The great improvement effected by the Swedish system.

The new Swedish electoral system, like all proportional systems, constitutes a striking advance upon the previous electoral conditions. The extent of the improvement will, of course, be seen from a comparison of some of its results with those of former years. For example, Stockholm used to be represented in the Lower Chamber by twenty-two members chosen by the "block" system, or scrutin de liste. The party in the majority monopolized the representation, and the absurdity of the system was well illustrated by an incident in the election of 1882, which was preceded by a severe struggle between the advocates of free trade and protection. At this election Stockholm returned twenty-two free traders, but as one of the elected members had not paid his taxes, all the voting papers containing his name were declared to be invalid. In consequence the twenty-two free traders were unseated and the twenty-two protectionist candidates were declared elected in their place. An attempt was made to ameliorate the evils of this system by dividing the town into five parliamentary districts, but, although so divided, Stockholm in 1908 returned twenty-one members, all of whom were either Liberals or Socialists, the large minority of Moderates being unrepresented. When the proportional system was applied in March 1910 to the election of the municipal council, each party obtained its fair share of representation in each of the six wards of the city, and the total result shows how large an improvement is effected by the new method:—

Parties. Votes Seats Seats in Obtained. Obtained. Proportion to Votes. Moderate 281,743 22 24 Liberal 142,639 12 12 Socialist 160,607 16 14 —————————————————- 584,989 50 50

In the election of the provincial council of Bleking the result was as follows:—

Parties. Votes Seats Seats in Obtained. Obtained. Proportion to Votes. ———————————— ———————————- Moderate 54,465 22 22.4 Liberal 36,595 10 15.1 Socialist 3,617 1 1.5 ————————————————— 94,677 39 39

The general fairness of these results is all the more remarkable, because in Stockholm there was a very considerable variation in the value of a vote in the different wards, whilst many of the constituencies in the province of Bleking returned only a few members, and these did not give full play to the proportional system. The figures confirm the experience of all other countries, that a proportional system, even when applied to comparatively small constituencies, yields results which approximate very closely to the ideal aimed at, the true representation of the electors.

[Footnote 1: The town councils were elected in one stage; each elector had one vote for every 100 kroner income, subject to a limit of 100 votes. The members of the town council, when electing members of the provincial councils, had only one vote each.]

[Footnote 2: A ballot paper is not declared invalid even if it contains the names of more candidates than there are members to be elected (except at the elections of parliamentary committees). The names in excess are regarded as suppleant candidates (see Election of Suppleants) to the number of two in the elections for the Riksdag and the town councils, and to a number equal to the number of members at the election for the provincial councils. Any additional names on a ballot paper are regarded as non-existent.]

[Footnote 3: This paper bore the signature of the elector.]

APPENDIX IV

THE FINLAND SYSTEM OF PROPORTIONAL REPRESENTATION

The influence of the Belgian system.

The system of proportional representation introduced into Finland by the electoral law of 1906, while it presents little or no difficulty to the voter, is, in its method of counting the votes, perhaps the most complicated of the systems at present in force. It has for its basis the Belgian List system and the d'Hondt rule, but the variations which were introduced with the object of safeguarding the rights of the electors against the possible tyranny of party managers are so important that at the first glance its resemblance to the parent system is not easily recognized. The Belgian model is followed more closely in the method of distributing the seats to the various parties than in the manner in which the successful candidates are chosen from the party lists. In its internal party arrangement the Finnish system shows boldness, originality, and, it must be added, no little complexity of procedure.

Schedules and "compacts" in place of lists.

