Proportional Representation: A Study in Methods of Election

by John H. Humphreys

CHAPTER VII

THE SINGLE TRANSFERABLE VOTE

"The law regulating the form of voting may be thus expressed. Every vote shall be given on a document setting forth the name of the candidate for whom it is given; and if the vote be intended, in the events provided for by this Act, to be transferred to any other candidate, or candidates, then the names of such other candidate, or candidates, must be added in numerical order."—Thomas Hare, The Election of Representatives (Fourth edition, 1873)

The single transferable vote was the distinguishing characteristic of the scheme of electoral reform proposed by Hare in 1857, but it was associated with the proposal to treat the whole kingdom as a single constituency. The later advocates of this new method of voting have recommended its application to constituencies of more moderate size, such as counties and large towns, and in this form the system has found a more ready acceptance and has been used with success in parliamentary elections.

Its present application.]

The first application of the single transferable vote took place in Denmark[1] in 1855, and it is still being used under the Constitution of 1867 in the election of members of the Danish Upper House. It is also used, as provided by the South Africa Act of 1909, in the elections of the Senate of the United Parliament and in the election of the Executive Committees of the Provincial Councils. In each of these cases the electorates are small, and the electors possess special qualifications. The Danish Upper House is elected in two stages, the transferable vote being used only in the final stage in which electors of the second degree alone take part. In South Africa the members of the first Senate were elected by members of the local parliaments of the several Colonies,[2] and the Executive Committees of the Provincial Councils by members of the Councils. The system has, however, been subjected to the test of popular parliamentary elections in Tasmania and of municipal elections in Pretoria and Johannesburg.

Ever since the publication of Hare's scheme, proposals for proportional representation have been associated in English-speaking countries with the idea of a transferable vote. Hare's proposals were warmly endorsed by John Stuart Mill first in Representative Government, and again in a memorable speech delivered in the House of Commons on 30 May 1867, when he moved an amendment to the Electoral Reform Bill.[3] Mill's amendment was defeated, but he retained to the full his faith in the great value and need of the improved method of voting, as the following passage from his Autobiography shows: "This great discovery," said he, "for it is no less, in the political art, inspired me, as I believe it has inspired all thoughtful persons who have adopted it, with new and more sanguine hopes respecting the prospects of human Society, by freeing the form of political institutions towards which the whole civilized world is manifestly and irresistibly tending from the chief part of what seemed to qualify and render doubtful its ultimate benefits. … I can understand that persons, otherwise intelligent, should, for want of sufficient examination, be repelled from Mr. Hare's plan by what they think the complex nature of its machinery. But any one who does not feel the want which the scheme is intended to supply; any one who throws it over as a mere theoretical subtlety or crochet, tending to no valuable purpose and unworthy of the attention of practical men, may be pronounced an incompetent statesman, unequal to the politics of the future."[4]

An English movement.]

The English advocates of proportional representation who have succeeded Mill have equally favoured the single transferable vote. This system was embodied in the Bill introduced into the House of Commons in 1872 by Mr. Walter Morrison, Mr. Auberon Herbert, Mr. Henry Fawcett, and Mr. Thomas Hughes; it was advocated in the important debates which took place in the House of Commons in 1878 and 1879; and the Proportional Representation Society, founded in 1884 in view of the Electoral Reform Bill of that year, created, under the leadership of Sir John Lubbock and Mr. Leonard Courtney, a strong movement in its favour. Owing to the agreement between the leaders of the Liberal and Conservative parties in favour of single-member constituencies this movement had no immediate result. Since its revival in 1905 the Proportional Representation Society has continued to press the claims of the single transferable vote, and with some success. The practicability of the system was admitted by the Select Committee of the House of Lords appointed to examine the Municipal Representation Bill introduced into that House by Lord Courtney in 1907; the model elections organized by the Society in 1906, 1908, and 1910,[5] have to some extent familiarized the British public with its details; it found, as already mentioned, a place in the South African Constitution of 1909, whilst the Royal Commission on Electoral Systems reported in 1910 that "of schemes for producing proportional representation we think that the transferable vote would have the best chance of ultimate acceptance."

The system in brief.]

