in the following form.
THE ELECTOR who does not approve of any of the preceding lists should
write here the names of his candidates in the order in which he wishes
them to be elected.
CANDIDATES
_Name_....................................................
_Profession or Occupation_................................
_Address_.................................................
_Name_....................................................
_Profession or Occupation_................................
_Address_.................................................
_Name_....................................................
_Profession or Occupation_................................
_Address_.................................................
FINLAND GENERAL ELECTION, 1907
Part of Ballot Paper--Nyland Division.
The Voters' Compact of the Swedish People's Party.
1
HELSINGFORS.
Experienced Members of the Diet:--
--Schybergson, E. K.
--Neovius, A. W.
--Soderholm, K. G.
33
EAST NYLAND-LOUISA.
Justice and Progress:--
--Rosenquist, G. G.
--Stromberg, J.
--Ehrnrooth, L.
34
MID-NYLAND-NIOKBY.
The Welfare of the Rural Population;--
--Topelius, G. L.
--Alfthau, K. von
--Rosenquist, B. T.
35
MID-NYLAND-ESBO.
The Welfare of the Rural Population:--
--Wasastjerna, O.
--Schybergson, E.
--Soderholin, K.
36
WEST NYLAND-KYRK-SLATT.
The Welfare ol the Rural Population:--
--Nordberg, G.
--Ehrnrooth, L.
--Oljemark, K. T.
37
WEST NYLANB-EKENAS.
The Welfare of the Rural Population. Law and Justice:--
--Oljemark, K. T.
--Schybergson, E.
--Soderholm, K.
38
BORGA.
Knowledge and Experience:--
--Runeberg, J. W.
--Bjorkenheim, G.
--Rosenquist, G. G.
39
HELSINGFORS.
Sound Development of the Community;--
--Westermarck, Helena.
--Rosenquist, B. T.
--Bjorkenheim, G.
40
HELSINGFORS.
Law and Justice:--
--Sorterholm, K.
--Alfthan, K. von
--Westermarck, Helena,
41
HELSINGFORS.
Legality and Progress:--
--Westermarck, Helena.
--Neovius, A.
--Ehrnrooth, L.
42
HELLSINGFORS.
Swedish Culture:--
--Rosenqnist, B. T.
--Gustafsson, F. prof.
--Soderholm, K.
43
HELSINGFORS.
Friends of Labour and of the People:--
--Alfthan, K. von
--Gustafsson, F. prof.
--Gronroos, F.
44
HELSINGFORS.
Experience and Practical Knowledge:--
--Runeberg, J. W.
--Schybergson, E.
--Neovius, A.
45
HELSINGFORS.
The Labourers' Welfare:--
--Ahlroos, F.
--Holmberg, W.
--Ehrnrooth, L.
46
HELSINGFORS.
Commerce and Industry:
--Heimburger, W. F.
--Bjorkenheim, G.
--Schybergson, E.
47
THE SKERRIES OF NYLAND:
Navigation and Fisheries:--
--Hjelt, Th.
--Renter, O.
--Alfthan, K.
48
THE PROVINCE OF NYLAND:
HELSINGFORS.
Temperance, Morality and Popular Education:--
--Sohlberg, H.
--Ahlroos, F.
--Rosenquist, G. G.
[Footnote 1: This right of addition is subject to a limit. The
reinforcements must not raise a candidate's total above what he might
obtain if the votes given to all compacts or lists, where his name
occurs, were divided by the figure which indicates his order within the
compact from which he derives his principal strength.]
[Footnote 2: This large reinforcement of votes came from the Christian
compact, where this candidate's name appeared as well as in the
Swedish compact.]
[Footnote 3: See reference to Miss Sohlberg in preceding paragraph.]
APPENDIX V
THE STATISTICS OF THE GENERAL ELECTIONS, 1885-1910
The following tables are taken, with permission, from a paper read on 12
December 1906, by Mr. J. Rooke Corbett, M.A., before the Manchester
Statistical Society, of which a second and revised edition was published
in April 1910 by the Proportional Representation Society.
In these tables the totals for England, Wales, and Monmouth, Scotland
and Ireland are shown separately, and the figures for England have been
further subdivided according to the ten divisions into which the kingdom
is divided by the Registrar General for the purpose of his work.
These ten subdivisions are as follows:
Metropolitan--
London.
South East--
Surrey.
Kent.
Sussex.
Hampshire.
Berkshire.
South Midland--
Middlesex.
Hertfordshire.
Buckinghamshire.
Oxfordshire.
Northamptonshire.
Huntingdonshire.
Bedfordshire.
Cambridgeshire.
East--
Essex.
Suffolk.
Norfolk.
South-West--
Wiltshire.
Dorsetshire.
Devonshire.
Cornwall.
Somersetshire.
West Midland--
Gloucestershire.
Herefordshire.
Shropshire.
Staffordshire.
Worcestershire.
Warwickshire.
North Midland--
Leicestershire.
Rutlandshire.
Lincolnshire.
Nottinghamshire.
Derbyshire.
North-West--
Cheshire.
Lancashire.
Yorkshire--
West Riding.
East Riding (with York).
North Riding.
Northern Division--
Durham.
Northumberland.
Cumberland.
Westmorland.
The first three columns, A, B and C, show the number of members allotted
to these several divisions, the number of registered electors, and the
number of members to which each division would be entitled if the 670
members of which the House of Commons is composed were divided among the
several divisions in proportion to their electorates.
In taking the electorate as the basis of a proportionate redistribution
of seats it is not intended to prejudge the question whether population
or electorate is the better standard. The electorate has been taken
because the figures are available for the very year in which the
election takes place, whereas the population is only enumerated once in
ten years.
The columns D and E show in two groups the number of members elected for
these divisions, Liberal, Labour, and Irish members being gathered
together in one column, Conservatives alone occupying the other.
