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Twll din pob Sais!

A massive “Llongyfarchiadau!” to the Rev. Bodvan Anwyl, R J Thomas, Gareth A Bevan and Patrick J Donovan, the progenitors of the “Geiriadur Prifysgol Cymru” (Dictionary of the University of Wales), the final volume of which has now been published after 82 years’ work. Anyone who cares about the preservation of minority languages should applaud this magnificent work of scholarship, the definitive historical dictionary of the Welsh language. Welsh nationalists should be particularly proud that the entirety of the work was carried out under the auspices of the University of Wales; it has been a minor scandal of British educational funding over the last few years that Oxford University for a long time had a higher-rated Celtic Studies department than Aberystwyth. Well done to all. I was going to buy myself a copy for Christmas but the fourth volume sold out on the first day of publication.

Anyway, the fact which interests me, from some of the press coverage in the FT, is that the next step for the tireless researchers and harmless drudges of the dictionary team, is a seven year plan to redraft the A and B sections. Apparently, these are now roughly fifty years out of date … which set me to thinking. Read on for some musings on economists and the way in which we think. While you’re reading, keep at the back of your mind your own experiences with management consultants, the last time you had a few round your place of work.

What is the optimal way to go about writing a dictionary? Since dictionaries take a very long time to write (the Welsh one was actually comparatively speedy at 82 years; the French version took 300 years, albeit that given that it was produced by the Academie Francaise, there were most likely a few egos involved), you really ought to take into account the fact that the dictionary will need to be used while it is being written. To write a dictionary by just starting with the A’s and ploughing straight on until you reach Z (see quiz below), means that people who want to know about words at the end of the alphabet are going to have to wait a bloody long time for your help. Which is not all that great even with a language like English, where most of the important words are in the front end of the dictionary, but is pretty disastrous for a language like Welsh, where the “Y” section is onle of the longest in the whole book.

Similarly, a bit of thought about the theory of optimal scheduling would suggest that revising a dictionary in the same manner — from start to finish — is unlikely to be the best way to go about it. In most commercial contexts, you prioritise maintenance of the machines which are most important to the overall production process, or those which are most often used. Not only is alphabetical order an arbitrary ranking which does not match up at all well with the needs of language users for different words, but a policy of revising the dictionary from start to finish means that the average time between revisions will be the same for all words, despite the fact that some words are used much more frequently than others, and some words will have their meanings drift much quicker than others.

Thinking like an economist, I’d start attacking the problem of developing an optimal algorithm for writing a dictionary by first tackling the easier problem of updating an already existing dictionary. After a cup of coffee’s worth of thinking, I’ve come up with the following pointers to a solution of that problem:

  1. First, we need to replace alphabetical order by some way of scheduling revisions which recognises their use in the language. The obvious (to an economist) way to achieve this would be to use “frequency-weighted random sampling” (FWRS).
  2. By FWRS, I mean that one should first get hold of a large representative sample of written Welsh, and then construct a frequency table of the words contained in it. Then, one should assign positive integers to each word in the table in proportion to their frequency. Then, instead of progressing through the words one by one, one should set up a random number generator to select a positive integer, then update the word which corresponds to that integer. In this way, over time, the frequency of updating of every word would correspond to the frequency of its appearance in the Welsh language.
  3. Two immediate refinements to this algorithm spring to mind. First, one could take into account differing speeds of meaning drift between words, by using a function which, every time one updated a word, compared the size of the revision (measured in some heuristic manner) to the length of time since the word had been last updated. Words which appeared to be subject to rapid meaning drift could have their “frequency” adjusted upward in the distribution.
  4. Second, one would presumably need to have an updating algorithm for the frequency table itself, to take account of changes in the popularity of different words.
  5. This algorithm can obviously be adapted to the problem of writing a dictionary from scratch. Just read widely in the Welsh language and choose words at random from the ones on the page before you.

