A Modification of Proposed Method.

It may be mentioned that there is another, but in general a more tedious, method of getting at a result, which cannot be shown to be erroneous in any case. This method has been adopted by the Trinity College Dialectic Society. It is as follows:—In the method proposed above, instead of rejecting all the candidates who are not above the average, reject the lowest only. It is obvious from what has been said above that this cannot lead to error. But a second scrutiny will always be required, whereas in the proposed method one scrutiny only may be necessary. There is another disadvantage: the result will not in all cases agree with that of the proposed method. For, let us suppose that a, b, c are all positive, and that a is the least of the three, and at the same time that 2c is less than a + b. On the method proposed, as we have already seen, C would be elected, but on the method now under discussion B would be elected. For the scores of A and B at the first scrutiny are 2N—b+c, 2N—c + a, respectively, and the first of them is the smallest, because 2c is less than a + b, and therefore c—b is less than a—c. Thus A would be thrown out at the first scrutiny, and a second scrutiny would be held to decide between B and C, and B would win because a is positive. Thus the result is that which would follow from abandoning the proposition "A is better than B," which is affirmed by a majority of 2c, whereas the result of the proposed method is that which would follow from abandoning the proposition page 22 "B is better than C," which is affirmed by a majority of 2a, which is smaller than the former majority.

There is, however, one point in favour of the modified method. The first scrutiny will at once give us the values of the three differences b—c, c—a, a—b. From these, of course, we cannot find a, b, c. In the modified method, however, a second scrutiny is always necessary, and this will at once give us the value of one of the three a, b, c. Having already found the three differences, we can at once find each of the quantities a, b, c, and hence we can ascertain if the result is demonstrably correct. Thus if the modified method be used, we can always ascertain, by a simple calculation, whether the result is perfectly satisfactory or not. The same remark applies to the proposed method in those cases in which two scrutinies are necessary.