I haven’t written on my blog for a really long time but I am starting to approach a point where I might actually have some time to post again somewhat regularly. My reason for writing this particular post is in response to a blog post by Noah Smith who took issue with Milton Friedman’s famous pool player analogy. Noah has concluded that “the pool player analogy is silly” and his reasons for arriving at this conclusion are
- If actual pool players never missed their shots, there would be no use for the physics equations as a prediction and analysis tool.
- People make mistakes so they don’t always optimize.
- People who make bad decisions don’t tend to go away over time.
- Unlike in pool, we rarely know what the objective is.
I must confess that the pool player analogy is one of my favorite analogies in economics and I use it often when I am talking to people about economics. The pool player analogy is a common response to typical criticisms of standard microeconomic analysis. Microeconomic conclusions like “consumers should make choices that equalize the marginal utility per dollar across goods” or “firms should make input choices so that the marginal product of capital equals the real (product) rental price of capital” often seem very abstract and technical and they invite natural objections like “real-life people don’t behave like that” or “in the real world, firms don’t make calculations like this.” Such reactions are natural and this is exactly where the pool player analogy fits in. In pool, making the best shots would seem to require a host of extremely involved calculations involving physics concepts that most real-life players won’t know. Making an optimal shot requires considerations of the friction of the felt on the table, considerations of angular momentum, transfers of energy, torque and so on. Even if a pool player knew about all of this stuff one would guess that it would require a long time between shots as the player made a series of complex calculations prior to taking the shot. Nevertheless, the actual shot taken will look a lot like the one implied by such a calculation. That is, the pool player’s actual behavior will closely resemble the behavior implied by the optimal physics calculation.
The central guiding principle of economic analysis is that behavior is guided by self-interest. Consumers and firms make choices that (in their assessment) make them as well-off as possible. Sometimes this principle is summarized by the term homo economicus or “economic man” which essentially views mankind as being comprised of many self-interested autonomous beings. The pool player is one manifestation of the behavior of a self-interested individual making choices under a constraint but so are ordinary people. If you go to lunch at a Chinese restaurant, you will in all likelihood be confronted with a staggering number of choices, options, prices, substitutions, and combinations. One might be tempted to conclude that it will be impossible to make an optimal choice from such a menu because there are simply too many possibilities to consider. However, when I actually go to lunch at the local Chinese restaurant I typically see people ordering relatively quickly, sometimes individualizing their choices and I suspect that most people do not anticipate that they typically made mistakes ordering lunch. Homo economicus does a pretty good job ordering lunch, commuting to work, etc. This is not to say that economic man doesn’t make mistakes or overlook things. This is inevitable and surely happens often in the real world. The question you have to ask yourself is – do you think people typically make something close to the best choices or do you think people typically make severe mistakes in their economic decisions. If you agree with the former then you are thinking like a mainstream economist.
Noah seems to think that because people make mistakes or because we can’t know the true (mathematical) objective functions that this appeal to optimal behavior is misguided. To me it seems like Noah is not criticizing “economic man” so much as he is criticizing “economic straw man.” In the article he arrives at this startling conclusion writing
[If] really good pool players made 100% of their shots, there wouldn’t be pool tournaments. It would be no fun, because whoever went first would always win. But in fact, there are pool tournaments. So expert pool players do, in fact, miss.
(… shocking, I know. How could we have not seen this?).
Economists do not assume that people don’t make mistakes (though in fairness it is not completely obvious how to analytically model mistakes). I can think of exactly zero economists who think that all behavior is optimal from some omniscient / omnipotent point of view. I certainly don’t believe this – I regularly play online chess and I always overlook moves that are to my advantage or moves my opponent could play that would be really bad for me. This doesn’t in any way suggest that my behavior isn’t guided by my own self-interest or that my move isn’t what I think is my best option given the current position. Moreover, I would think that, in chess, starting from the point of view of making choosing one of the better moves available would often provide a good guide to actual game play – this is almost certainly true for professional and semi-professional players.
Imagine, if you will, actually trying to construct a model of pool playing. Specifically let’s consider 9 ball. In 9 ball the balls are sunk in order (unless the 9 goes in on the break). This greatly reduces the strategic nature of the game and makes it more like the players know which shot they want to hit and now there is simply the task of actually making the shot. If I were to approach such a problem (which might actually be interesting from a behavioral economics point of view) I might adopt the following approach: Suppose the best shot could be described by a vector S. S would include spin, speed/power, angle, etc. A perfect player would simply take a shot given by S. We could think about a real-world player as taking a shot that might include an error e. The spin will be a little off, the angle will be off a bit too, and so forth. So any one actual shot could be given by S + e. You might think that the best players typically make small errors while inexperienced players would make bigger errors. I would think this would be a pretty good description of actual pool but note I would absolutely begin with the idealized shot S (the shot made by homo economicus).
Noah also makes a big deal about the fact that we don’t know the objective. The fact that we typically don’t know the objective is not necessarily a problem. If an economist looks at a game being played where she isn’t familiar with the rules then she will still tend to treat the moves she observes as though they are guided by some latent objective. (And you might guess that after looking at such behavior for a while, the economist might be able to deduce the objective even if she doesn’t have advanced knowledge of it.)
In short, I have always felt – and I continue to feel – that Friedman’s pool player is an excellent way to convey how economists approach their subject. Only if we were to insist that people really were computerized robots or Vulcans always making perfectly optimal, logical choices with regard to some easily described mathematical objective would this analogy present a problem – in fact it’s only a problem for the economic straw man. So, until Noah comes up with some more serious objections I’m going to keep this analogy on my go-to list of explanations for basic economics.
In the meantime, let me leave you with this opening quote from The Color of Money.
A player can make eight trick-shots in a row, blow the 9 and lose.
On the other hand, a player can get the 9 in on the break, if the balls are spread right, and win.
Which is to say that, luck plays a plays a part in 9-ball.
But for some players,
Luck itself is an art …