and it is quite easily checked by any other accountant and skilled computer.  A reader with a bad arithmetical education, ignorant of the very existence of such a thing as a slide rule, knowing nothing of account keeping, who thinks of himself working out the resultant fractions with a stumpy pencil on a bit of greasy paper in a bad light, may easily think of this transfer of fractions as a dangerous and terrifying process.  It is, for a properly trained man, the easiest, exactest job conceivable.  The Cash Register people will invent machines to do it for you while you wait.  What happens, then, is that every candidate with more than a quota, beginning with the top candidate, sheds a traction of each vote he has received, down the list, and the next one sheds his surplus fraction in the same way, and so on until candidates lower in the list, who are at first below the quota, fill up to it.  When all the surplus votes of the candidates at the head of the list have been disposed of, then the hopeless candidates at the bottom of the list are dealt with.  The second votes on their voting papers are treated as whole votes and distributed up the list, and so on.  It will be plain to the quick-minded that, towards the end, there will be a certain chasing about of little fractions of votes, and a slight modification of the quota due to voting papers having no second or third preferences marked upon them, a chasing about that it will be difficult for an untrained intelligence to follow. But untrained intelligences are not required to follow it.  For the skilled computer these things offer no difficulty at all.  And they are not difficulties of principle but of manipulation.  One might as well refuse to travel in a taxicab until the driver had explained the magneto as refuse to accept the principle of Proportional Representation by the single transferable vote until one had remedied all the deficiencies of one’s arithmetical education.  The fundamental principle of the thing, that a candidate who gets more votes than he wants is made to hand on a fraction of each vote to the voter’s second choice, and that a candidate whose chances are hopeless is made to hand on the whole vote to the voter’s second choice, so that practically only a small number of votes are ineffective, is within the compass of the mind of a boy of ten.

But simple as this method is, it completely kills the organization and manipulation of voting.  It completely solves the Goldbug-Wurstberg-Sanity problem.  It is knave-proof—­short of forging, stealing, or destroying voting papers.  A man of repute, a leaderly man, may defy all the party organizations in existence and stand beside and be returned over the head of a worthless man, though the latter be smothered with party labels.  That is the gist of this business.  The difference in effect between Proportional Representation and the old method of voting must ultimately be to change the moral and intellectual quality of elected persons profoundly.  People are only beginning to realize the huge possibilities of advance inherent in this change of political method.  It means no less than a revolution from “delegate democracy” to “selective democracy.”