What then is the single transferable vote, and how does it help to secure a true representation of the electors? Its mechanism and advantages will best be understood by a comparison with the existing system. The city of Birmingham is at present divided into seven single-member constituencies, with the result that the majority in each of these constituencies secures a representative, while the minority in each case is unrepresented. Suppose there were in Birmingham 40,000 Unionist, 20,000 Liberal, and 10,000 Labour voters: it might easily happen that the Unionists would be in a majority in each of the seven divisions and, if so, the 40,000 Unionist electors would obtain the seven seats and the remaining 30,000 voters none. The transferable vote, as will presently appear, would enable these 70,000 citizens to group themselves into seven sections of equal size, each returning one member, so that there would be four Unionist groups returning four members, two Liberal groups returning two members and one Labour group returning one member; and this is the ideal representation of such a community.

Large constituencies.]

In order to achieve this result several changes in electoral mechanism are required. In the first place, Birmingham, instead of being divided into seven constituencies, must be polled as one constituency, otherwise the necessary grouping could not take place. This change is not in itself sufficient, because if Birmingham were polled as one constituency electing seven members, and if each elector could give, as with the "block" vote, one vote apiece to seven candidates, then the seven nominees of the majority would all receive a higher number of votes than the seven nominees of the minority. In the numerical case cited above, each Unionist candidate would command 40,000 votes, each Liberal 20,000, and each Labour candidate 10,000, and the largest party would win all the seats.

The single vote.]

It is therefore necessary, however many may be the number of members to be elected, to limit the voting power of each elector to one vote—hence the name "the single vote." An obvious result of this limitation is that if a group numbering 10,000 electors concentrates its support upon one man, then the group is certain of returning that candidate, because not more than six equally large groups can be formed out of the remaining electors. With open voting the grouping of electors could be arranged with comparative ease, for if more electors than were sufficient to constitute his group desired to vote for a particular candidate, those who arrived late at the poll could be asked to give their votes to another candidate, and so help to build up another group of the requisite size. Or, if a candidate was receiving so little support that he had no chance of election, the small group that had gathered round him could be disbanded and these electors, instead of having their votes wasted, could make their selection from among the other candidates available. In this way seven groups could be formed, each of which would obtain a representative.[6]

The vote made transferable.]

As, however, the ballot is secret and the result of the voting is not known until the close of the poll, some provision must be made to facilitate the equal grouping of the electors upon which fair representation depends. This will be made clear by an example. Were Mr. Joseph Chamberlain one of the Unionist candidates for Birmingham, the group of voters who would record their votes for him would probably considerably exceed the number required for his election. His Unionist colleagues might, in consequence, find themselves left without adequate support, and the party might fail to secure its fair share of the representation. In order to prevent a mischance of this kind the very simple device has been adopted of making the vote transferable. By this means the necessary accuracy in grouping is secured automatically.

How votes are transferred.]

The transferable vote enables the elector to instruct the returning officer to whom his vote is to be transferred in the event of his first favourite either receiving more support than he requires or receiving so little as to have no chance of election. Continuing the example already given, an elector who desired to vote for Mr. Chamberlain would place on the ballot paper the figure 1 against his name. If, in addition, he placed the figures 2, 3, &c. against the names of other candidates in the order of his choice, these figures would instruct the returning officer, in the event of Mr. Chamberlain obtaining more votes than were necessary to secure his election, as to whom the vote was to be transferred. The votes given to Mr. Chamberlain in excess of the number required for his election would thus be rendered effective. They would be used and not wasted. If, on the other hand, an elector had recorded his vote for a candidate who, after all excess votes had been transferred, was found to be at the bottom of the poll, the returning officer would similarly give effect to the wishes of the elector as recorded on the ballot paper by transferring the vote to the elector's second choice. Again the vote would not be wasted, but would be used in building up a group sufficiently large to merit representation.

The ideas which have led up to the single transferable vote are, therefore, of a simple character. Constituencies returning several members are formed. A representative is given to every group of electors which attains to a definite proportion of the whole, the proportion depending upon the number of members to be returned. If a candidate receives more votes than are sufficient, i.e. if too large a group is formed, the surplus votes are transferred. If, after all surplus votes have been transferred, there still remain more candidates than there are vacancies, the lowest candidate on the poll is eliminated from the contest, i.e. the smallest group is disbanded. The transfer of surplus votes and of votes recorded for the candidates lowest on the poll are all carried out in accordance with the wishes of the electors as indicated by them on the ballot paper at the time of the poll. The proportionate representation of all the electors is secured; each party obtains the number of members to which it is entitled.

