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 …
Orderstatistic 
Great response. The pool player analogy might be the most succinct explanation of the epistemology of economists that you can get. Important concepts like WARP are basically built on it!
I’m sorry, but I don’t have time to read your and Noah’s posts carefully and completely now, and it may be a while before we can. But this claim and paper of Freidman’s is discussed in Stanford economist Paul Pfliederer’s profoundly important “Chameleons” paper in 2014:
An absolutely literal interpretation of Friedman’s claim that models should be judged
only by their predictions leads to nonsense. As I will argue below, the only way the
extreme Friedman view can be supported requires that we come to any prediction
problem with completely agnostic Bayesian priors about the world. For example, assume
that we are interested in economic models designed to predict the U.S. inflation rate in
year T based on information known in year T-1. Let us take literally the notion that we
should judge these models only by the success of their predictions and we should
completely ignore the realism of these models’ assumptions. In this context we would
simply be looking for the model with the best inflation prediction record. If we allow any
assumptions to be made no matter how fanciful they are, we can use any data that are
available at T-1 to predict the inflation rate in period T.
The number of models we could develop that make (within sample) extremely accurate
predictions is extremely large if not infinite. Friedman, of course, recognizes that within
sample fit is meaningless in this context and states that the goal is to obtain “valid and
meaningful (i.e., not truistic) predictions about phenomena not yet observed.”11 However,
if we wait a few years and use the new out-of-sample data to “test” all of our contending
inflation prediction models, it is not the case that the one “true” model will emerge
victorious and all the “false” models will crash and burn. We will, of course, find that the
performance of most of the models that we identified as stellar within-sample performers
is severely degraded in the out of sample period, but an extremely large number will still
survive. Many of the surviving ones will no doubt be based on fanciful and unrealistic
assumptions. For example, we may find that in one of the many surviving models the
inflation rate in year T is determined by a simple function of the average height of male
Oscar award winners in year T-1. Of course, I am well aware this is argumentum ad
absurdum, but I am taking Friedman’s claim that we should ignore the realism of the
assumptions quite literally. In fact, from what Friedman writes it is difficult to know how
he separates the absurd from the merely unrealistic. He writes:
“Truly important and significant hypotheses will be found to have “assumptions”
that are wildly inaccurate descriptive representations of reality, and, in general,
the more significant the theory, the more unrealistic the assumptions (in this
sense).”12
11 Friedman, “The Methodology of Positive Economics,” page 7. 12 To be fair, Friedman does in a footnote state that “the converse of the proposition does not of course
hold: assumptions that are unrealistic (in this sense) do not guarantee a significant theory.” Note that
despite this qualification, Friedman is still suggesting that a very unrealistic set of assumptions can be the
basis for a “significant” theory and seems to hold that unrealism is a virtue. None of this gives us any
guidance for determining which (if any) of the extremely large number of models that make “accurate”
predictions with very unrealistic assumptions should be taken seriously. In other parts of his essay
15
He also writes
“Complete ‘realism’ is clearly unattainable, and the question whether a theory is
realistic ‘enough’ can only be obtained by seeing whether it yields predictions that
are good enough for the purpose in hand or that are better than predictions from
alternative theories.”