It is one of the disadvantages of our present system of representation
that it makes it quite impossible to ascertain the relative strength of
the several parties into which the voters are divided. In the great
majority of contests there is a Liberal, Labour, or Irish Nationalist
candidate on one side, and a Unionist candidate on the other, and there
is practically no evidence as to how many of the supporters of either
candidate belong to each of the parties concerned. Any estimate of the
relative strength of the Liberal and Labour parties or of the Unionist
Free Traders, and Tariff Reformers must be largely a matter of
guesswork. All that is possible, therefore, is to divide the voters into
two groups, as has been done in these tables.
The columns F and G show the total electorate of the constituencies held
respectively by the two groups of members shown in columns D and E.
The figures in these two columns are of value in showing the probable
result of a scheme of redistribution. The South-Eastern counties may be
taken as an example. These are at present represented by 48 members. The
Liberals held three constituencies in January 1910 containing an
electorate of 31,221 (columns D and F); the Conservatives held 45
constituencies containing an electorate of 604,887 (columns E and G). If
a redistribution of seats was made on the basis of equal electorates,
the South-Eastern counties would be entitled to 55 members (column C).
It may be assumed that in any rearrangement of constituencies the
parties would retain their predominance in the areas which they now
represent, and if so the result of a rearrangement of constituencies on
the basis of equal electorates would be that in January 1910 the
Conservatives would have obtained 52 seats and the Liberals 3 (column
K). Similarly in the General Election of 1906 the Liberals in Wales and
Monmouth held 34 seats, the Conservatives none. If the constituencies
had been rearranged, the Liberals would have held 35 seats, the
Conservatives none. The majorities throughout the United Kingdom which
would be obtained under a scheme of equal electorates are shown
in column K.
The columns H and I show the number of electors who voted for the
candidates of the two groups; Liberal, Labour, and Irish Nationalist
voters in one group, Conservative voters in the other.
In computing the figures in these columns an allowance has been made for
uncontested constituencies on the following basis. It has been supposed
that the changes of public opinion which affect the contested
constituencies affect uncontested constituencies also, and in estimating
the number of voters in an uncontested constituency it has therefore
been assumed that the strength of each party varies from one election to
another in the same ratio as in the contested constituencies in the
same county.
The three columns J, K and L show respectively the actual majorities
obtained, the majorities which would have been obtained if the country
had been divided into single-member constituencies of equal size, and
the majorities under a system of proportional representation.
The figures in the last two columns have been calculated with reference
to the totals in column C, which gives the number of members to which
each division would be entitled on a proportional basis.
In order to ascertain the figures given in column K _(i.e._ the probable
results with equal single-member constituencies) it has been assumed, as
already explained, that the two groups would, after the redistribution
of seats, be predominant in the same areas as before the rearrangement.
_The representation of minorities._
The tables give abundant evidence of the anomalies associated with our
electoral system. One of the most striking is the great difference in
the amount of representation secured by minorities in different parts of
the country. The amount of representation secured by a minority has not
depended upon its size, but upon the way in which it has been
distributed. The following table shows the amount of representation
obtained by important minorities in the General Election of
January 1910:--
THE REPRESENTATION OF MINORITIES, ELECTION JAN. 1910
Size of Seats Total Seats
Area. Minority. Obtained. for Whole Area
Ireland . . . . . . . 145,437 21 103
Scotland . . . . . . . 265,770 11 72
S. East: Counties. . . 220,995 3 48
Wales and Monmouth . . 116,696 2 34
Northern Counties . . 75,897 9 32
The figures show that in Ireland a minority of 145,437 obtained
twenty-one representatives, whilst a minority of 116,696 in Wales and
Monmouth obtained only two. The good fortune which befel the minority in
Ireland, not only in the elections of 1910 but in all the elections
since the Redistribution Bill of 1885, has been due to the fact that
this minority is concentrated in one corner of Ireland and can transform
itself into local majorities. The larger minority in Scotland, owing to
its distribution throughout the country, obtains much less
representation; the minorities in the south-eastern counties of England
and Wales are also distributed throughout these two areas and likewise
suffer. The minority of 75,879 in the northern counties being less
evenly diffused was more fortunate, and obtained nine representatives.
The figures for the election of December 1910 disclose similar
anomalies.
GENERAL ELECTION, 1885
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 489,396 57 LLI 22 165,345 162,228
Con 38 324,051 188,067 16 19 3
England
South-East 48 406,955 47 LLI 4 34,883 144,659
Con 44 372,072 187,831 40 39 7
S.Midland 38 312,477 36 LLI 14 123,665 124,717
Con 24 188,811 129,544 10 8
East 29 257,022 29 LLI 18 173,521 107,710 7 11 1
Con 11 83,501 98,137
South-West 40 314,603 36 LLI 27 229,612 144,273 14 16 4
Con 13 84,991 117,442
W.Midland 58 544,415 63 LLI 45 427,549 248,825 32 36 8
Con 13 116,866 198,212
N.Midland 34 328,844 38 LLI 26 255,836 55,503 18 22 4
Con 8 73,008 120,933
North-West 70 654,751 76 LLI 24 231,123 263,670
Con 46 423,628 292,942 22 22 4
Yorkshire 52 536,553 62 LLI 36 398,426 248,078 20 30 8
Con 16 138,127 189,930 20 30 8
North 32 305,015 35 LLI 25 262,287 144,803 18 25 5
Con 7 42,728 96,708
ENGLAND 461 4,150,031 480 LLI 241 2,302,248 1,740,466 21 52 16
Con 220 1,847,783 1,619,746
Wales and
Monmouth 34 286,145 33 LLI 30 263,199 149,782 26 27 11
Con 4 22,946 79,006
Scotland 72 576,828 67 LLI 58 485,116 289,032 44 45 15
Con 14 91,712 181,706
Britain 567 5,013,004 580 LLI 329 3,050,563 2,179,230 91 124 42
Con 238 1,962,441 1,880,458
Ireland 103 777,954 90 LLI 85 624,760 404,892 67 54 44
Con 18 153,194 139,273
Total 670 5,790,958 670 LLI 414 3,675,323 2,584,122 158 178 86
Con 256 2,115,635 2,019,731
Majority 158 1,559,638 564,391
NOTE.--The figures in columns K and L are calculated with reference to
the totals in column C. Thus the figure L 54 for Ireland in column K of
the last section of the table indicates that under a system of equal
single-member constituencies Ireland's 90 members would be Liberal etc.
