The Ballot-Box

Abstract

MR. HOOKER, in NATURE of March 21, seems not to have quite appreciated my principal contention in the letters “One Vote, One Value” and “Vox Populi” of February 28 and March 7 respectively. It was to show that the verdict given by the ballot-box must be the Median estimate, because every other estimate is condemned in advance by a majority of the voters. This being the case, I examined the votes in a particular instance according to the most appropriate method for dealing with medians, quartiles, &c. I had no intention of trespassing into the technical and much-discussed question of the relative merits of the Median and of the several kinds of Mean, and beg to be excused from not doing so now except in two particulars. First, that it may not be sufficiently realised that the suppression of any one value in a series can only make the difference of one half-place to the median, whereas if the series be small it may make a great difference to the mean; consequently, I think my proposal that juries should openly adopt the median when estimating damages, and councils when estimating money grants, has independent merits of its own, besides being in strict accordance with the true theory of the ballot-box. Secondly, Mr. Hooker's approximate calculation from my scanty list of figures, of what the mean would be of all the figures, proves to be singularly correct; he makes it 1196 lb, (which is the mean of the deviates at 5°, 15° 95°) whereas it should have been 1197 lb. This shows well that a small orderly sample is as useful for calculating means as a very much larger random sample, and that the compactness of a table of centiles is no hindrance to their wider use. I regret to be unable to learn the proportion of the competitors who were farmers, butchers, or non-experts. It would be well in future competitions to have a line on the cards for “occupation.” Certainly many non-experts competed, like those clerks and others who have no expert knowledge of horses, but who bet on races, guided by newspapers, friends, and their own fancies.