I came up with the thoughts above while drinking a cup of coffee and reading a 200 word article in the FT, so I think that they’re pretty representative of the way in which an economist might think of this sort of problem. And (although I am obviously poorly placed to judge this matter), I think I make a pretty plausible case for my suggested algorithm. Which is interesting and worrying because … it’s a really stupid suggestion. I’m not trying to make a self-deprecating point here; those really were my first thoughts on reading about the University of Wales team’s approach to the scheduling algorithm. And it took me a couple of weeks to realise what is wrong with my approach:

Who needs a dictionary to look up common words that they use and read every day?

Of course. Words that are common in a sample of written language, are words that everyone knows the meaning of. You get the dictionary out for words that you don’t see all the time.

This isn’t actually a particularly fatal objection to my algorithm, although it is interesting that it took me so long to realise it. All you have to do is to construct a frequency table not of appearances in written language, but of words as they are looked up in the dictionary (if you put your dictionary online, this frequency information can be collected automatically for you). Of course, this makes the frequency table much more difficult practically to construct, and it does mean that the updating algorithm can no longer be used as a dictionary construction algorithm, but it still feels like we’re making progress.

We’re not. There’s a real killer objection to this whole approach to the problem.

Random sampling of the kind described is a really terrible way to update a dictionary which is meant to be complete and authoritative

Given that we now know that the main usefulness of the dictionary is in the infrequent cases, a lot of the implicit assumptions in my “optimal” updating algorithm fell apart. Like the economist I am, I made considerable use of the asymptotic, large-sample properties of the statistical measures I used. Put into plain language, I made the assumption that if something is optimal on average, probabilistically, then it will work out to be optimal for certain, in the long run. But now we know that we need to be dealing with the infrequent cases at the end of the frequency distribution, that assumption looks much less valid. It’s quite probable that, under a random selection algorithm, some words will get updated several times, and some will never get updated at all. (NB at this point that, unlike my usual objections to misuse of probability theory by economists, this one has nothing to do with nonergodicity. It’s purely to do with sampling theory, and the number of draws you would need in order to make the sampling distribution of something as massive as a language coincide with the underlying distribution).

This problem is disastrous for the manufacturers of a scholarly dictionary. If you have some words that never get updated at all (or even worse, if we try to design a construction algorithm based on this one, never get included at all), then a researcher who is using your dictionary can’t be sure if the particular word he is looking for is one of these unlucky words. If he can’t be sure that your dictionary isn’t going to give him a bum steer, then your dictionary is no use at all. The alphabetical algorithm has the distinct advantage that if someone knows the alphabet, and knows what the most recent volume of updates was, then he has a good estimate of where you are in the update cycle and thus, what parts of your dictionary will be of use to him. So in fact, score one for the lexicographers and minus a million for me. In actual fact, my algorithm above would not be all that bad for constructing an adbridged dictionary for the mass market, when the only thing you care about is to trade off cost the probability that a given word looked for will be in the subset of the dictionary included. But we’re talking about a reference work here.

[An engineer would at this point argue that there are low-discrepancy deterministic series which could be used instead of a random number generator to pick from the frequency table, and that using one of these would in principle ensure that all words got updated on a constant cycle, and would allow someone to determine the time to last revision by running the calculation. Perhaps so, but it seems like a hell of an inconvenience to put languages scholars to, in return for not that much gain.]


So how the hell did I come up with this lexicographer’s nightmare of a plan? Well, attempting to self-diagnose, I come up with two common pathologies of economic thinking.