72, Unionist 18, a Liberal majority of 54, and the corresponding figure
L 44 in column L indicates that under proportional representation the 90
members which Ireland would return would be Liberal etc. 67, and
Unionist 23. a Liberal majority of 44.
GENERAL ELECTION, 1886
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 489,396 57 LLI 11 87,974 125,457
Con 49 401,422 185,072 38 37 11
England--
South-East 48 406,955 47 LLI 0 - 114,518
Con 48 406,955 184,221 48 47 11
S.Midland 38 312,477 36 LLI 9 73,292 94,213
Con 29 239,185 128,339 20 20 6
East 29 257,022 29 LLI 4 87,975 81,838
Con 25 219,047 102,732 21 21 3
South-West 40 314,603 36 LLI 7 63,063 96,753
Con 33 251,540 129,056 26 22 6
W.Midland 58 544,415 63 LLI 15 136,518 173,463
Con 43 407,897 218,753 28 32 8
N.Midland 34 328,844 38 LLI 14 147,138 125,078
Con 20 181,706 126,547 6 4
North-West 70 654,751 76 LLI 13 123,459 236,134
Con 57 531,292 282,187 44 48 6
Yorkshire 52 536,553 62 LLI 33 359,414 214,407 6
Con 19 177,139 180,728 14 22
North 32 305,015 35 LLI 23 247,275 123,901 5
Con 9 57,740 96,404 14 21
ENGLAND 461 4,150,031 480 LLI 129 1,276,108 1,385,762
Con 332 2,873,923 1,634,039 203 188 42
Wales and
Monmouth 34 286,145 33 LLI 27 240,752 123,186 20 23 7
Con 7 45,393 82,179
Scotland 72 576,828 67 LLI 43 339,726 218,561 14 11 5
Con 29 237,102 188,164
Subtotal 567 5,013,004 580 LLI 199 1,856,586 1,727,509
Con 368 3,156,418 1,904,382 169 154 30
Ireland 103 777,954 90 LLI 84 616,735 376,445
Con 19 161,219 144,755 65 52 38
Total 670 5,790,958 670 LLI 283 2,473,321 2,103,954 8
Con 387 3,317,637 2,049,137 104 102
Majority 104 844,316 54,817
GENERAL ELECTION, 1892
Table headings:
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 552,024 60 LLI 23 186,572 183,967
Con 37 365,452 214,275 14 20 4
England:
South-East 48 463,073 50 LLI 4 38,534 147,136
Con 44 424,539 206,075 40 42 8
S.Midland 38 340,650 38 LLI 15 139,228 120,844
Con 23 210,422 147,347 8 8 4
East 29 276,491 30 LLI 13 134,632 108,866
Con 16 141,859 110,849 3
South-West 40 325,769 35 LLI 15 136,061 125,392
Con 25 189,708 136,449 10 5 1
W. Midland 58 577,397 63 LLI 16 143,567 204,453
Con 42 433,830 248,774 26 31 7
N. Midland 34 347,482 38 LLI 22 232,970 145,587 10 14 2
Con 12 114,512 130,380
North-West 70 707,392 77 LLI 26 284,970 282,139
Con 44 422,422 307,698 18 15 3
Yorkshire 52 571,864 62 LLI 35 418,414 244,099 18 28 6
Con 17 153,450 204,492
North 32 328,189 36 LLI 25 264,483 143,172 18 22 4
Con 7 63,706 115,626
ENGLAND 461 4,499,331 489 LLI 194 1,979,431 1,705,655
Con 267 2,519,900 1,821,985 73 57 15
Wales and
Monmouth 34 314,063 34 LLI 31 294,395 152,326 28 30 10
Con 3 19,668 86,576
Scotland 72 606,203 66 LLI 52 449,994 267,631 32 32 8
Con 20 156,209 214,448
Subtotal 567 5,419,497 589 LLI 277 2,723,820 2,125,612 5 3
Con 290 2,695,777 2,123,009 13
Ireland 103 746,781 81 LLI 80 561,938 345,548 57 41 31
Con 23 184,843 157,181
Total 670 6,168,388 670 LLI 357 3,285,758 2,471,164 44 46 34
Con 313 2,880,620 2,280,190
Majority 44 405,138 190,974
GENERAL ELECTION, 1895
Table headings:
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 573,141 61 LLI 8 70,056 161,328
Con 52 503,085 242,999 44 47 13
England:
South-East 48 472,725 50 LLI 2 24,057 152,213
Con 46 448,668 217,096 44 44 8
S.Midland 38 358,501 38 LLI 3 30,569 116,143
Con 35 327,932 164,052 32 32 6
East 29 294,153 31 LLI 8 70,467 101,736
Con 21 223,686 122,999 13 15 3
South-West 40 330,670 35 LLI 10 76,141 124,852
Con 30 254,529 144,435 20 19 3
W.Midland 58 589,881 63 LLI 9 85,544 195,545
Con 49 504,337 259,382 40 45 9
N.Midland 34 351,792 37 LLI 16 186,167 143,142 1
Con 18 165,625 149,436 2 1
North-West 70 728,292 78 LLI 10 114,035 273,585
Con 60 614,257 332,101 50 54 8
Yorkshire 52 565,799 61 LLI 28 317,932 238,032 4 7 1
Con 24 247,867 225,871
North 32 339,289 36 LLI 20 222,202 145,085 8 12 2
Con 12 117,087 124,697
ENGLAND 461 4,604,243 490 LLI 114 1,197,170 1,652,261
Con 347 3,407,073 1,983,068 233 236 48
Wales and
Monmouth 34 320,532 34 LLI 25 241,750 148,552 16 18 6
Con 9 78,782 108,036
Scotland 72 636,106 68 LLI 39 335,143 243,425 6 4 2
Con 33 300,963 234,138
Subtotal 567 5,560,881 592 LLI 178 1,774,068 2,044,238
Con 389 3,786,818 2,325,242 211 214 40
Ireland 103 727,562 78 LLI 82 549,467 317,910 61 42 28
Con 21 178,095 154,379
Total 670 6,292,443 670 LLI 260 2,323,530 2,362,148
Con 410 3,964,913 2,479,621 150 172 12
Majority 150 1,641,383 117,473
GENERAL ELECTION, 1900
Table headings:
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 601,925 60 LLI 8 73,718 150,047
Con 52 528,207 247,777 44 46 14
England:
