The Double Vote Method.

In this method each elector votes for two candidates, and the candidate who obtains the largest number of votes is elected. This method is erroneous, for it may lead to the rejection of a candidate who has an absolute majority of votes in his favour as against all comers. For suppose that there are twelve electors, and that the votes polled are, for A, nine; for B, eight; for C, seven, then A is elected. Now, in order to show that this result may be erroneous it is merely necessary to observe that it is possible that each of the seven electors who voted for C may consider C better than A and B; that is to say, an absolute majority of the electors may consider C to be the best man, and yet the mode of election is such that not only does C fail to win, but in addition he is at the bottom of the poll. This is an important result; we shall see presently the effect it has on other methods of election.

In the case in which there are only three candidates this method is, in fact, equivalent to requiring each elector to vote against one candidate, and then electing the candidate who has the smallest number of votes recorded against him.