Finland is divided into sixteen electoral districts returning from six to twenty-three members, with the one exception of Lapland, which is a single-member constituency. In each constituency any group of not less than fifty electors can put forward a schedule of not more than three candidates, however many may be the total number of members to be elected. Each of these schedules may be headed with the name of a party or some political motto. The persons responsible for these schedules may, and commonly do, combine them in groups known as "compacts," and it is these compacts, and not the original schedules, which correspond roughly to the party "lists" of the Belgian system, the only limit to this power of combination being that the combined schedules must not contain the names of more candidates than there are vacancies to be filled. But as the names of the same candidates may, and constantly do, occur in many different schedules within a single compact, a first glance at a Finnish polling paper would seem to show in each combination the names of more candidates than there are vacancies. The compact bears the name of the political party to which it belongs. Combination into compacts is, of course, optional, and a certain number of schedules are put forward independently. A vacant corner is reserved on the ballot paper where any elector who is not content with any of the schedules submitted may make his own schedule.

An election in Nyland.

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 Haeninan Social Dem. 40,951 6.5 40,957.5 3 Soderholm Swedish 22,272 0.33 22,272.33 4 Sillanpaeae Social Dem. 20,475.5 8.83 20,484.33 5 Kaekikoski Old Finn 20,402 9.33 20,411.33 6 Oljemark Swedish 14,848 — 14,848 7 Siren 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 Palmen Old Finn 10,201 8.83 10,209.83 12 Pertillae (E.) Social Dem. 8,190.2 4.67 8,194.87 13 Ahlroos Swedish 7,424 1 7,425 14 Pertillae (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—

"Returning Officer" means the Returning Officer for the District:

"Quota" means the number of votes sufficient to elect a candidate:

"Surplus" means the number of votes which a candidate has obtained, at any stage of the scrutiny, over and above the quota:

"First choice recorded for a candidate" means a voting-paper on which the number 1 is placed in the square opposite the name:

"Second choice recorded for a candidate" means a voting paper on which the number 2 is placed in the square opposite his name:

"Transfer value" means that portion of a vote which is unused by—

(a) an elected candidate who has obtained a surplus,

(b) a candidate excluded on account of his being lowest on the poll, and which is therefore transferred to the candidate next in the order of the voter's preference. The transfer value of all votes is either 1 or some fraction of 1.

METHOD OF COUNTING VOTES

First choice of each candidate to be counted.]

1. The number of first choices recorded for each candidate shall be counted, and all informal voting papers shall be rejected.

To find the quota.

2. The aggregate number of such first choices shall be divided by one more than the number of candidates required to be elected, and the quotient increased by one, disregarding any remainder, shall be the quota, and (except as hereinafter provided in Rule 10) no candidate shall be elected until he obtains a number of votes equal to or greater than the quota.

Candidates who have the quota to be declared elected.

3. Any candidate who has, upon the first choices being counted, a number of such votes equal to or greater than the quota shall be declared elected.

If first choices exactly equal to quota, voting papers to be set aside.

4. Where the number of such votes obtained by any candidate is equal to the quota, the whole of the voting papers on which a first choice is recorded for such elected candidate shall be set aside as finally dealt with.

If a surplus, surplus to be transferred.

5. Where the number of such votes obtained by any candidate is in excess of the quota, the proportion of votes in excess of the quota shall be transferred to the other candidates not yet declared elected, next in the order of the voters' respective preferences, in the following manner:—

Voting papers reexamined and second choices counted.

(i) All the voting papers on which a first choice is recorded for the elected candidate shall be re-examined, and the number of second choices, or (in the case provided for in Rule 12) third or next consecutive choices, recorded for each unelected candidate thereon shall be counted:

Find the transfer value. (ii) The surplus of the elected candidate shall be divided by the total number of votes obtained by him on the counting of the first choices, and the resulting fraction shall be the transfer value:

Multiply second choices by transfer value.

(iii) The number of second or other choices, ascertained in paragraph i, to be recorded second for each unelected candidate, shall be multiplied by the transfer value:

Add result on.

(iv) The resulting number, disregarding any fractional remainder, shall be credited to each unelected candidate, and added to the number of votes obtained by him on the counting of the first choices.

If more than one surplus, largest to be first dealt with.

6.—(a) Where, on the counting of the first choices or on any transfer, more than one candidate has a surplus, the largest surplus shall be first dealt with. If then more than one candidate has a surplus, the then largest surplus shall be dealt with, and so on: Provided that, if one candidate has obtained a surplus at a count or transfer previous to that at which another candidate obtains a surplus, the surplus of the former shall be first dealt with.