South-East 48 512,408 51 LLI 3 23,362 140,277
Con 45 489,406 220,829 42 47 11
S. Midland 38 388,361 39 LLI 6 63,375 120,012
Con 32 324,986 164,148 26 27 7
East 29 319,997 32 LLI 9 80,447 101,785
Con 20 239,550 125,375 11 8 4
South-West 40 337,449 33 LLI 14 122,410 127,086
Con 26 215,039 142,269 12 9 1
W. Midland 58 630,931 63 LLI 10 96,089 200,113
Con 48 534,842 261,474 38 43 9
N. Midland 34 378,996 38 LLI 18 211,280 149,794 2 4 0
Con 16 167,716 153,294
North-West 70 794,142 79 LLI 14 176,183 281,634
Con 56 617,957 351,243 42 43 9
Yorkshire 52 612,892 61 LLI 26 326,841 239,045 5 1
Con 26 286,051 238,870
North 32 367,007 36 LLI 16 197,102 147,017 2 2
Con 16 169,905 135,459
ENGLAND 461 4,944,108 492 LLI 124 1,370,807 1,657,814
Con 337 3,573,301 2,040,508 213 212 52
Wales and
Monmouth 34 342,209 34 LLI 28 286,628 161,190 22 24 8
Con 6 55,581 103,396
Scotland 72 683,840 68 LLI 34 312,781 254,112
Con 34 371,059 258,836 4 6
Britain 567 5,970,187 594 LLI 186 1,970,216 2,073,116
Con 381 3,999,941 2,402,740 195 194 44
Ireland 103 765,258 76 LLI 82 598,469 318,203 61 44 28
Con 21 166,757 145,906
Total 670 6,735,415 670 LLI 268 2,568,685 2,391,319
Con 402 4,166,698 2,548,736 134 150 16
Majority 134 1,598,013 157,417
GENERAL ELECTION, 1906
Table headings:
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 626,011 57 LLI 40 385,762 251,937
Con 20 240,249 225,725 20 13 3
England
South East 48 583,000 54 LLI 22 273,398 245,046
Con 26 309,602 241,097 4 4
S.Midlands 38 441,803 40 LLI 27 328,386 193,594 16 20 2
Con 11 113,417 172,159
East 29 368,662 34 LLI 25 333,564 170,039 21 28 4
Con 4 35,098 128,991
South-West 40 371,300 34 LLI 34 321,822 176,478 28 24 4
Con 6 49,478 144,342
W.Midland 58 679,903 63 LLI 35 402,148 288,832 12 11 1
Con 23 277,760 286,862
N.Midland 34 420,677 39 LLI 28 358,852 205,066 22 27 5
Con 6 61,825 151,924
North-West 70 869,792 80 LLI 55 680,843 420,969 40 46 12
Con 15 188,949 321,560
Yorkshire 52 667,863 62 LLI 41 556,233 340,865 30 42 14
Con 11 111,635 218,778
North 32 409,843 38 LLI 27 345,353 215,748 22 26 10
Con 5 64,490 123,003
England 461 5,438,859 501 LLI 334 3,986,356 2,508,574 207 233 53
Con 127 1,452,503 2,014,441
Wales and
Monmouth 34 387,585 35 LLI 34 387,585 217,462 34 35 13
Con 0 -- 100,547
Scotland 72 750,401 70 LLI 60 629,360 367,942 48 48 16
Con 12 121,041 235,098
Britain 567 6,576,845 606 LLI 428 5,003,301 3,093,978 289 316 82
Con 139 1,573,544 2,350,086
Ireland 103 693,417 64 LLI 85 545,748 301,833 67 36 22
Con 18 147,669 144,708
TOTAL 670 7,270,262 670 LLI 513 5,549,049 3,395,811 356 352 104
Con 157 1,721,213 2,494,794
Majority 356 3,827,836 901,017
GENERAL ELECTION, JANUARY 1910
Table headings:
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 658,795 57 LLI 26 246,838 254,154
Con 34 411,957 298,821 8 15 5
England:
South-East 48 636,108 55 LLI 3 31,221 220,995
Con 45 604,887 334,022 42 49 11
S. Midland 38 490,592 43 LLI 11 146,312 197,717
Con 27 344,280 235,776 16 17 3
East 29 400,062 35 LLI 15 236,234 173,465 1 7 1
Con 14 163,828 170,027
South-West 40 386,514 34 LLI 18 201,726 172,692 2
Con 22 184,788 175,010 4
W. Midland 58 713,761 62 LLI 17 227,430 284,629
Con 41 486,331 334,874 24 22 6
N. Midland 34 446,752 39 LLI 23 334,766 216,469 12 19 3
Con 11 111,986 181,209
North-West 70 928,640 81 LLI 47 636,497 449,324 24 35 7
Con 23 292,143 382,796
Yorkshire 52 701,856 61 LLI 89 564,418 365,185 26 37 11
Con 13 137,438 248,507
North 32 430,594 38 LLI 23 354,697 216,760 14 24 6
Con 9 75,897 150,471
ENGLAND 461 5,793,674 505 LLI 222 2,980.139 2,551,390 21 3
Con 239 2,813,535 2,521,513 17
Wales and
Monmouth 34 425,714 37 LLI 32 414,613 243,383 30 35 13
Con 2 11,101 116,696
Scotland 72 785,391 68 LLI 61 675,723 394,103 50 50 14
Con 11 109,668 265,770
Sub total 567 7,004,779 610 LLI 315 4,070,475 3,188,876 63 106 30
Con 252 3,188,876 2,903,979
Ireland 103 688,284 60 LLI 82 518,154 356,223 61 30 26
Con 21 170,130 145,437
Total 670 7,693,063 670 LLI 397 4,588,629 3,545,099 124 136 56
Con 270 3,104,434 3,049,416
Majority 124 1,484,195 495,683
GENERAL ELECTION, DECEMBER 1910
Table headings:
Col A: Members
Col B: Registered Electors
Col C: Proportionate Number of Members
Col D: Members - Liberal, Labour and Irish
Col E: Members - Conservatives
Col F: Electorate of Constituencies held by - Liberal, Labour,
and Irish Nationalists
Col G: Electorate of Constituencies held by - Conservative
Col H: Voters - Liberal, Labour, and Irish Nationalist
Col I: Voters - Conservative
Col J: Majority - Actual
Col K: Majority - With equal Single Member Constituencies
Col L: Majority - Under Proportional Representation.
