Dear Vanity,—The commencement of the second year of the Doublets competition seems to afford a good opportunity for introducing a change into the system of marking. I have considered the subject very carefully, and have come to the conclusion that the present system does not accurately measure the skill employed, and that I can suggest one which will do more justice to the rival merits of your little army of Doubleteers.
I propose, then, to substitute for Rules 1, 2, in the chapter headed “Method of Scoring,” the following:—
- The shortest Chain which can be made on a given Doublet will have so many marks assigned to it as there are letters in the Links employed, “Set Links” counting as ordinary Links.
- Each competitor who completes his Chain with the least possible number of Links will receive the marks assigned by Rule 1; and each who uses more than the least possible number will forfeit, for every extra Link, as many marks as there are letters in it.
To illustrate the New Rules, let us take the Doublet (the first one ever published) “Drive PIG into STY.” The shortest known Chain for this (“PIG, wig, wag, way, say, STY”) contains 4 Links. Here a competitor using only 4 Links would score 12 marks; one using 5 Links, 9 marks; 6 Links, 6 marks; 7 Links, 3 marks; and any competitor using 8 or more Links would score nothing.
The points of agreement and of difference between the two systems will be best illustrated by examples.
Take a 3-Letter Doublet and a 4-Letter Doublet, and suppose that the shortest Chains made on them contain 5 Links each. By the present system one would score 6, the other 8; by the new, one would score 15, the other 20. Here, so far as the proportion is concerned, the two systems agree.
Again, take two 3-letter Doublets, and suppose that the shortest Chains made on them contain, respectively, 4 Links and 8 Links. By the present system each would score 6; by the new, one would score 12, the other 24. This is surely more just, since the second would require about twice as much mental labour as the first.
Again, take a 3-letter Doublet and a 6-letter Doublet, and suppose there are two competitors, one of whom beats the other, on each Doublet, by one Link. By the present system he would gain one mark in each case; by the new, he would gain 3 marks in the first, and 6 in the second. And surely this also is more just, since it would require about twice as much mental labour to save a 6-letter Link as to save a 3-letter one.
I feel confident that your adoption of the new system will prove satisfactory to your readers, and that the future drivers of (mental) Pigs into (mental) Sties will find their skill more exactly measured, and therefore more justly rewarded.
Lewis Carroll