Hi there, argmin readers! Today’s post is a live blog of Class 9 of my graduate seminar “Forecasting: A Critical Retrospective.” The syllabus and list of past posts are here.
Every class I teach seems to require a lecture or two on expected utility maximization. It’s the basis of classification rules, so it’s integral to machine learning classes. It’s the simplest stochastic optimization problem, so it appears in my optimization classes. It’s a great motivator for probabilistic thinking, so it appears in probability classes. Perhaps a bit less well appreciated, it’s an indirect proper scoring rule for forecasts, so we have to talk about it in this class. And, I suppose, it’s a mathematical tool that scarily dominates the philosophy of many powerful people in government and industry alike. It’s worth understanding the nuts and bolts!
Part of what makes utility maximization so appealing is how simple the core idea is. We want to decide whether to act or not. We build a probabilistic model of the world under the action and compute the expected value of the benefit. We also build a model for what would happen if we don’t act and compute the expected value of the benefit of inaction. We choose to act if our calculations imply that action has more benefit than inaction.
What could be simpler? You compute probabilities. You compute costs. You multiply them together and add them up. Everything is beautifully quantified and calculable.
The only problem is these numbers are all made up. They are forecasts, and they are rarely justifiable. Outside of the casino, we rarely know how to calculate precise odds of outcomes. Worse, forecasting the prices out in the future is also inherently uncertain, often more uncertain than the odds calculations. Maximizing the utility of a rational actor or a general population is an appealing philosophical goal, but the precise rational calculations are always made about fantasy stories. Economists know this, and proceed with caution. In the comments of Tuesday’s post, Jordan Ellenberg flagged this quote from John Maynard Keynes.
“By ‘uncertain’ knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty… Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealthowners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed.”
Keynes here seems to be reluctantly defending utility maximization as the best of many bad options for decision making in the face of uncertainty. But I don’t think that’s his point at all! Keynes is defending his “General Theory of Employment” and arguing against this sort of utilitarian calculation.
As it is colloquially known, “Keynesian economics” — a term that sadly oversimplifies Keynes’ brilliant collected works — tells governments to stimulate economies during recessions. Keynes argues that we can’t accurately predict the future, and hence people tend to lean on status-quo bias. The safest bet is to assume nothing changes. But when the status quo is bad, people become risk-averse and hold their money. This hoarding prolongs recessions. Because the future is uncertain, people don’t act “rationally” when they fear they might not have money to spend later. Keynes thus argues that governments should step in to nudge citizens out of their undue pessimism by giving them extra money to spend.
Written in the pits of the Great Depression, Keynes’ argument in his 1937 article in the Quarterly Journal of Economics articulates how utility maximization goes wrong. The future is unknowable. Uncertainty makes people afraid. Fear makes hoarding more attractive. Mass hoarding perpetuates a vicious cycle of societal hardship. At this point, someone needs to step in to get the ball rolling, eating up some of the risk to inspire more confidence in people to spend their money.
In this class, we’re not going to debate the merits and challenges of recessionary stimulus spending. But Keynes’ article (which I have added to the reading list) articulates the nuance of forecasting under great uncertainty. Human psychology plays a key role. Today we’ll go through how this appears in the mathematics, with different utility functions expressing different models of risk aversion, and different algorithms for action. We’ll see that not only are the costs and benefits uncertain, but the algorithm itself can be shaped by different models of psychology. Expected utility maximization might be a reasonable way to engineer machines, but it’s not something that reasonable people do. Understanding the many hyperparameters of optimal decision making can help us better understand the psychology of people obsessed with forecasting.
. In the meeting, I will talk about problems around Borsuk’s conjecture.