If surpluses equal, last difference to decide.

(b) Where two or more surpluses are equal, the surplus of the candidate who was the highest on the poll at the count or transfer at which they last had an unequal number of votes shall be first dealt with; and if they have had an equal number of votes at all preceding counts or transfers, the returning officer shall decide which candidate's surplus shall be first dealt with.

If transfer raises candidate up to or above quota, he is to be declared elected.

7.—(a) Where the number of votes obtained by a candidate is raised up to or above the quota by a transfer as aforesaid, he shall thereupon be declared elected. And in such case, notwithstanding the fact that he may have reached the quota, such transfer shall be completed, and all the votes to which he is entitled there from shall be transferred to him, but no votes of any other candidate shall be transferred to him.

If votes exactly equal quota, voting papers to be set aside.

(b) Where the number of votes obtained by a candidate is raised up to, but not above, the quota by a transfer as aforesaid, the whole of the voting papers on which such votes are recorded shall be set aside as finally dealt with.

If surplus created, surplus to be transferred.

(c) Where the number of votes obtained by a candidate is raised above the quota by a transfer as aforesaid, his surplus shall be transferred to the candidates next in the order of the voters' respective preferences, in the following manner:—

Voting paper of last transfer re-examined and third choices counted.

(i) The voting papers on which are recorded the votes obtained by the elected candidate in the last transfer shall be reexamined, and the number of third, or (in the case provided for in Rule 12) next consecutive choices recorded for each unelected candidate thereon counted:

Find the transfer value.

(ii) The surplus of the elected candidate shall be divided by the total number of voting papers mentioned in paragraph i, and the resulting fraction shall be the transfer value:

Multiply third choices by transfer value.

(iii) The number of second (or other) choices, ascertained in paragraph i, to be recorded for each unelected candidate, shall be multiplied by the last-mentioned transfer value:

Add result on.

(iv) The resulting number, disregarding any fractional remainder, shall be credited to each unelected candidate, and added to the number of votes previously obtained by him.

When all surpluses dealt with candidate lowest on poll to be excluded, and his votes transferred. 8.—(a) Where, after the first choices have been counted and all surpluses (if any) have been transferred as hereinbefore directed, no candidate, or less than the number of candidates required to be elected, has or have obtained the quota, the candidate who is lowest on the poll shall be excluded, and all the votes obtained by him shall be transferred to the candidates next in the order of the voters' respective preferences, in the same manner as is directed in Rule 5.

First choices to be transferred first.

(b) The votes obtained by such excluded candidate as first choices shall first be transferred, the transfer value of each vote in this case being 1.

Then other votes in order.

(c) The other votes of such excluded candidate shall then be dealt with in the order of the transfers in which, and at the transfer value at which, he obtained them.

Each transfer deemed a separate transfer.

(d) Each of the transfers which takes place under the two previous clauses of this rule shall be deemed for all purposes to be a separate transfer.

If transfer raises candidate up to quota, he is to be declared elected.

9.—(a) Where the number of votes obtained by a candidate is raised up to or above the by any such transfer as aforesaid, he shall thereupon be declared elected. And in such case, notwithstanding the fact that he may have reached the quota, such transfer shall be completed, and all the votes to which he is entitled therefrom shall be transferred to him, but no other votes shall be transferred to him.

If votes exactly equal to quota, voting papers to be set aside.

(b) Where the number of votes obtained by a candidate is raised up to, but not above, the quota by any such transfer as aforesaid, the whole of the voting papers on which such votes are recorded shall be set aside as finally dealt with.

If surplus created, surplus to be transferred.

(c) Where the number of votes obtained by a candidate is raised above the quota by any such transfer as aforesaid, his surplus shall be transferred to the candidates next in the order of the voters' respective preferences in the same manner as is directed in Rule 7, Clause (c): Provided that such surplus shall not be dealt with until all the votes of the excluded candidate have been transferred.

