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.