The Quota.

A few questions will at once occur to the reader as to the application of these simple rules. How is the number of votes required for success to be determined? In what way are the surplus votes to be distributed? What is the order in which the elimination of unsuccessful candidates shall proceed? The number of votes necessary to secure the election of a candidate is called the "quota." At first sight it would seem that this number should be ascertained, as suggested in the preceding paragraphs, by dividing the number of votes by the number of vacancies. But a smaller proportion is sufficient. Thus, in a single-member constituency a candidate has no need to poll all the votes; it is evident that if he polls more than a half he must be elected. No other candidate can equal him; the quota in this case is, therefore, one more than a half. So, in a two-member constituency the quota is one more than a third, for not more than two candidates can poll so much; in a three-member constituency, one more than a fourth, and so on. In a seven-member constituency, like that of Birmingham, the quota would be one more than an eighth. In general terms the quota is ascertained by dividing the votes polled by one more than the number of seats to be filled and adding one to the result.[7]

A simple case.

The processes involved in distributing the votes are described at some length in the account which appears further on in this chapter of the model election organized by the Proportional Representation Society in 1908, but the method of transferring votes and deciding the result of an election may be more easily understood from a simple case. Let us imagine there are six candidates for three seats, of whom A, B, C belong to one party and X, Y, Z to another. On the conclusion of the poll the ballot papers would be sorted into heaps, or files, corresponding to the names against which the figure 1 had been marked, and in this way the number of votes recorded for each candidate would be ascertained. Let us assume that the result of the sorting is as follows:—

A is marked 1 upon 1801 papers, and therefore has 1801 votes
B " 1 " 350 " " 350 "
C " 1 " 300 " " 300 "
X " 1 " 820 " " 820 "
Y " 1 " 500 " " 500 "
Z " 1 " 229 " " 229 "
—— ——
Total number of papers 4000 Total number of Votes 4000

As there are three seats the quota is one more than a fourth of the total of the votes polled. The total in this case is 4000, and the quota is therefore 1001.

A, having obtained more than the necessary quota of votes, is declared elected.

The transfer of surplus votes.

It will be seen that A has obtained nearly two quotas of votes, and his supporters, in the absence of any provision for the use of his surplus votes, would not obtain the full share of representation to which they are entitled. The next step is therefore to transfer A's surplus votes in accordance with the wishes of his supporters. These have indicated on the ballot papers to whom they desire their vote to be transferred. The different methods in which the transfer of votes can be carried out will be described, but for the present it may be assumed that the result of the operation was to transfer:

648 of the 800 surplus votes to B (a member of the same party as A) 132 " 800 " C (also a member of A's party) 20 " 800 " Z

The votes transferred to the several candidates are added to those already obtained by them as follows:—

Original Votes. Transferred Votes. Total.
B 350 + 648 = 998
C 300 + 132 = 432
X 820 nil = 820
Y 500 nil = 500
Z 229 + 20 = 249

The elimination of the lowest unelected candidate.]

Had any candidate, as a result of the transfer of A's surplus votes, been raised above the quota he would have been declared elected and his surplus distributed in the manner just described. In this case no candidate, as the result of the transfer, has obtained the quota, and there are, therefore, no further surplus votes to distribute. There are, however, two vacancies still remaining unfilled, and the next operation is to distribute the voting papers of Z, who, being the lowest on the poll, is clearly out of the running. Z's papers are sorted, as in the previous process, according to the candidates who are marked by the voters as their next preferences, and it may be supposed that the result is as follows:—

B is marked as next preference on 20 papers
X " " 200 "
Y " " 29 "

These papers are then added to the heaps of the respective candidates, B, X, and Y, and, with these additions, the votes credited to each candidate may be shown thus:—

Previous Transfer of
Total. Z's Votes. Total.
B 998 + 20 = 1018
C 432 + nil. = 432
X 820 + 200 = 1020
Y 500 + 29 = 529

Since B and X, as a result of the distribution, each obtain a quota of votes, they are declared elected, and all the vacant seats now being filled, the election is at an end.

The result.

The candidates elected, A, B, and X, each represent a "quota" of voters. Each considerable section of the constituency is thus able to choose a representative, whilst the party to whom both A and B belong return two members, these candidates taken together having secured the support of two quotas of voters. The voters who failed to secure a representative, namely the supporters of C and Y, number less than a quota.

