Economics and similar, for the sleep-deprived

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Thursday, November 07, 2002

Why Formula One this year is going to suck, and other philosophical topics

Or, subtitled, "Descent Into Self-Parody". Apologies in advance, readers; this is a long one. Basically, I spent five years of my life, eighteen and a half thousand pounds of my own money, and probably the same again of the British taxpayers and more from my parents, on being educated by the British university system. And by God are you lot going to suffer for it. The current post is intended to discuss sports psychology, ergodicity, broadcasting rights, the von Neumann/Morgenstern axioms in economics, Turing Machine incomputability, the Rand Corporation, medieval alchemists and option pricing. Although it may end up digressing ....

I have slightly unusual taste in sports, because I basically like boring sports (I find them interesting) and dislike interesting sports (I find them boring). Football, basketball, etc: forget it. I really can't be bothered watching any competition of pure athleticism which lasts longer than the 100 metres final. Sure, there's a lot of physical skill and grace involved, but you can get that at the ballet, and I don't like ballet either. There's always action going on, thrills of excitement and disappointment and all that, but it just doesn't do anything for me.

Give me a good darts match on the TV, on the other hand, and I'm as happy as a pig in a nice clean sty (the preferred environment for pigs). Snooker is good too, as is crown green bowling. When the Scots started doing well in the Olympics and we had curling on the tele every night, I was enthralled. I even enjoy watching golf when I'm drunk enough to forget how much I hate the game (for social and political reasons, natch).

It took me a while to work out why my taste in sports runs this way ... in fact, it's pretty hard to see why anyone bothers with these sports at all. Fair enough, there is quite a lot of skill involved in being able to play snooker or darts -- I'm complete shit at both -- but the actual physical skill involved is an utterly derisory one. Being able to poke a ball with a stick really accurately? Rolling a counterbalanced ball in a reasonably straight line? Sliding things on ice and sweeping the ice with a fcking broom? I think it's pretty safe to say that these sports are products of an advanced society; one wouldn't want to categorically say that Steven Pinker couldn't come up with a story about how taking iron shots over water hazards is a skill developed from instincts that were vital to our survival on the African veld, but it would surely take him at least a couple of coffee breaks. These skills suffer to a great extent from the "juggler paradox"; the principle that juggling is such a stupid fcking skill that the better someone is at it, the stupider they are, because they've wasted more time on that pointless, stupid skill. (NB to any jugglers reading: D-Squared Digest does not propose to enter into any correspondence on this point. Having offended hobbyists in the past with some pointed remarks about Linux, I know how passionate they can be. But the fact remains; Catherine Zeta Jones is an international megastar, whereas the greatest juggler in the world is a geek act. Deal with it.)

But the point is, precisely because the physical skill is so risible, that the sport itself has to take place on a higher level. At the top levels of snooker, darts, bowling etc, all the people present have the physical skills to win, as long as they maintain their concentration and focus. Or in other words, the winner is the guy whose nerve cracks second.

And, human psychology being what it is, beginning to lose a bit is a self-reinforcing process; a player's performance in sequential vists to the table or the oche will tend to have positive, destabilising feedback. Regular readers will recall my discussion a few weeks ago of nonergodic processes; well, darts scores would be a great example of a real world nonergodic process. In principle, both players in an evenly matched game of darts will have about the same expected points score from every visit to the oche, so you would expect that both players scores would follow a random walk, with the winner beg the player whose random walk drifts across the winning line first. In amateur and low-level games, based on my casual empiricism of watching pub teams, this is close to being the case. At the professional level, however, you will tend to find that as a long match goes on, the player who started off losing will get worse, while the player who started off winning will hit his 180s more often. The statistical properties of darts scores at the professional level give a decent picture of nonergodicity; the average scores taken from the first 50 sets of arrows will most likely be completely misleading as to the result of the match.

