Live After Quit

Milton Friedman’s Methodological Mistake

In 1966, famed Chicago School economist Milton Friedman wrote a hugely influential essay on the methodology of economics entitled “The Methodology of Positive Economics” (contained in the volume Essays in Positive Economics). In distinguishing economics as a “positive science”, Friedman focuses on the use of empirical investigation where the “ultimate goal … is the development of a “theory” or, “hypothesis” that yields valid and meaningful (i.e., not truistic) predictions about phenomena not yet observed.” Focusing on prediction rather than explanation of observation presents the first step wrong, but as can be seen later in his essay, Friedman doesn’t even stick to this requirement for prediction, saying that the theorist’s role is in part “to specify the circumstances under which the formula works or, more precisely, the general magnitude of the error in its predictions under various circumstances.” He even goes so far as to discount possible theories that can give more accurate predictions, saying “it does not always pay to use the more general theory because the extra accuracy it yields may not justify the extra cost.”

In short, Friedman is arguing that the truth of a theory’s statements does not matter. All that matters is whether the theory makes “good” (i.e., accurate enough) predictions. The case Friedman would make against, for instance, the phlogiston theory of combustion is not that the theory of elements is simpler, explanatory of phenomena unrelated to combustion, nor that no one has ever discerned a phlogiston’s existence or presented any way to do so. Instead, Friedman would simply argue that the predictions of phlogiston theory were not accurate enough. Enough for what? I don’t know that he could even say so.

These methodological errors come to a head when Friedman presents an analogy to a “theory” that predicts the shots of billiards players. Here Friedman tells us that we should

[c]onsider the problem of predicting the shots made by an expert billiard player. It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the billiard player made his shots as if he knew the complicated mathematical formulas that would give the optimum directions of travel, could estimate accurately by eye the angles, etc., describing the location of the balls, could make lightning calculations from the formulas, and could then make the balls travel in the direction indicated by the formulas. Our confidence in this hypothesis is not based on the belief that billiard players, even expert ones, can or do go through the process described; it derives rather from the belief that, unless in some way or other they were capable of reaching essentially the same result, they would not in fact be expert billiard players.

So here we have a “theory” of billiards. We can, supposedly, assume that “expert” billiards players operate in an idealistic world where they perform their shots perfectly using precise mathematical calculations and estimations. Here we can—in our theory—assume away all difficulty of the game, all inaccuracy of estimation, and all imperfection of human ability. Instead we can treat the players as if they were perfect billiards-shooting robots and proceed to make “reasonable” (even “excellent”!) predictions from there.

But it is not difficult to see that if we actually tried to predict the outcome of a game of billiards—even one played by experts—in such a fashion, we would quickly run into problems.

The first issue we would run into is … what is billiards anyway? None of the complexities of the math of a billiards shot can help you determine what the goal of the game is: not the angles of deflection, the velocity of the cue as it strikes the cue ball, the geometry of the balls scattered on the table. We must include in our theory the “rules of the game”. And here we thus introduce, by necessity, a teleological element. The billiards player is not making a shot at random; each and every action taken in the game is directed at a set goal (within set constraints), and these goals are defined by the objective and constraints of the game as played. Whether these players are playing 8-ball or 9-ball pool, or even something totally different like carom or artistic billiards, is a completely necessary part to predicting what shots a player will make.

Having added that in, we are still no closer to making any sort of predictions about the outcome of the game, however. Now we must account for the player’s ability to choose their shot. Fundamentally, we are presented with a praxeological element of action to the problem. The player, as a free actor, can choose between various shots. Do they choose the easier shot that might get a target ball in a pocket, but not set up the next shot well, or some more difficult shot that would readily lead into future shots? The assumption Friedman’s toy theory makes of essential perfection may incline us to assume the most difficult shots will be made every time (though it isn’t too hard to see how this would not conform to any real game of billiards), but even there we run into complications: two shots could be of essentially equal mathematical “difficulty”, but the player would still have to choose just one. This element of action also combines with the teleological element: the player’s goal may not match the described role of the game, as they could be playing for another reason, such as to show off their skill (even if they could make more strategic shots) or make a friend feel better (say by losing intentionally). These reasons can not be divined by others, but exist only in the mind of the player.

Do we throw our hands up and say we can only give probabilities at this point? Many would probably assume this is the answer that gets us out of this quandary: a “reasonable” assumption that the player makes the “best” shot (according to some mathematical criteria) with probabilities thrown in to account for cases where there are multiple “best” shots. As natural as this escape hatch might be at first blush, we can see on further reflection that it doesn’t really address the issue at hand. Different players will have different willingness to take risks, understandings of what it means to “line up a shot”, play preferences: no mathematical model can accurately account for the varying potentialities here, even when factoring in probabilities.

And all this is to say nothing of the fundamental differences in reality that would naturally exist: imperfections in player ability, the table, cues, or billiard balls. Or any of the various mental and emotional pressures on a competitive player going up against a well-skilled opponent. These are no small facet of the outcome of various shots and the billiards game itself, but a rather large component of it. Competitive billiards games can and do rest on one player losing focus and missing a shot he should have made, or mistakenly choosing one shot when they could have chosen another, potentially superior option. They can rest on the angle of deflection off one of the table’s side boards being just slightly off—and whether players can adapt to these differences quickly. Even predicting what shots players would make given a certain table setup, which has already proven impossible, could not allow for predicting how the game would evolve from there.

What could actually be predicted about billiards is thus rather small, and almost entirely inconsequential: assuming an ideal environment, the trajectory of a shot once the balls are in motion can be roughly predicted by the laws of physics. Physicists often use such idealizations to try to reason about isolated effects, using the generally accepted fact that physical forces are additive in predictable manners to explain (but generally not predict) larger-scale phenomenon. However, even the most studied physicist will acknowledge that predicting any “real world” phenomena outside of heavily isolated experiments is a job for supercomputers at best and essentially impossible at worst. (There is a reason that quantum mechanics class exercises mostly involve at most a handful of particles “in a box” and not macroscopic objects comprised of billions of such particles in complex interactions: performing the mathematical calculations would be nigh impossible with even the best computers.) As the old physics student joke goes, “first, assume the horse is a sphere….”

These conclusions can only be drawn more strongly when, instead of unthinking and predictably responsive objects like subatomic particles or billiard balls, we introduce human beings with goals and choices of their own into the mix. Prediction becomes essentially impossible except by rough chance, and provides no guide towards any explanation of how things are or why. Instead we must turn to logical deduction from basic facts like praxeology’s action axiom (“human beings act”) and teleological constructs like imputed goals to make sense of what is going on. This is even more true of the large complex of human interaction that produces a national economy as it is about anything as relatively simple and intuitive as a game of billiards.

Originally published Disinthrallment.