A B C DE FG HI J K L
Prop Memb Electorate Voters Majority
Memb Elect Memb Act Eq PR
Metropolis 60 658,795 57 LLI 29 279,492 223,151
Con 31 379,303 264,281 2 9 5
England--
South-East 48 636,108 55 LLI 5 58,248 209,434
Con 43 577,860 311,888 38 45 11
S. Midland 38 490,592 43 LLI 14 170,762 190,120
Con 24 319,830 219,876 10 13 3
East 29 400,062 35 LLI 16 256,750 164,849 3 9 1
Con 13 143,312 154,529
South-West 40 386,514 34 LLI 14 159,494 164,698
Con 26 227,020 168,992 12 6 0
W. Midland 58 713,761 62 LLI 19 246,842 268,125
Con 39 466,919 316,574 20 20 6
N. Midland 34 446,752 39 LLI 21 298,037 202,351 8 13 3
Con 13 148,715 173,545
North-West 70 928,640 81 LLI 39 524,682 400,508 8 11 1
Con 31 403,958 386,045
Yorkshire 52 701,856 61 LLI 40 570,544 321,622 28 39 9
Con 12 131,312 239,067
North 32 430,594 38 LLI 25 375,574 200,583 18 28 6
Con 7 55,020 142,388
ENGLAND 461 5,793,674 505 LLI 222 2,940,425 2,345,441 7
Con 239 2,853,249 2,377,185 17 5
Wales and
Monmouth 34 425,714 37 LLI 31 388,507 210,525 28 31 9
Con 3 37,207 121,013
Scotland 72 785,391 68 LLI 61 678,395 372,313 50 50 10
Con 11 106,996 277,183
Subtotal 567 7,004,779 610 LLI 314 4,007,327 2,928,279 61 88 14
Con 253 2,997,452 2,775,381
Ireland 103 688,284 60 LLI 84 536,675 350,029 65 34 24
Con 19 151,609 146,982
Total 670 7,693,063 670 LLI 398 4,544,002 3,278,308 126 122 38
Con 272 3,149,061 2,922,363
Majority 126 1,394,941 355,945
APPENDIX VI
PREFERENTIAL VOTING: THE TRANSFER OF SUPERFLUOUS VOTES
(A Memorandum by the Rt. Hon. J. Parker Smith)[1]
(1) _The Element of Chance Involved: Its Magnitude_
An objection, which occurs to every one who considers schemes of
Preferential Voting, is that an element of chance is introduced into the
result by the methods for the transfer of the superfluous votes of
successful candidates. Supposing one part of the supporters of A, a
successful candidate, have put down B as their second choice, and the
remainder C, and that a certain number of A's votes are superfluous, and
have to be transferred, how is it to be determined what number of AB
votes, as they may be called, and what number of AC votes shall be
transferred? If the question is settled by chance, as, by drawing the
necessary number at random from A's heap, by declaring that voting
papers shall be used in the order in which they were handed in at the
polling booths, or by laying down any other set of arbitrary rules to
determine the order in which they shall be counted, an element of
uncertainty is introduced by which there seems to be serious danger that
B and C will gain or lose unfairly.
Those who are accustomed to dealing with statistics will be prepared to
find this danger less than might have been expected; but even they will
be surprised to find of how small importance the arbitrary element is
discovered, by actual calculation, to be.
The difficulty can be made clear by a numerical instance. Take the case
of an election for several seats, where the necessary quota is 6000, and
where a favourite candidate, whom we will call A, has received the first
votes of 10,000 voters. Though all those voters have agreed in putting
the same candidate first, they are divided as to who may wish to be
returned next. Six thousand of them put B as their second choice, and
the other 4000 C. If the 6000 votes which A requires are drawn wholly
from the AB votes, the result of the transfer will be that C is credited
with 4000 votes and B with none. This would be clearly unfair, for, in
reality, B has received among A's voters much more support than C. To
use up the 4000 AC votes and only 2000 AB votes, and to transfer 4000
votes to B and none to C would be equally unfair to C. The course which
is exactly fair to both B and C is that the votes which are transferred
should be divided between them in the same proportion as that in which
the opinions of the whole number of A's supporters is divided. That is
to say, strict justice will be done if every 1000 votes which are used
or transferred are made up of 600 AB votes and 400 AC votes.
Accordingly, A's quota of 6000 must be made up of 3600 AB votes and 2400
AC votes, and the 4000 papers left to be transferred will consequently
consist of 2400 votes for B and 1600 votes for C.
This principle avoids all uncertainty, and is indisputably fair. It
remains to consider how to carry it into effect. In most cases there
would, in reality, be many more classes of votes than in the instance
taken above. Even in such cases it is practicable, as will presently be
shown, to divide the votes proportionately by an actual process of
counting and separation. A certain amount of complication is, of course,
introduced, but the extra labour involved does not seem impossible. The
question whether this extra labour is necessary must be answered by
examining the magnitude of the evil which it is sought to remedy.
If the votes are counted in a random order, it is clear there is a
probability that the order in which they are drawn will correspond to
the total numbers of each class in the ballot-box. It is reasonable to
expect that when there are 10,000 ballot papers in an urn the
composition of the first thousand drawn out will nearly be the same as
that of any other thousand, or of the whole 10,000. The amount of this
probability may be determined mathematically, and is very great.