So anyway, basically, the thing which makes boring sports more interesting is that you watch, over the course of a couple of hours, the complete psychological destruction of a human being. Which, in all honesty, probably means that Pinker the Thinker might have had a point in coming up with an evolutionary pop-psychology explanation of the putting green. This also fits as a psychological explanation of what I like about boring sports, because it fits an out-of-sample data point; the only exciting and physical sport I like is boxing, a sport which is also entirely about the destruction of one human being by another for the entertainment of third parties. This would rather tend to have the conclusion that I'm not a very nice person, but that information has always been free for the asking.

Cricket and Formula One have always been rather marginal sports for me. Clearly, both of them have this psychological edge to them, but it isn't quite as pure; it's tainted by elements other than pure mental attrition. I love cricket, but if I were being honest, the main reason I watch it is that you can have a drink and a chat during the boring bits. It doesn't have that gripping quality that the boring sports have; often, it's just boring.

With Formula One, however, it's a bit different. The psychological game is utterly swamped by the fact that, up to a first approximation, the championship is won by the guy who signs the biggest cheque for engine development and chassis testing. If things were rushed, or cars became illegal or something, you could continue to simulate the Formula One season by just persuading ten motor manufacturers to burn a suitcase full of $100 bills and smash a crate of champagne. There are a lot of people who prefer going to motor shows to sports competitions, but I'm not one of them, and in general, they're not a monetisable audience to advertisers.

Which is why the Formula One boys have a whole load of tricks up their sleeve for changing the face of motor racing this year. They want to break into the North American market, which is currently dominated by NASCAR. And, to their way of thinking, that means that they've got to have MORE ACTION! More overtaking, more uncertainty about the outcome of a race, more personalities and so on. They're basically pondering a whole set of rule changes relating to design restrictions, all of which are more or less explicitly designed to a) stop Ferrari and Michael Schumacher from winning and b) make the sport look a bit more like NASCAR.

It sounds horrendous because it is. In principle, reducing the element of technological differentiation could (although probably won't) make it more of a psychological battle, appealing to people like me. It could (although probably won't) make it more of a contest of driving skill, appealing to people not like me. In actual fact, the rule changes are much more likely to make Formula One into a complete lottery, appealing to absolutely nobody, since you can't even bet on it at any decent odds. But even if they were per impossibile to design the absolute perfect set of restrictions on the design specs, balanced perfectly to give the most even and fair chance to every team, this would still be a bad idea.

The reason it would be a bad idea is that the appeal of Formula One is qualitatively different from that of any of the other kinds of sports we've discussed so far. The reason that people care passionately about Formula One is that when you are watching it, even though the actual racing is usually dull as sht, you can be absolutely, totally, one hundred per cent sure, that the cars you are watching are the fastest possible cars that could be racing on that circuit. This is a qualitative difference between F1 and most other sports because what the spectators care about is the actual *facts* of what is going on in front of them, not the experience that they're having themselves. If F1 are going to try to make the experience better, at the expence of making it no longer the case that the cars are as fast as they can be, then we might as well fuck off and watch NASCAR. After all, NASCAR's much more exciting, it's more dangerous and quite visually spectacular. The only reason why NASCAR is not as good as Formula One is as follows; NASCAR cars aren't as fast as Formula One cars, therefore NASCAR is sht. End of argument. Anyone who tries to pretend that, when the topic is car racing, any criteria are relevant other than the fastness of the cars on offer, is kidding themselves and on some level or other knows it. As you can tell, I started to go off F1 when they banned turbochargers.

With sickening inevitability, like the one-issue bore I am, this whole discussion set off in my mind a train of thought relating to (go on, close your eyes and guess) some serious problems with the logical underpinnings of neoclassical economics (yup, well done). Fundamentally, preferences of the kind which I was describing in relation to Formula One motor racing, can't be described at all well in the terms of utility theory, and you get into some pretty bad logical tangles if you try to force them to fit.

The problem is the one I hinted at above; what's valuable about the experience of watching Formula One is not something intrinsic to that experience, but a fact about the cars; something about the relationship between that experience and the rest of the world. For example, let's assume that someone starts up, on the other side of the world, a new auto racing league in which turbos aren't banned, electronic braking systems are allowed, and various other design items ruled "unfair" by the F1 committees are let back in. Such a league would be pretty similar to Formula One, but the cars would be faster.

