Francis Galton was interested in political systems including the “trustworthiness and peculiarities of popular judgements”. He wrote an article for Nature magazine[1] entitled “One Vote, One Value” where he makes the case that group decisions (such as juries deciding compensation) should be determined by median rather than by mean.
The following week, Galton had an article published in the same journal further investigating “the voice of the people”. Galton observed at a County Fair a broad-based public competition based on judgement. He persuaded the organisers to lend him the tickets afterwards for examination[2].
The basis of the competition was to judge the weight of an ox – after it had been “slaughtered and dressed[3]”. Numbered tickets were sold at 6d each (deterring frivolous answers). Some 800 tickets were sold (Galton remarked[4] this to be more than the likely number of farming experts).
A few were discounted as illegible and Galton rank-ordered the ones that remained. The median value was 1207 pounds (approx 547.5 kg). Galton cited his previous article as the rationale for choosing the median.
The official weight of the slaughtered, dressed ox was 1198 pounds (within 0.8%[5]). Galton seems surprised the value was so close.
This story was featured in the opening section of James Surowiecki’s book – the Wisdom of Crowds[6].
[1] Feb 28th 1907 page 414.
[2] As recounted in Galton’s article about the expression of public opinion “Vox Populi” Nature 1907 Volume 75 Number 1949 page 450.
[3] “dressed” – generally an ambiguous term sometimes (or not) including head, tail, legs and other internal organs. – but likely very well defined in the local context.
[4] Nature (Letters to editor) March 28 1907 p509.
[5] Median Value. By March 21st a Mr Hooker has a letter of reply printed where he reverse-engineered Galton’s published (summarised) results to estimate a mean, which he notes is even closer to the official value (1196 lb mean vs 1197 lb official). In the March 28th edition Galton confirms (from original data) Hooker’s estimate, while reasserting the preferable characteristics of the median view.
[6] James Surowiecki “The Wisdom of Crowds”. He only refers to the closer mean figure, described by Hooker and doesn’t mention Galton’s original figure or defence of approach. Perhaps because just one pound out makes a more interesting story?