It will almost always be the case that the seemingly “best” models for prediction (based
on the data we have available) will be “fantasy” models like the “Oscar Award” model…
… Since little or nothing in the Oscar Award model is in accord with our background knowledge about the world, we reject it. It does not pass through any sensible real world filter. This is because our Bayesian prior on the Oscar Award model is effectively zero and a track record of prediction successes does essentially nothing to change that prior. This Bayesian prior is based on our knowledge of the world and the only way to give the Oscar Award model any standing would be to ignore our knowledge of the world and have a “completely uniform” or “agnostic” Bayesian prior, assuming that this could be defined. We can also think of the Oscar Award model as making other predictions than the inflation rate. If there is a causal chain between actor heights and inflation rates, we Friedman suggests that we should value simple models over more complex ones, but this does not seem to get us very far since some of the best predicting models may be quite “simple,” perhaps depending on only one variable, e.g., the height of male actors. 16 would expect to see further evidence for this chain than just the resulting inflation rates. For example, do we see economic agents who make purchasing and price-setting decisions actually checking on the heights of the leading male Oscar contenders? For anyone who takes the Friedman claim quite literally, this is a probably an illegitimate question to ask since it seems to be addressed to the realism of the model’s assumptions not the accuracy of its predictions, which is a no-no. For the rest of us, this is quite a sensible question to pose, since it is part of passing the model through the real world filter. The question is not whether we should judge the practical utility and applicability of models by the realism of their assumptions. We should (and we routinely do). The question is what types of unrealism are relatively innocuous – simplifications that make the model tractable and useful but do not create a serious disconnect with the real world or take us into fantasy land – and what types should lead us to reject the model. This is a question that is not easily answered and no doubt one that involves judgment. Friedman’s claim might be viewed as a valiant attempt to completely avoid having to address this difficult question, since his claim seems to suggest that the realism of a model’s assumptions is of no import, only the accuracy of its predictions. But Friedman’s claim cannot be used to avoid these questions, since it gives life to the Oscar Award model and myriad other models like it. We cannot avoid the need to run models through the realworld filter. The literal interpretation of Friedman’s claims cannot be taken as an argument for allowing chameleons to bypass these filters.
At: https://www.gsb.stanford.edu/sites/default/files/research/documents/Chameleons%20-The%20Misuse%20of%20Theoretical%20Models%20032614.pdf
Most people don’t know what marginal utility means, but they largely try to do the basic concept of utility optimization in making choices, or adopting rules of thumb. It’s actually not that unrealistic an assumption. They don’t know the jargon, and aren’t that precise, but they by and large do the main idea, which counts a lot.
But, when they don’t do the main idea at all, and it’s very material to what you’re interested in, then there’s a serious problem.
Also, people are usually very expert on what foods taste good to them (at least in the short run, taste buds adapt a lot), but about other things they have very poor and inexpert or incorrect information. For example, health care, or what the government spends money on, and surveys confirm this very dramatically. So, in this area the assumption of quite accurate optimization and the resulting policy implications can be horrendously off.
The big economic decisions most people make are about getting married, buying houses, buying cars, and, for some choosing a college or graduate school. Anyone who thinks people made these decision rationally is either insane or an economist. The same goes for various medium scale decisions. A whole industry, advertising, is based on people not being rational about these decisions.
John, you are making a very important point. It is the decisions that we make every day, again and again, where we will be most confident in efficient rational behavior. Things like doing your job day in and day out, shopping for food and clothing, deciding what to have for lunch and dinner, deciding which routes to take commuting to work, how to run your business on a day-to-day basis etc. should be the activities where we should expect the most efficient behavior.
As you point out however, there are many important decisions that are made infrequently and so we have much less experience to draw on. You mentioned getting married, buying a new home and choosing a college — I think I would add career choice to the list as well. These are all situations where we can expect rational behavior in the sense that people will try to make the best decisions they can given what they know but where they might make substantial (ex post) errors. I don’t think its correct to say that these decisions are necessarily more important than the frequent decisions but they are certainly quite important.
In the pool player story, this would be like saying that for some shots the errors are quite small but for other shots we should expect large errors.
“That’s because higher education is a complicated market. It’s easy to spend $3 on a cup of coffee that suits your tastes. It’s a lot harder to make smart choices when you can’t experience the college you’ve chosen until after you’ve taken out expensive, nonrefundable loans…
…Considering the scale of what went wrong for many students enrolled in ACICS-accredited colleges, it’s hard to see how to fix things without government action.”
At: http://www.nytimes.com/2016/06/22/upshot/for-profit-college-fiasco-why-a-watchdog-needs-a-watchdog.html?rref=collection%2Fsectioncollection%2Fupshot&action=click&contentCollection=upshot®ion=stream&module=stream_unit&version=latest&contentPlacement=3&pgtype=sectionfront
Here is my take on optimization and the pool player analogy:
In a model you find what the optimum is for the agents (people). The people may not go through the math you did in the model to find that optimum. They may use rules of thumb. They may use non-verbal, non-conscious, algorithms built into their brains by evolution, and combined with the data of personal experience. But, if those ways are pretty effective, then they may usually find the optimum, or, on average, get very close.