This fact was clearly seen by Mr. Andrae, the statesman by whom the
method of preferential voting was introduced into Denmark in 1855, and a
mathematician of undisputed eminence. In answer to an objection of the
kind now under discussion, he replied: "If this law of mine had already
been in operation over the whole of Europe (including Turkey), for a
period of 10,000 years, and if the elections in every part of Europe to
which the law was applied were to take place, not every one, or three,
or seven years, but every week in regular repetition, these elections
throughout Europe, at the rate of a general European election per week,
would still have to go on for more than a thousand times the period of
years already stated; that is to say, for more than a thousand times ten
thousand years, before the chances would be equal that the voting papers
should come out of the urn in the order required to form the basis of
this problem. Although, therefore, the supposed combination is,
mathematically speaking, only an enormous improbability, yet,
practically speaking, it is absolutely impossible."[2]
To state the matter more exactly, and as the result of an independent
mathematical investigation, it appears that in the case we have stated,
if 4000 voting papers were drawn out of A's heap at random, instead of
the papers being carefully sorted and proportionately divided, the
probability is that neither B nor C would gain or lose more than 11
votes. In other words, it is just even betting that the number of AB
votes in the 4000 drawn would lie between 2411 and 2389 (inclusive), and
consequently that the number of BC votes will lie between 1589 and 1611.
The odds are more than 3 to 1 neither B nor C would gain or lose more
than 20 votes, _i.e._ that the number of AB votes drawn will lie between
2420 and 2380; more than 10 to 1 that neither would gain or lose more
than 30 votes; just 50 to 1 that neither would gain or lose more than 40
votes; and about 2000 to 1 that neither would gain or lose more than 60
votes. If the number of classes were larger or the number of votes to be
drawn smaller, the effect would be much less. It will thus be seen
that it is only in the case of very closely contested elections that the
element of chance can affect the result. It will also be observed that
the _element of chance will not be of importance as between the
different parties,_ but only as _between different individual candidates
of the same party_, since in almost all cases the electors who are
agreed upon the candidate they most desire will also put for their
second choice candidates of the same party.
In closely contested elections it must, of course, be admitted that as a
result of this method, chance might decide which of two candidates of
the same party should be elected. But in closely contested elections in
large constituencies so many elements of chance are always and
necessarily involved, that the introduction of a fresh one does not, in
reality, make the result more arbitrary. Putting aside all the slight
influences which at the last moment decide a score or two of
featherweight votes, and assuming that every voter is profoundly
convinced of the truth of his opinions, there remains the question of
boundaries. A slight change in the line of the boundaries of the
constituency might easily make a difference of fifty votes--a larger
difference than what we are concerned with. To carry the dividing lines
from North to South instead of from East to West, would, in many
localities, completely alter the character of the representation.
These are, in reality, matters of chance, and more arbitrary in their
nature than the order in which voting papers are drawn from an urn.
(2) _Method of Eliminating the Chance Element_
If, however, special precautions are still thought necessary, the
following method of counting the votes appears to reduce, as far as
practicable, the element of chance involved in the transfer of
superfluous votes:--
The whole set of voting papers of the constituency being mixed, the
papers, not yet unfolded, are drawn out one by one. Each is stamped, as
it is drawn, with a corresponding number, 1, 2, ... in order. It is then
unfolded, and sorted according to the names of the candidates marked
first and second upon it. Suppose there are six candidates, A, B, C, X,
Y, Z; the votes of any candidate, A, will be sorted into six heaps,
viz., A votes (_i.e._ votes where A only is voted for), AB, AC, AX, AY,
and AZ votes. If A is found to have received more votes than he
requires, the order in which the votes will be counted to him will be as
follows: Use first the A votes, then use up those heaps where the second
name also is that of a candidate who has received more than the
necessary minimum. If these heaps give A more than he requires, take the
same proportion out of each of such heaps, taking out of each heap the
last drawn votes first. If, however, these heaps are used up without
giving A as many votes as he requires, take an equal proportion of the
votes of each of the remaining heaps--taking out of each heap the last
drawn votes first.
_Example_.--Take an election where 6000 is the necessary minimum, and
suppose A has 8650 votes, composed as follows:
A 600
AB 2,700
AC 4,500
AX 50
AY 200
AZ 600
-----
8,650
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 classes--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 Municipal 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 MUNICIPAL 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.
(4) The surplus votes of any candidate elected under this rule who has
received more than the quota shall be distributed in the manner directed
by and subject to the conditions of the last preceding rule.
_Further distributions_.
8. The process directed by the last rule shall be repeated on the
successive exclusions one after another of the candidates with the
lowest numbers of votes until the last vacancy is filled either by the
election of a candidate with the quota or under the next following rule.
_Filling the last vacancy_.
9.--(1) When the number of continuing candidates is reduced to the
number of vacancies remaining unfilled, the continuing candidates shall
be declared elected.
(2) When only one vacancy remains unfilled and the votes of some one
continuing candidate exceed the total of all the votes of the other
continuing candidates together with any surplus votes not transferred,
that candidate shall be declared elected.
(3) When more than one vacancy remains unfilled and the votes of the
candidate, who, if all the vacancies were filled by the successive
elections of the continuing candidates with the largest numbers of
votes, would be the last to be elected, exceed the total of all the
votes of the continuing candidates with fewer votes than himself
together with any surplus votes not transferred, that candidate and all
the other continuing candidates who have not less votes than himself
shall be declared elected.
(4) When only one vacancy remains unfilled and there are only two
continuing candidates, and those two candidates have each the same
number of votes and no surplus votes remain capable of transfer, one
candidate shall be declared excluded under the next following rule and
the other declared elected.
_Provisions for exclusion of candidates in special cases._
10. If at any time when a candidate has to be excluded under these rules
two or more candidates have each the same number of votes, regard shall
be had to the number of votes counted to each candidate under Rule 1,
and the candidate lowest on that count shall be excluded, but, if the
numbers of votes on that count were equal, the returning officer shall
decide which candidate shall be excluded.
