_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 const.i.tuencies, with the result that the majority in each of these const.i.tuencies 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 const.i.tuencies_.]

In order to achieve this result several changes in electoral mechanism are required. In the first place, Birmingham, instead of being divided into seven const.i.tuencies, must be polled as one const.i.tuency, otherwise the necessary grouping could not take place. This change is not in itself sufficient, because if Birmingham were polled as one const.i.tuency 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 const.i.tute 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. Const.i.tuencies 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 ent.i.tled.

_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 const.i.tuency 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 const.i.tuency the quota is one more than a third, for not more than two candidates can poll so much; in a three-member const.i.tuency, one more than a fourth, and so on. In a seven-member const.i.tuency, 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 I had been marked, and in this way the number of votes recorded for each candidate would be ascertained. Let us a.s.sume 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 ent.i.tled. 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 a.s.sumed 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 const.i.tuency 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 Munic.i.p.al 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 ill.u.s.tration 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. a.s.sume 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 ent.i.tled 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 const.i.tuting 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