Although this would not alter the intrinsic qualities of watching a Grand Prix in the slightest, it would utterly devalue the experience. Rather than watching the pinnacle of man and machine operating together in harmony, you'd be watching the best that engineers could do under some rather arbitrary constraints put together by a committee of jobsworths led by a man in silly glasses. Rather than watching the fastest cars in the world, you'd be watching a bunch of random autos that were pretty damn fast, but not the fastest in the world. In other words, you might as well be watching NASCAR.

This seems like a pretty trivial and dull philosophical point, the sort of discussion of "intrinsic" and "nonintrinsic" properties of things that excites people writing dissertations on the subject of "Locke's Theory of Primary and Secondary Qaulities", but nobody else. Actually, it's incredibly important, and the reason it's important lies in the innocent-looking phrase "you might as well be watching NASCAR".

I hate NASCAR and think it's completely pointless. But I have to admit it's quite a spectacle. The reason I don't like it is that I don't like motor racing per se all that much, and therefore if I'm going to watch motor racing, I want it to be the top end of motor racing; Formula One. But the only good thing about Formula One is that the cars are the fastest that there are. If someone were to launch the hypothetical Formula Minus One superleague I was talking about, then there would be absolutely no point in F1 as she currently is. In fact, if the option of F Minus-1 were to be offered, I'd prefer NASCAR to F1.

This still seems pretty trifling, but actually, it's deadly to utility theory. One of the mathematical conditions that have to hold if my preferences are going to give the right kind of ordering necessary to get a consistent utility map, is that it must be the case that my preferences are "independent of irrelevant alternatives". In other words, that my choice between A and B is not affected by anything other than A and B. If this isn't satisfied, we can't prove that there is a definable optimum outcome for me; there might be points in my utility map in which consumption bundle X is not preferred to Y, Y is not preferred to X and I am not indifferent between X and Y. That sounds like a psychologically implausible situation, and it is, but remember that we're not talking about my actual preferences here, we're talking about mathematical representations of my preferences. Specifically, we're talking about whether certain kinds of mathematical representations of my preferences are possible, and the conclusion is that if preferences of the kind outlined by my NASCAR/F1 example above are possible, the kinds of representations usually assumed by economists, aren't possible.

This is a general problem with the current state of mathematical economics; that the mathematical conditions needed to prove any of its theorems are too strong, and it's insoluble. Not insoluble in the sense of being very difficult, but insoluble in the sense that the pair of equations 5x=4 and 2x=3 are insoluble. J. Barkley Rosser has a load of great papers on this subject on his website; I'm not going to link directly because you'll enjoy (no really) browsing around, but there is one called "All That I Have To Say Has Already Crossed Your Mind" (based on a Sherlock Holmes quotation) which proves that, so long as there are at least two individuals in an economy, there will be some situations in which equilibrium is not achievable. This is basically because, at the highest level of abstraction, the decision-making processes of economic agents as modelled by economists, can be represented as Turing Machines. And, for common economic situations, the problem of constrained optimisation by one individual conditional on the other's response (which in turn has to be conditional on the other's expectation of one's own action -- it is here that we get the sort of "I think you think I think" sentences which give this branch of mathematics its Alice In Wonderland quality) can be shown to be analogous to the Halting problem for those Turing machines.

(As with all Goedelian arguments, the easiest way to understand this is to just do what I did and spend six months being taught formal logic, but think about it this way; if you're deciding what to do, and you're interacting strategically with another player, then your decision is going to depend on what he thinks you're going to do. Unless you're going to attribute systematic error to him, what he thinks you're going to do ought to be the same as what you're actually going to do. But if one of the inputs to your calculation of what you ought to do, is what you're going to do, then it's quite clear that you've got a problem on your hands. This is hopelessly unrigorous and hand-waving, but gives you a flavour of the argument).