The math tells you what the optimal pool shot is. The good pool player uses evolutionarily developed algorithms combined with experience to devise his shot. But the point is, if he’s a professional pool player, the optimal shot will be a very good approximation of how he actually hits it, and so it’s a very valuable thing to use in a model, and in devising related policies.
You don’t care that much, at least for many important questions, and real world applications and policies, whether people do it exactly like the optimization in the model, but you do care that that optimization leads to close to the end decisions people will actually make. And it looks like based on many of the things I have heard Freidman say in his life, he doesn’t care about this second part, as it often makes his libertarian philosophy look horrible to the vast majority of people, and that get you nowhere in a democracy (a big reasons libertarians are very derisive to, and hostile to, democracy).
And, just in general, when you do make highly unrealistic assumptions in a model, you, of course, think intelligently about what you can apply to the real world, and what you can’t, and how it will differ when you relax the assumptions. You don’t just automatically literally assume the real world will behave exactly the same, or very close. Many obviously know this, but ignore it to make their ideology look better, or their hard won modeling expertise more valued, expertise that gets them tremendous monetary, prestige, and power rewards. And this approach can be very effective for them, as their mathematical papers are incomprehensible to 99%+ of the population, and often to more than 90% even of other PhD economists who are not in their specialty.
The big problem I see with Freidman’s pool player analogy is that it’s often applied when the pool player makes shots far from the optimum that comes from the formulas. For example, when the pool player has incorrect information that is highly material, like if someone had an adversarial incentive to fool him into thinking that he optimizes by avoiding the holes, and instead trying to get all of the balls touching the far end. And we see this kind of successful fooling all the time, sadly, in economics (and politics), from sales of horrendously bad and risky annuity plans to seniors, to for-profit universities, to CT scans that are unnecessary, harmful, and are priced 10 times what they are available for elsewhere. In such cases, the models have severe problems when fully interpreted literally to reality and government policy
If the pool player uses a set of genetically programed algorithms, calibrated by experience that are very different than applying Newtonian equations, but they do lead to extremely similar shots, then it’s a fine analogy. But in many extremely important cases that kind of thing is far from the truth.
Actually, I unfortunately thought of this after my last tour de force comment, but there’s a good chess analogy.
I’m a chess fan too. I don’t know how much you’re into the Michigan chess scene, but I was one of Andy Bider’s kids many decades ago. I usually took my age group in the Michigan Junior championships. I played in Metro League if that’s still around. Good times…
Anyway, a computer chess program finds it’s moves in a very different way than a human grandmaster, but the move selection will typically be very similar. There’s just more than one way to find the optimum, or very close. So, the move found by a computer chess algorithm will be a very good approximation for the behavior of a grandmaster, but a terrible approximation for the behavior of the median person. In one case, a pretty literal interpretation of a chess program based model makes sense; in another case, it doesn’t, and your interpretations to reality, and real world policy have to be very much modified, and thought out with your real world knowledge (Bayesian priors) in mind.
All this misses the conceptual problem with the pool player analogy and homo econimus. People may always act rationally, but not to maximize their economic utility. Incentives matter is the central point of economics. But what are incentives? Thomas Sowell points out that culture matters in examining what behavioral incentives exist. And homo econimus assumes that actors have access to relevant information. But this is NEVER true. Information is always incomplete and asymmetrical. Look at it this way, maybe the pool player values hitting the 8 really hard and likes watching balls roll around. Or maybe he thinks the table is rectangular with six pockets based on his quick glance, but it actually is a polygon with 7 unevenly spaced pockets, cushions that do not react consistently and send balls away at odd angles and isn’t flat or level. Now with an ‘irrational” rational player on an undetermined misunstood surface you have real microeconomics, not make believe.
Firms don’t make choices; the employees who manage the firms make choices, and unless there are sufficient controls, the employees maximize their own self-interest at the expense of the firms. It wasn’t in the interest of banks to engage in transactions that drove them into insolvency, but it was in the interest of the bank employees whose pay was based on the volume of the transactions. It’s the deliberate ignoring of this fact that makes so much of economics a fundamentally dishonest enterprise.
Well written. This is very interesting to think about.
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