Comparison of Proposed Method with Condorcet's Theoretical Method.

Comparing the method proposed in this paper with Condorcet's theoretical method, we see that, so far as any conclusion can be drawn from the votes of the electors the two methods always agree. In those cases in which no conclusion can be drawn from the votes the results of the two methods will not always be the same. It is equally impossible to prove either of these results wrong. Con- page 34 dorcet's method always shows whether the result is incapable of being proved wrong or not, but the proposed method gives us no information on this point. With the proposed method, however, there is no difficulty in arriving at the result in any case, whereas Condorcet's method is, by his own admission, so complicated as to be quite impracticable. Condorcet returns the candidate who is superior to the largest number of other candidates, without reference either to the numbers of votes by which the candidate is superior to those other candidates, or to the number of votes by which the candidate is inferior to the remaining candidates. Now in the proposed method both these elements are taken into consideration. Each candidate is, in fact, credited with the numbers of votes by which he beats all candidates he is superior to, and is debited with the numbers of votes by which he is beaten by all candidates he is inferior to. All candidates who have the balance against them are excluded, and the election then proceeds as if the remaining candidates were the only ones eligible.

It seems clear, then, that the proposed method is quite as rigorous as that of Condorcet. It gives the same result as Condorcet's in the case of three candidates, and it agrees therewith in all cases so far as any conclusion can be drawn from the votes. In those cases in which no valid conclusion can be drawn from the votes the two methods may not agree, and although nothing can be proved one way or another in these cases, the principles on which the proposed method is founded seem quite as sound as those of Condorcet's method. The proposed method has, however, great practical advantages over Condorcet's method, for the process of arriving at the result is the same in all cases; the operations throughout are of the same kind. The number of numerical results which have to be arrived at is much smaller than in Condorcet's method. For instance, if there be sixteen candidates we should expect, in the long run, to have four scrutinies, involving thirty numerical results, whereas Condorcet's method would require the computation of the votes for and against one hundred and twenty different propositions. When the numerical results are arrived at there is not the slightest difficulty in applying them, whereas in Condorcet's method the rules are very complicated. It may be claimed, then, that the proposed method has all the rigour of Condorcet's method and none of its practical difficulties.