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Methods of Election.

By Professor E. J. Nanson. [Read 12th October, 1882.]

If there be several candidates for an office of any kind, and the appointment rests in the hands of several persons, an election is held to decide who is to receive the appointment. The object of such an election is to select, if possible, some candidate who shall, in the opinion of a majority of the electors, be most fit for the post. Accordingly, the fundamental condition which must be attended to in choosing a method of election is that the method adopted must not be capable of bringing about a result which is contrary to the wishes of the majority. There are several methods in use, and none of them satisfy this condition. The object of this paper is to prove this statement, and to suggest a method of election which satisfies the above condition.

Let us suppose, then, that several persons have to select one out of three or more candidates for an office. The methods which are in use, or have been put forward at various times, may be divided into three classes.

The first class includes those methods in which the result of an election is arrived at by means of a single scrutiny.

The second class includes those in which the electors have to vote more than once.

The third class includes those in which more than one scrutiny may be necessary, but in which the electors have only to vote once.

In describing these methods, the number of candidates will in some cases be supposed to be any whatever, but in other cases it will be assumed, for the sake of simplicity, that there are only three candidates. The case in which there are only three candidates is the simplest, and it is of frequent occurrence. I propose, therefore, to examine, for the case of three candidates, the results of the methods which have been proposed, and to show that page 2 they are erroneous in this case. This will be sufficient for my purpose, for it will be easily seen that the methods will be still more liable to error if the number of candidates be greater than three. I shall then discuss at some length the proposed method in the case of three candidates, and afterwards consider more briefly the case of any number of candidates.