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