elector should be required to place the whole ten in the order of his preference, 1, 2, 3, &c.  Let the maximum degree of merit be denoted by ten marks, so that every first preference will count as ten marks.  Then, although an individual elector might be disposed to give his second preference only five marks, and the rest of his preferences, say, two marks, Laplace demonstrated that it is most probable that the total result would be the same if each elector be assumed to give his second preference nine marks, his third preference eight marks, and so on.  Therefore, if all first preferences be multiplied by ten, second preferences by nine, and so on in regular order down to last preferences multiplied by one, the total number of marks will be an index of the order in general favour.  If there is one office to be filled, the candidate with the highest number of marks should be elected; if there are two offices, the two highest candidates, and so on.

But the assumed condition must be rigidly complied with; each elector must express his honest preferences.  Whether he will do so or not depends upon the circumstances.  Laplace recognized this element of human nature, and declared that if electors are swayed by other considerations independent of the merit of the candidates the system would not apply.  For instance, if the candidates are the nominees of a number of independent sections, each of which is anxious only to secure the return of its own candidate, and to defeat those who stand most in his way, the tendency will be general to place the more popular candidates, those whose success is most feared, at the bottom of the list, so as to give them as few marks as possible.  The result would be to favour mediocre men, or even in extreme cases the most inferior.

Practically, therefore, the system is not applicable where any of the electors are personally interested in the result.  If a number of judges were called on to decide the relative merits of several essays or prize designs, and the competitors’ names were not known to them, the system might be used.  But even in such a case a simpler method is available; for, although it may be difficult to pick out the best, it is generally easy to agree upon the worst.  It is usual, then, to gradually eliminate the worst, and when the number is reduced to two to take the decision of the majority.

This process of elimination may be, however, combined with the preferential system, and the result is more accurate than if one count only be made.  At the first count the candidate with the fewest marks would be eliminated and his name struck out on all the papers.  All those under him on each paper would then go up one point in order of favour, and further counts would be held, eliminating the lowest candidate each time till the candidates were reduced to the number desired.  This method is very complicated, and involves a great amount of trouble.