Different methods of transferring surplus votes.—The Hare Method.]

There are several methods by which surplus votes may be transferred. In the case imagined the simplest way to distribute A's surplus votes is to take the 800 papers last filed and to sort these papers according to the second preferences indicated thereon. This method, which was recommended by the advocates of proportional representation in the movement of 1884-85, is based upon that contained in Mr. Hare's proposals. It has, however, been objected that if some other 800 voting papers are taken the result may be different, and that in this way an element of chance is introduced. This objection is considered in detail in Appendix VI., and it will be sufficient to state here that, when large numbers of votes are dealt with and the papers are well mixed, this element of chance is negligible. But small as it is it can be eliminated by adopting more accurate methods of transferring the votes.

The Hare-Clark method

One of these more accurate methods was embodied in the Tasmanian Act of 1896, and also in the Municipal Representation Bill approved by the Select Committee of the House of Lords in 1907. It is known as the Hare-Clark system, its inception being due to Mr. Justice Clark, of Tasmania. With this method the surplus votes of any successful candidate are transferred to the unelected candidates in such a way that each unelected candidate marked as the voter's next preference on the successful candidate's papers receives a proportionate share of the surplus. Continuing with the illustration already given, the returning officer, instead of taking from A's heap the 800 papers last filed, takes the whole of A's heap and sorts all these papers according to the next preferences. Assume that the result is as follows:—

B is marked 2 on….. ……………… ..1296 papers
C " 2 on……… ………….. .. 264 "
Z " 2 on…………. ………. .. 40 "

Total papers showing second preferences .. 1600

Papers on which no further preferences are shown …201

Total of A's papers……………….. …1801

In this case there are 800 surplus votes, whilst there are in all 1600 papers on which next preferences have been marked. It is therefore clear that each of the candidates B, C, Z is entitled to receive one-half the papers on which his name has been marked as the next preference. Each of the three bundles of papers showing next preferences for B, C, Z are divided into two portions. One portion is transferred to the next preference, the other is retained for the purpose of constituting A's quota, in which is included the papers on which A's name is alone marked.

The complete operation is shown below:—

Candidate indicated as Number Number of Number of
next Preference. of next Papers Transferred Papers
Preferences. to the next Retained for
Preference. A's Quota.

B 1290 648 648
C 264 132 132
Z 40 20 20
—— —- —-
Total of next preferences 1600 800 800

Papers showing no further preference 201 — 201 —— —- ——

Totals 1801 800 1001

In this way each of the candidates B, C, and Z obtains in strict proportion that share of A's surplus to which he is entitled, and, so far as this operation is concerned, the element of chance is wholly eliminated.[8]

The papers selected for transfer, however, are those last filed in the process of sorting, and should it become necessary to transfer these papers a second time there would enter in this further distribution an element of chance which, as explained in the Appendix already referred to, is so trifling as to have no practical effect upon the result unless the number of electors is small as compared with the number of members to be elected.

The Gregory Method.

A third method, in which the element of chance is eliminated from every transfer, has been embodied in the Tasmanian Act of 1907. Whenever it is necessary to transfer surplus votes, the whole of the successful candidate's papers on which preferences are marked are transferred, but at a reduced value. In the example given the whole of A's papers on which next preferences had been marked for B, C, and Z would be carried forward to those candidates, but each paper would be transferred at the value of one-half, the remaining portion of the value of each paper having been used for the purpose of electing A. This method is known as the fractional, or Gregory, method of transfer, having been first suggested by Mr. J. B. Gregory of Melbourne, in 1880. The regulations for the conduct of elections contained in the Tasmanian Act are given in Appendix VIII.