  • Over-reliance on asymptotic properties. This is the problem with respect to sampling distributions which I identified above. This goes straight back to introductory game theory; von Neumann and Morgenstern showed that there is always a mixed strategy which is as good as any other strategy for a large and useful class of problems, so my first reaction on seeing the problem was to look for a solution based on a randomised mixed strategy. A common source of economic mistakes is to treat a solution which gives an ex ante optimal solution in static one-period games as being the definition of optimality, and ignore the genuine dynamics of a problem. This is an organisational pathology of the “risk management” profession, and is similarly endemic to discussions of the “risk premia” paid by developing countries and the “moral hazard” implicit in official sector lending to them. I strongly believe that the decision to let Argentina go bust in order to convince the markets that the IMF was serious about bailouts was based on this kind of thinking. Certainly, any discussion of social equality based on “equality of opportunity” is rotten with it.
  • Uncritical use of frequency as a substitute for importance. Obviously, for the most part, popular things are popular because they want them. But the fact that I missed such an obvious property of dictionaries suggests that one has to guard against the overuse of this assumption. One thing that I missed almost completely was the fact that dictionary entries have group properties as well as individual properties; you could have, on average, the best individual entries in the world, but if they were mixed randomly with a few truly terrible ones, your dictionary would be unusable. An example of this sort of thinking at work might be the current proposal in the UK for the staffing of fire stations, whereby it is suggested that firemen change from a military-like “watch” system, under which stations are staffed by three crews who rotate at eight-hourly intervals, to a shift-based system under which staffing levels are calibrated to coincide with the frequency of fires. All very sensible, as long as one ignores the obvious benefits of keeping the coherency of the watches; as long as one ignores that, in complicated group physical activities, stability of the teams involved is a huge benefit in and of itself.

But the real error was just a pure and simple case of economists’ arrogance, the belief that as a clear-thinking outsider with a training in constrained optimisation, I would be able to design a much better way of going about things than the people actually doing the job. This is the sort of “blackboard economics” that Ronald Coase always railed against, which is why he’s a bit of a hero of mine and it’s genuinely saddening to me that he blotted his copybook so badly over the lighthouse business.

The root of this counter-strand of economic thinking is in Hayek’s political philosophy. Like Coase, Hayek is often really badly abused by people on the political Right who believe that he was nothing more than a yah-boo cheerleader for free markets (and woefully neglected by people on the Left for the same reason). In actual fact, Hayek, and a few of the other Austrian economists sit very uncomfortably with the Libertarian thinkers which they are usually lumped with, for the decent reason that Hayek is actually a conservative.

Hayek’s arguments for free markets, as expressed in The Road to Serfdom and other works, don’t come from the Lockean natural rights tradition. Hayek believes in market liberalism because he is against liberalism, and he thinks that the only non-tyrannical way in which one can organise society is a market-liberal way, because this form of social organisation is the only one in which it is possible to make use of “tacit knowledge”.

Tacit knowledge is the wisdom of the lexicographers, who don’t go around looking for optimised scheduling algorithms for writing their dictionaries, but instead follow their own values of diligence, thoroughness and alphabetisation; by following these goals, they end up producing something much more suited to its needs than any blackboard economist is ever likely to come up with. And we can see from this example that tacit knowledge is an inherently conservative concept. Hayek might not go quite so far as Roger Scruton, who famously stated that “prejudice”, meaning “pre-judgement”, or the assembled judgements of past generations, was an excellent way in which to acquire the majority of one’s beliefs, but it’s clear that he’d go some of the way down that same track. What isn’t emphasised enough in most modern libertarian use of Hayek is that, although he in the main addressed his arguments against socialist planning, as the great evil of his day, he was not so much opposed to it because it was socialist as because it was planning. In other situations, one could easily imagine him a man of the left, railing against the similar blackboard-economics tendency of the Right.

Which is quite a revealing thing to notice. Hayek was a keen advocate of privatisation, but this should be seen as a contrast to nationalisation, not to public ownership per se. In many cases, tacit knowledge is best made use of by the market, but that’s just because most human activity has been mediated through market goods for the last few centuries. There are plenty of professions — teachers, firemen, lexicographers — who have a huge store of tacit knowledge of their own, and to introduce the “free market” into some of these areas is just as much an instance of blackboard economics, and just as stupid, as nationalising agriculture.

Edit: Oor Brad has a bit up at the moment where an Actual Economist avows his belief that introducing competition and bankruptcy into the school system would make education better. That’s exactly the sort of thing I’m talking about. Maybe it would, maybe it wouldn’t. But to assert it either way without incredibly detailed analysis of the tacit knowledge of the teaching profession is pure blackboard economics.

Second edit: Despite appearances, this is not an invitation for anyone to start telling me things I already know about the “Milwaukee experiment“.

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