Oh goody, I’ve been waiting for Pile On Stephen Landsburg Week. That column of his in Slate has been winding me up for years.
As my contribution, check out this guest contribution to Marginal Revolution, where half-understood physics meets half-understood economics, with predictable results.
The guts of the post are as follows:
Let’s play a coordination game: You and I are each asked a single question, either “Do you like cats?” or “Do you like dogs?”. Our questions are determined by independent coin flips. We both win if our answers differ, unless we’re both asked about dogs, in which case we both win if our answers match.
Here’s a pretty good strategy we could agree on in advance: We’ll contrive to always differ. Whatever we’re asked, I’ll say yes and you say no. That way we win 3/4 of the time.
Can we do any better? No, if we live in a world governed by classical physics. Yes, if we live in the world we actually inhabit—-the world of quantum mechanics.
I think I know a way to do better, using only classical physics.
If I take in my right hand a notepad and in my left hand a pencil (both objects of classical physics), then I can simply write down the sentence [for example] “They asked me about dogs and I said yes”. Then I take it round to Landsburg’s office and show it to him, then he answers.
I estimate that I could get roughly 90% wins in this method (it would be 100%, but I’m allowing for the fact that 1 time in 10, Landsburg will fuck it up on purpose and write an article about how “counterintuitive” he’s being). This is better than chance, and also better than the 85% win rate that you can apparently get with some sort of funky quantum nonlocality or other.
The point is quite simple. A non-communication game is a non-communication game, and a communication game is a communication game. It doesn’t matter (for the purposes of economics) whether the communication takes the form of face-to-face contact, Bell’s effect or carrier pigeons. What does matter is whether the communication is credible or not; whether it is “cheap talk” whereby it doesn’t cost me anything to give a false signal, or whether there is an incentive condition which means that Landsburg could rely on my not intentionally misrepresenting things to gain some advantage, and whether or not the signal is observed perfectly or with noise. Landsburg is simply wrong to say that “game theory changes dramatically when players have access to quantum technology”, because no important points of economics turn on the precise mechanism of communication.
(In fairness to the authors of the paper Landsburg cites, they aren’t responsible for the use he made of their work; the “games” in their paper have no economic significance and are just being used as convenient ways to describe bounds on the information that can be communicated through a quantum channel. This way of talking about information transfer has been a standard in the engineering literature ever since the original Kelly Betting paper.
Anyone who was thinking for even a minute would have realised that this paper had nothing to do with game theory, and that the “co-ordination game” example was a clear cheat. So why didn’t Landsburg? I can only assume that it’s part of a more general phenomenon; the tendency of economists (and social scientists in general) to drop all their critical phenomena and fall into a swoon when they see the manly form of a physicist. Phil Mirowski makes a decent case that modern economics was conceived in this kind of physics-envy so it’s not exactly surprising, but that doesn’t make it any more correct. Here’s a few things that social scientists should always remember:
1) Despite what they tell you, physicists are human beings. They eat, fart and have sex more or less like the rest of us. There is no secret caste of physicists set apart from humanity; the difference between them and us is that they did a physics degree.
2) There is, to a first approximation, a continuum of physicists on a quality scale going from “genius” to “halfwit”. They come in good and bad varieties, and the bad ones are really quite bad. Furthermore, it is not difficult to tell the difference if you are prepared to learn a little mathematics and apply yourself. Cosma Shalizi tells the tale of statistical physicists who identify power law distributions by considering the R^2 value from a linear regression, and get their papers published. This on its own ought to diminish one’s respect for physicists to healthy levels.
3) That subset of physicists who regularly publish papers on social sciences is unlikely to be a sample from the cream of the profession. To the best of my knowledge, Steven Hawking has kept his opinions on the stock market to himself, and so did Richard Feynman. There are some very good papers in the econophysics literature (if you really want to know about quantum mechanics applied to game theory, here’s an introduction for you, but it doesn’t make the claim to have overturned the fundamentals of the field, or that quantum effects make a difference to classical games. NB also that Landsburg’s paper doesn’t cite Eisert et al’s paper on quantum game theory, illustrating my point that it’s not about economics), but they are massively outnumbered by pieces of work written by second-rate physicists who have decided to set out an ill-informed brain dump on some aspect of the social sciences because they erroneously believe them to be “easier” than doing physics. Have a look on the arxiv if you don’t believe me.