Odd this day

7 March 1907

118 years ago today, that most prestigious of journals, Nature, published Francis Galton’s account of a visit to the West of England Fat Stock and Poultry Exhibition at Plymouth. You may know the story…

A fat ox having been selected, competitors bought stamped and numbered cards, for 6d. each, on which to inscribe their respective names, addresses, and estimates of what the ox would weigh after it had been slaughtered and ‘dressed’. Those who guessed most successfully received prizes.

Image from Museum of English Rural Life. Obviously.

A more recent telling sums up what followed:

Once the competition was over Galton, an explorer, meteorologist, scientist and statistician, took the 787 guesses and calculated the average, which came to 1,197 pounds. The actual weight of the ox was 1,198 pounds. In effect, the crowd had provided a near perfect answer.

Now, you may be thinking that I’m planning to debunk this with some attempt at wit like: if large groups of people are so clever, why [makes sweeping gesture at the absolute fucking state of fucking everything]? But that would be a cheap shot. The Conversation article I linked to above points out that “four criteria are important in making this an effective tool”, and the first of them is:

Independence: The various guesses have to be independent of one another. That is, each person must guess without the knowledge of what other people have guessed.

…and — whether your ballot is secret or not — that does not apply to elections. You’re not being asked something specific, like ‘what will GDP be in five years’ time if I vote for this lot?’, but an entirely nebulous question (which of these people will fuck things up least?) based on vibes and quite possibly weeks of discussion with friends and family. But I digress.

There are a number of things to say about this story, one of which Professor Graham Kendall in The Conversation nails in his first sentence:

The great Victorian polymath, Sir Francis Galton was at a country fair in 1906, so the story goes… [my emphasis]

Because he wasn’t. At the country fair, that is. For a start, at no point in the Nature article does he say he went. Instead he uses the words:

A weight-judging competition was carried on at the annual show … About 800 tickets were issued, which were kindly lent me for examination after they had fulfilled their immediate purpose.

Note the use of the passive voice (“was carried on”). It’s a small detail, really, but another account — by a statistician who specialises in business analysis — points out that, while Galton definitely went to Plymouth in late 1906, this was because he was in his mid-80s, had been writing letters complaining of being an invalid, had suffered “12 days of Rheumatics and Bronchitis”, and wanted to be somewhere warm for winter because

London in November would help to, or quite, kill me.

…so he might not have been all that up for gallivanting about at country fairs admiring admittedly admirable fat beasts.

That blog also links to UCL’s collection of Galton’s papers, which contains a letter about the livestock show.

If Galton had been there, why would he need to write to (one assumes) one of the organisers to get hold of the entry cards for the Guess the Weight of the Absolute Unit competition? And yet, almost any time the story is told, he is apparently there. Somewhat remarkably, a 2004 book, The Wisdom of Crowds, even opens with:

Now, look: the author of this may have written for the New Yorker, and have got a fuck of a sight more in print than I ever have, but this is, to use the technical term, pure balls. For a start, if he set out in spring 1907, even if he’d teleported to south Devon, he would have had to work extremely fast to have a paper published in Nature by 7 March that same year (even allowing for the fact that the wheels of academic publishing seemed to turn faster in those days than they do now).

To be fair, this only seems to be in the first edition, and later versions say he set out “One day in the fall of 1906”, but this is still embellishment on a grand scale.

As he walked through the Exhibition that day, Galton came across a weight-judging competition. A fat ox had been selected and placed on display, and members of the gathering crowd were lining up to wager on just how much the ox weighed. … At contest’s end, he borrowed the tickets from the organizers and ran a series of statistical tests…

To be fair, what the author is doing is adding colour to what could be a dry story in order to make his book more saleable in a crowded market, but… do me a favour.

There are other quibbles, such as whether Galton used the mean or the median. The book says mean (“he added up all the contestants’ estimates, and divided that sum by the number of contestants”) while the blog says median, and Galton says “the middlemost estimate” (which means ‘median’), but seeing as I had to use BBC Bitesize to remind myself what the hell those are, that really is just a quibble.

You can, if you have an interest in these things, read either the blog I’ve linked to above, or Statistical Science, vol.29. no.3 for in-depth analysis of how Galton came to his conclusions and whether the numbers and his workings were accurate. Legend, as you can see at the top, says the crowd was out by 1lb. The facts seem to suggest a larger, if still impressively small, margin of error.

But the main point is that Galton was right about this. There was, it must be said, much about which he was not right. Being profoundly racist and the inventor of eugenics do not appear in his credit column, let’s say. But the wisdom of crowds stands up. It is true that

…but as long as you meet the right criteria — everyone guessing independently; a diverse range of guesses; everyone using their own knowledge; some way of bringing together and analysing the results — a collective guess will often be right.

Prof Kendall even gives some examples, including, incredibly, the random guesses of the financial markets after the space shuttle Challenger disaster:

investors started selling stocks of the four main contractors involved … Of the four companies Morton Thiokol fell the most, almost 12% by the end of trading on that day, compared to about 3% for the other three companies.

When, six months later, Richard Feynman famously showed the commission of inquiry how the O-rings failed, he was handling something manufactured by Morton Thiokol.

Kendall also links to a BBC article about the wisdom of crowds going wrong, which gives the obvious example of a fucking stupid decision made by a lot of people at once — but the 2008 financial crash, of course, didn’t meet the criteria, because

social influence can refine rather than degrade their collective decision.

Basically, there are lots of sources on this, and we should, as ever, read as many of them as possible and retain an open, sceptical mind — had we but world enough and time. I think the easiest thing might be just to find out more about historical oversized cattle — and we all know there’s really only one place to go for that:

Consuming the fat cows - The Museum of English Rural Life

One final word, though, from another unreliable narrator. Charles Mackay, in Extraordinary Popular Delusions and the Madness of Crowds, in which he basically invented the story of Tulip Madness…

Odd this day

…also wrote:

Men, it has been well said, think in herds. It will be seen that they go mad in herds, while they only recover their senses slowly and one by one.

…and I’m afraid [makes sweeping gesture at the absolute fucking state of fucking everything] that rings all too fucking true.

(Yes, this edition has been a bit sweary, but [repeats gesture].)