Surpluses to be dealt with before further exclusion.

(d) Where any surplus exists it shall be dealt with before any other candidate is excluded.

Process of exclusion to be repeated until there remain number of candidates required.

10. The same process of excluding the candidate lowest on the poll and transferring to other candidates his votes shall be repeated until all the candidates, except the number required to be elected, have been excluded, and the unexcluded candidates, who have not already been so declared, shall then be declared elected.

If lowest candidates equal last, difference to decide.

11. Where at any time it becomes necessary to exclude a candidate, and two or more candidates have the same number of votes and are lowest on the poll, then whichever of such candidates was lowest on the poll at the last count or transfer at which they had an unequal number of votes shall be first excluded, and if such candidates have had an equal number of votes at all preceding counts or transfers, the returning officer shall decide which candidate shall be first excluded.

If a candidate elected or excluded, his name not considered on voting paper.

12. In determining what candidate is next in the order of the voter's preference, any candidates who have been declared elected or who have been excluded shall not be considered, and the order of the voter's preference shall be determined as if the names of such candidates had not been on the voting paper.

Exhausted votes.

13. Where on any transfer it is found that on any voting paper there is no candidate opposite whose name a number is placed, other than those who have been already either declared elected or excluded, such voting paper shall be set aside as exhausted.

APPENDIX IX

THE SINGLE TRANSFERABLE VOTE

REGULATIONS FOR THE ELECTION OF SENATORS UNDER THE SOUTH AFRICA ACT, 1909

I. In these Regulations:—

(1) "Continuing Candidates" mean candidates not elected or not excluded from the poll at any given time.

(2) "First Preference" means the figure 1 set opposite the name of any candidate; "second preference" similarly means the figure 2; "third preference" the figure 3, and so on.

(3) "Unexhausted papers" mean ballot papers on which a further preference is recorded for a continuing candidate.

(4) "Exhausted papers" mean ballot papers on which no further preference is recorded for a continuing candidate, provided that a paper shall also be deemed to be exhausted in any case in which—

(a) The names of two or more candidates, whether continuing or not, are marked with the same figure and are next in order of preference, or

(b) The name of the candidate next in order of preference, whether continuing or not, is marked

(i) By a figure not following consecutively after some other figure on the ballot paper, or

(ii) By two or more figures.[1] (5) "Original Votes" in regard to any candidate mean the votes derived from ballot papers on which a first preference is recorded for such candidate.

(6) "Transferred Votes" in regard to any candidate mean votes, the value or part of the value of which is credited to such candidate and which are derived from ballot papers on which a second or subsequent preference is recorded for such candidate.

(7) "Surplus" means the number by which the value of the votes of any candidate, original and transferred, exceeds the quota.

II. (1) The Governor in Council shall by Proclamation fix a date on or before which every candidate for election shall be nominated by two members of the Legislature in writing addressed to the Clerk of the Legislative Assembly. Such nomination shall contain the candidate's full name and address, shall be signed by two members of the Legislature, and shall be accepted in writing by the candidate.

A nomination paper may include any number of names not exceeding eight, but no member shall sign more than one nomination paper, and no candidate shall sign a nomination paper on which his name appears. The Clerk of the Legislative Assembly shall, after consultation with the Assessors hereinafter referred to, reject all nominations not made in accordance with these regulations.

(2) Immediately after the date fixed for receiving nominations the Clerk of the Legislative Assembly shall make a return to the Governor in Council showing the names and addresses of the candidates who have been duly nominated, together with the names of the members who have nominated them. He shall at the same time certify that such nominations have been duly made in accordance with these regulations, and forward to the Governor-in-Council the certificate by the Assessors mentioned in Regulation IV. (2).

In case of disagreement between the Clerk of the Legislative Assembly and the Assessors, the Speaker of the Legislative Assembly shall, at the request of the Governor-in-Council, inspect the nomination papers, and his decision on the point at issue shall be final.