The committee which investigated the working of this system as applied to the Tasmanian General Election of 1909, made a very valuable comparison between the rules contained in the Municipal Representation Bill[9] and the more exact rules of the Tasmanian Act. A fresh scrutiny, based on the rules of the Municipal Representation Bill, was made of all the ballot papers used in that election. It was found that in each district the same candidates were excluded in the same order and the same candidates returned as at the actual election. The same results would, therefore, have been attained and much labour saved if the rules of the Municipal Representation Bill had been used. This committee, however, in view of the fact that the more exact method had already been established in Tasmania, and that the ascertainment of the results only involved an expenditure of a few hours more time, and that there were no data available to show the frequency of close contests in which a small change in the distribution of votes might possibly affect the result, recommended that no change should be made in the law. Still it would seem that the rules of the Municipal Representation Bill are sufficiently exact for all practical purposes except where the number of electors is small. The fractional transfer is of course the most perfect from the mathematical point of view, but the Royal Commission on Electoral Systems, after a careful examination of its working, report that "we agree with the Proportional Representation Society in regarding the additional labour involved as greater than it is worth."[10]

Where the number of electors is small, however, it is not only desirable to carry out the transfers with the exactness prescribed by the Tasmanian rules, but in important elections, such as those of the Senators in South Africa, it is desirable to introduce a further modification. In transferring the votes in ordinary elections fractions of votes are ignored, because such fractions do not affect the result. Where, however, there are only a few electors such fractions may become important, and, for this reason, the regulations (see Appendix IX.) adopted by the South African Government for the election of Senators provided that each ballot paper should be treated as of the value of 100, or, in other words, that fractions should be taken into account as far as two places of decimals. The application of these regulations presented no difficulty; the counting of the votes in each of the four Colonies proceeded without the slightest hitch.

The Gove or Dobbs Method.

The methods of transfer hitherto described all enable the voter to maintain complete power over the disposal his vote. It has, however, been suggested that the candidate for whom the vote is recorded should have the privilege of deciding to whom it should be transferred. The suggestion was first made by Mr. Archibald E. Dobbs, who, in 1872, in a pamphlet entitled General Representation, made the proposal that before the date of the election each candidate should publish a schedule of the names of any of the other candidates to whom he desired his vote to be transferred. This method of transfer by schedule is usually known as the "Gove" method, and was contained in the Bill submitted by Mr. W. H. Gove to the Legislature of Massachusetts, in 1891. Section 7 of this Bill reads as follows: "Votes shall be transferred according to the request of the candidate for whom they were originally cast to a person named in the list furnished by said candidate before the date of the election." With this method the elector in recording his vote for any one candidate would have no independent power of indicating to whom the vote should be transferred, and Mr. Dobbs, in a later pamphlet[11] has suggested that the elector should be given the option of accepting the schedule of preferences published by the candidate, or of indicating his own. Mr. Dobbs thus gets rid of the compulsory acceptance of a schedule of preferences, a proposal to which most English-speaking electors would have an instinctive dislike. But even to an optional schedule certain objections remain. The system has lost in simplicity, and the order of the candidates in the particular schedules would be determined in most cases by the party organizations.

The transferability of votes is the connecting link between all these systems; it is the essential feature upon which depends the proportionate representation of the contending parties, and the mode of transfer is properly regarded as a matter upon which different views may be held. As regards the second and third systems of transfer outlined above—which so far are the only ones which have been put into practice—experience confirms the theoretical conclusions of mathematicians that, save in the case of small electorates, both methods yield the same result. The second method was that used by the Proportional Representation Society for the purpose of its model elections, and is now applied in the election of Municipal Councils in Johannesburg and Pretoria. A description of the Model Election of 1908 will serve to illustrate the various processes involved in the sorting and counting of votes.

The model election of 1908.

In this election it was assumed that the voters in a constituency returning five members were asked to make their choice among twelve candidates. These candidates were all well-known political men, and were chosen with an attempt at impartiality from the Liberal, the Unionist, and the Independent Labour parties. As no Irish newspaper was publishing the ballot paper, no Nationalist was included.[12] This ballot paper, a copy of which appears on page 147, was sent, accompanied by a short explanatory article, for publication to, and appeared in, the following newspapers: The Times, The Morning Post, The Spectator, The Nation, The Daily News, The Financial News, The Manchester Guardian, The Yorkshire Post, The Yorkshire Daily Observer, The Western Morning News, The Western Daily Mercury, The Glasgow Herald, The Dundee Advertiser, The Woolwich Pioneer, and The Labour Leader. Readers of the newspapers were asked to cut out the ballot paper, mark it and return it to Caxton Hall by the first post on the morning of Tuesday, 1 December 1908. Ballot papers were also circulated independently among members of the Proportional Representation Society and their friends. About 18,000 papers were returned by newspaper readers, and about 3700 by members of the Society and their friends. In all a constituency of 21,690 electors was formed, a number whose votes were enough, but not too many, for counting in a single evening.