Now most economists tend to think that this problem (in its game-theoretic incarnation, anyway) was solved by John Nash, and that for this reason he deserved his Nobel Prize and that godawful Russell Crowe film. Not so and not so. As Philip Mirowski's excellent (by which I mean, I literally can't recommendit highly enough) book "Machine Dreams: Economics Becomes A Cyborg Science" shows, Nash's equilibrium concept won over because of internal politics in the American military's "operations-research" community which provided the foundations of the modern economics profession after the Second World War. Nash's equilibrium concept is actually not all that great; Nash equilibria don't always exist, and there is no centripetal force which draws you toward one, so even if one does exist, there's no guarantee that anyone will find it, particularly if calculating the Nash equilibrium of a particular game is actually formally impossible. This should be contrasted with that other great achievement of postwar economics; the development by Fischer Black and Robert Merton (Myron Scholes helped) of "arbitrage-free" models.

Rather than making unwarranted assumptions about fixed points in undecidable calculations, or by assuming putative auctioneers that don't exist, the Black & Merton approach builds up solutions by taking cases where, at every point, if the economic agents don't follow the equilibrium path, one of them can make theoretically unlimited amounts of money at the expense of the other. This approach, combined with the old gambler's principle of the "martingale" (basically the principle that if you double your bets every time you lose, you can guarantee to at least break even ... so long as your bankroll holds out), allows one to recast a surprisngly large portion of economics in its own terms, as anyone masochistic enough to struggle through Merton's "Continuous Time Finance" will have repressed memories of. Merton et al. don't get as much respect as they used to ever since the Long Term Capital Management shenanigan, but I think that's unfair; when it comes to the application of economic theory to the real world, we should take a leaf out of Dr Johson's book and wonder not that it was done badly, but that it was done at all.

The von Neumann/Morgenstern equilibrium concept, which takes coalition-forming and co-operative behaviour as a fact of nature rather than a subject of analysis, would have made a better foundation for game theory in my view; less susceptible to wholly rigorous proof through topological fixed-point theorems, but for this reason more dependent on specific application to real-world institutions and all the better for that. A succint way of putting across the point I am trying to make here might be that the well-known question of the "Prisoners' Dilemma" is a question that needs to be unasked; it's a red herring. Nash's proof that the optimal solution to a one-period noncommunicative Prisoner's Dilemma is the strategy pair (default, default) is only persuasive if we accept Nash's solution-concept as being a good definition of an equilibrium and we shouldn't. It's much better for our thinking if we just accept that Prisoner's Dilemma as being an intrinsically insoluble problem, and deal with real-life situations which resemble the Prisoner's Dilemma (nuclear deterrence, overfishing, etc) by looking more closely at the actual dynamics of the situation -- the power relationships and the decision making processes -- and modelling those, rather than pretending that we can flatten everything down into a one-period model with a "well-defined" solution.

You won't learn any of this on an undergraduate economics course, of course, which in my humble opinion is why economics is in such a bloody awful state these days as a discipline. The trouble with current economic theory is partly that we don't have the right mathematical tools (we don't have tractable ways to model dynamic systems), partly that we can't have the right mathematical tools (some important things about choice and social interaction are formally undecidable), and partly that we aren't even asking the right questions. I don't pretend to have a solution to this problem by the way; I'd just suggest that the current state of economics looks to me to be much more like medieval alchemy than any real science. Which is not to say too much of a bad thing about modern economics; the alchemists did real, good work, and most of them were very clever men (about 20% of Charles MacKay's "Extraordinary Popular Delusions and the Madness of Crowds" is about the alchemists if you get the proper version and not the crap expensive abridged one with a foreword by Warren Buffet, and it's surprisng how few genuine charlatans there were). I personally think that the Black/Merton/Scholes approach is the right way forward, and that it is at its heart a quite philosophically radical way of thinking about the discipline of economics -- not as the science of what people choose to do, but of what they can be forced to do, through fear of loss. But I think it is time to end here, as I have an appointment to play snooker at four 'o'clock.
0 comments this item posted by the management 11/07/2002 07:46:00 AM

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