_Public notice of transfers._
11. The returning officer shall record and give public notice of any
transfer of votes made under these rules and of the total number of
votes counted to each candidate after any such transfer in addition to
the particulars prescribed by Rule 45 to the First Schedule to the
Ballot Act, 1872. Such public notice may be in accordance with the form
given in the appendix to these rules.
_Recounts._
12.--(1) Any candidate or his agent may at any time during the counting
of the votes, either before the commencement or after the completion of
the transfer of the votes (whether surplus or otherwise) of any
candidate, request the returning officer to recount the papers then
comprised in the parcels of all or any candidates (not being papers set
aside as finally dealt with) and the returning officer shall forthwith
recount the same accordingly. The returning officer may also at his
discretion recount votes either once or more often in any case in which
he is not satisfied as to the accuracy of any previous count. Provided
that nothing herein shall make it obligatory on the returning officer to
recount the same votes more than once.
(2) If upon an election petition--
(i) any ballot papers counted by the returning officer are rejected as
invalid,
or
(ii) any ballot papers rejected by the returning officer are declared
valid,
the court may direct the whole or any part of the ballot papers to be
recounted and the result of the election ascertained in accordance with
these rules.
(3) Except as in this rule expressly provided, no recount shall be had
whether on an election petition or otherwise.
_Determination of questions as to transfers.
13.--(1) If any question shall arise in relation to any transfer, the
decision of the returning officer, whether expressed or implied by his
acts, shall be final unless an objection is made by any candidate or his
agent before the declaration of the poll, and in that event the decision
of the returning officer may be reversed upon an election petition.
(2) If any decision of the returning officer is so reversed, the
transfer in question and all operations subsequent thereto shall be
void, and the court shall direct what transfer is to be made in place
thereof, and shall cause the subsequent operations to be carried out and
the result of the election to be ascertained in accordance with
these rules.
_Definitions_.
14. In these rules--
(1) The expression "votes capable of transfer" means votes given on
ballot papers on which a further preference is indicated for a
continuing candidate. Provided that a vote shall be deemed not capable
of transfer in any case in which--
(a) The names of two or more candidates (whether already excluded from
the poll or declared elected or not) are marked with the same figure and
are next in order of preference, or
(b) The name of the candidate to whom the transfer is to be made or of
some candidate (whether continuing or not) higher in the order of the
voters' preference is marked
(i) by a figure not following consecutively after some other figure on
the ballot paper, or
(ii) by two or more figures.
(2) The expression "continuing candidates" means candidates not already
declared elected or excluded from the poll.
APPENDIX TO SCHEDULE
EXAMPLE OF AN ELECTION CONDUCTED ON THE SYSTEM OF PROPORTIONAL
REPRESENTATION SET OUT ABOVE
Let it be assumed that there are five members to be elected, and that
there are ten candidates.
The valid papers are drawn from the general heap of ballot papers and
arranged in separate parcels under the names of the candidates marked
with the figure 1. (Rule 1.)
Each separate parcel is counted (Rule 1) and the total of all the valid
votes is ascertained (Rule 2). It is found that the total of all the
valid votes is 6000.
This total is divided by six (_i.e._ the number which exceeds by one the
number of vacancies to be filled), and 1001 (_i.e._ the quotient 1000
increased by one) is the number of votes sufficient to elect a member,
and is called the "quota" (Rule 2).
The result of the count may be supposed to be as follows:--
A 2,009 Elected
B 952
C 939
D 746
E 493
F 341
G 157
H 152
I 118
K 93
-----
6,000
A's votes exceed the quota and he is declared elected (Rule 3).
_First Transfer_.
It now becomes necessary to transfer A's surplus votes (Rule 4 (1)). A
has in fact (2009 less 1001 or) 1008 surplus votes. All A's 2009 voting
papers are examined and arranged in separate sub-parcels according to
the second preferences indicated thereon (Rule 4 (1) (_a_)). A separate
sub-parcel is also formed of those papers on which no second preference
is shown, and which are therefore not capable of transfer. (Rule 4 (1)
(_b_).) The result is found to be as follows. (Rule 4 (1) (_c_).)
A second preference is shown for G on 1,708 papers
" " " D " 257 "
" " " E " 11 "
" " " F " 28 "
-----
Total of votes capable of transfer 2,004 "
No second preference is shown on 5 "
-----
Total of A's votes 2,009
The total number of votes to be transferred is 1008, and it is necessary
that they should be taken from the several sub-parcels in the
proportions which the latter bear to all the votes capable of transfer;
that is, there must be transferred, _e.g.,_ to G a number of votes
bearing the same proportion to 1008, the total to be transferred, as
1708, the number of votes in G's sub-parcel, bears to 2004, the total of
votes capable of transfer. In other words the number of the ballot
papers on which each candidate is next preference must be multiplied by
a fraction of which the surplus is the numerator and the total of votes
capable of transfer the denominator, in order to ascertain the number of
votes to be transferred to the candidate in question. In making the
transfers fractions of votes are neglected (Rule 4 (1) (
e) and (f)).
The process is as follows:--
To G there are to be transferred 1,708 x 1,008 / 2,004 = 589 votes
" D " " " 257 x 1,008 / 2,004 = 129 "
" E " " " 11 x 1,008 / 2,004 = 5 "
" F " " " 28 x 1,008 / 2,004 = 14 "
-------
1,007
859, 129, 5 and 14 votes are now transferred to G, D, E, and F
respectively, the particular voting papers taken being those last filed
in their sub-parcels, and therefore at the top of the sub-parcels. These
voting papers are added in separate sub-parcels to G, D, E, and E (Rule
4 (2)).
Their totals then become--
G . . . . . 157 + 859 = 1,016
D . . . . . 746 + 129 = 875
E . . . . . 493 + 5 = 498
F . . . . . 341 + 14 = 355
All the other voting papers in A's parcel (1002 in number) are set aside
as finally dealt with (Rule 4 (3)), the figure 1002 being the quota 1001
with the addition of the one further vote of the surplus which, owing to
the disregard of fractions, is not transferred. G having obtained more
than the quota is now declared elected (Rule 5), and the poll stands as
follows:--
A 1,002 Elected
G 1,016 Elected
B 952
C 939
D 875
E 498
F 355
H 152
I 118
K 93
_Second Transfer_
G has now more than the quota, and his surplus votes (1016 less 1001 or
15) would have to be transferred (Rule 6(1)) were it not for the
provisions of Rule 6(7). But under that rule, the process of
transferring a surplus is postponed in a case where the surplus is less
than the difference between the two lowest candidates on the poll, and
where, therefore, the transfer would produce no practical effect. In
this case the difference between I and K, the two lowest candidates, is
118 - 93, or 25, and therefore it is not necessary to transfer
G's surplus.
The returning officer proceeds to distribute the votes of the candidates
with the smallest totals (Rules 7 and 8).
K's parcel is therefore examined and is found to contain 89 papers on
which F is next preference, and 4 on which C is next preference.
Therefore 89 votes are transferred to F and 4 to C.
The poll now stands--
A 1,002 Elected
G 1,016 Elected
B 952
C 943
D 875
E 498
F 444
H 152
I 118
No further candidate has the quota.
_Third Transfer_
The difference between I and H exceeds G's surplus, which therefore is
allowed to remain (Rule 6 (7)), and the votes of I as now lowest on the
poll have now to be distributed in the same manner as K's (Rule 8). But
as the combined votes of H and I, together with G's surplus (152 + 118 +
15 = 285), are less than 444, the total of F, the next highest
candidate, the returning officer avails himself of Rule 7 (2), and
distributes both H and I's votes at one operation.
I's parcel is found to contain 107 papers on which D and 11 on which B
is next preference, and H's parcel is found to contain 108 papers on
which B is next preference, and 44 on which there is no available
preference marked. (In some cases, some or one of A, G, I, H, and K are
marked as next in order of preference on the papers examined, but as all
of them are already either elected or excluded they are left out of
account.) Therefore, 107 votes are transferred to D, and 119 (108 + 11)
to B, while 44 are set aside as finally dealt with (Rule 7 (1)). The
result is to give B the quota, and he is declared elected.
The poll now stands--
A 1,002 Elected
G 1,016 Elected
B 1,071 Elected
D 982
C 943
E 498
F 444
_Fourth Transfer_
B has now a surplus of 70 votes, and it is necessary to distribute this
(Rules 7 (4), 6, and 4) as it exceeds the difference between E and F,
which is 54 (Rule 6 (7)).
For this purpose only the 119 votes last transferred are taken into
account (Rule 6 (2)).
These are examined and arranged in sub-parcels, in the same manner as
A's votes were examined and arranged, with the following result: A next
preference is shown for E on 84 papers. No further preference is shown
on 35 papers. The total number of votes capable of transfer (84) is thus
greater than the surplus (70), but, as there is only one possible
transfer, the process is simple: 84 x 70/84 = 70; and so the 70 votes
last filed in E's sub-parcel are transferred to E.
The poll now stands--
A 1,002 Elected
G 1,016 Elected
B 1,001 Elected
D 982
C 943
E 568
F 444
_Fifth Transfer_
G's surplus is still not distributable (Rule 6(7)), but F is now lowest
on the poll and his votes have to be distributed (Rule 8).
On examination it is found that of F's 444 papers, 353 show a next
preference for C, and the remainder, 91, contain no further preference.
The 353 are transferred to C, who thus has more than the quota, and is
declared elected, and the 91 are set aside as finally dealt with (Rule
7(1)).
The poll now stands--
A 1,002 Elected
G 1,016 Elected
B 1,001 Elected
C 1,296 Elected
D 982
E 568
This terminates the election; for, even if all C's surplus votes (295)
and all G's surplus votes (15) were transferred to E, his poll would
only amount to 878. But D's votes (982) exceed this total, D is
therefore declared elected (Rule 9 (2)).
The final result is that A, G, B, C, and D are elected.
Public Notice of the Result of the Poll and of the Transfer of Votes
Number of valid votes ... 6,000
Number of members to be elected ... 5
Quota ... 1,001
[column names-- ]
N: Names of Candidates
V: Votes
TA: Transfer of A's surplus
RA: Result
TK: Transfer of K's Votes
RK: Result
THI: Transfer of H and I's Votes
RHI: Result
TB: Transfer of B's surplus
TB: Result
TF: Transfer of F's Votes
RF: Final Result
N: V: TA: RA: TK: RK: THI: RHI: TB: TB: TF: RF:
A 2,009 -1,007 1,002 -- 1,002 -- 1,002 -- 1,002 -- 1,002(E)
B 952 -- 952 -- 952 +119 1,071 -70 1,001 -- 1,001(E)
C 939 -- 939 + 4 943 -- 943 -- 943 +353 1,296(E)
D 746 +129 875 -- 875 +107 982 -- 982 -- 982(E)
E 493 + 5 498 -- 498 -- 498 +70 568 -- 568
F 341 + 14 355 +89 444 -- 444 -- 444 -444 --
G 157 +859 1,016 -- 1,016 -- 1,016 -- 1,016 -- 1,016(E)
H 152 -- 152 -- 152 -152 -- -- -- -- --
I 118 -- 118 -- 118 -118 -- -- -- -- --
K 93 -- 93 -93 -- -- -- -- -- -- --
___ ___ ___ ___ ___ ___
Effective votes
6,000 -- 6,000 -- 6,000 -- 5,956 -- 5,956 -- 5,865
Preferences exhausted
-- -- -- +44 44 -- 44 +91 135
Total valid votes
6,000 -- 6,000 6,000 -- 6,000 -- 6,000 -- 6,000
[Candidates A, B, C, D, and G are elected.]
[Footnote 1: The rules contained in this schedule were examined and
approved by the Select Committee of the House of Lords in 1907. They are
substantially identical with those embodied in the Transvaal Municipal
Act of 1909, and used in the municipal elections of Pretoria and
Johannesburg in 1909, as well as in the model elections conducted by the
Proportional Representation Society in 1906, 1908, and 1910.]
APPENDIX VIII
THE SINGLE TRANSFERABLE VOTE
SCHEDULE (4) OF TASMANIAN ELECTORAL ACT, 1907
In this Schedule, unless the contrary intention appears--