Revelation through Randomness

Randomness is often portrayed as the enemy. We are fooled by it, puzzled by it, and must suffer the consequences of it when our best-laid plans are disrupted by it.

But randomness can be our friend too. In particular, randomness can be a powerful instrument of revelation- of learning about how things are, and not necessarily how we believe them to be.

The most commonplace idea about using randomness to learn might be that of representative sampling. You need to determine the quality of a batch of manufactured products. How many will you test? If the testing is destructive (or even just expensive), as few as possible! But which piece do you pick to test- the ones that appear defective or normal? The answer is neither. You pick at random. This ensures that the sample you selected is representative of the entire batch- and because you picked randomly, there can be no systematic differences between what you picked and what you did not. Randomness works for you by helping you learn about a large number of things by only looking at a few of them. That’s the idea behind market research and voter surveys, not only quality testing.

Randomization of treatments is another, perhaps not as well-known, approach to revealing the truth using randomness.

Let’s say we see that A and B happen together (e.g., a surge in ice cream sales and deaths due to drowning). Could one have caused the other? Or is the relationship spurious, with something else — a hidden factor- causing both A and B (e.g., a heat-wave)? You might say that common sense makes this obvious, but that too had to come from somewhere; and in many other cases of A and B, there is no common sense to draw upon. (That was the case for most cures for most diseases till a few hundred years ago).

Randomness can help solve this “hidden factor” problem as follows: select a group of people at random (you can flip a coin) and deprive them of ice cream. Compare their drowning rates to that of the group that continued to buy ice cream. “At random” is crucial because it means that there can be no hidden factors that are systematically higher or lower for the group that was deprived of ice cream. For instance, we can rule out that only the people who live in low-temperature localities were systematically deprived of their sugar rush. So, heat waves cannot produce a fake link between ice cream and drowning. In fact, nothing can — because by definition, depriving people at random means there is no systematic factor that is correlated with them suffering in this way.

This is the logic underlying experimental design. It is easily one of the most important pieces in the toolkit for learning about how our world works- whether to discover cures (clinical trials), better-selling online ads (A/B testing) or even poverty alleviation policies that work (randomized control trials).

This second use of randomness is related to the first. Randomizing who gets a “treatment” and who does not (“control”) is the same thing as randomly sampling from a group to create a treatment group (leaving the rest as a control group). Since the sampling is random, there will be no systematic differences between the two, since one set is representative of the other. Then, we introduce the only difference- the treatment itself. Any difference we observe in outcome must have been due to this treatment.

There is a third, perhaps less widely known benefit of randomness for learning. Doing things at random helps overcome biased views of the world that are self-confirming.

Suppose you believe doing A is better for you than doing B. Therefore, sensibly, you do A and find the outcome to be what you expected. Your beliefs are strengthened about the wisdom of doing A instead of B. But should they be? Maybe not. It is possible that in fact your views about B are biased- it would have been better to do B. But you did not, and you will never know. Your biased beliefs about B being inferior to A are self-confirming because acting on these beliefs prevented you from discovering they are false. (Self-disconfirming biased beliefs could also exist, for instance when you think doing A is better for you than doing B, and you discover by choosing A that you were wrong. This is not such a big problem- that’s how we learn from failure. Self-confirming biased beliefs in contrast involve overlearning from success).

To the extent we learn about how to act by learning from what happens when we act, there is always a risk of biased beliefs becoming self-confirming. To escape biases in one’s thinking, it is therefore important to do things that seem counter-intuitive given our current beliefs. This challenge of balancing “exploration” (for better actions, by trying non-intuitive actions) with “exploiting” the value of current wisdom (by acting consistently with current best beliefs) is known to be a staple feature in learning systems of all kinds, from rats in mazes to chess-playing algorithms and self-driving cars. We are no exception.

In fact, the second application (experimental design) can be viewed as a particular case of the third (exploration to avoid self-confirming biased beliefs). Consider a situation in which we have two choices again, A and B. We might believe (erroneously) that doing A is better for us than doing B. Where does this bias come from? Perhaps nobody has ever thought of doing B; the absence of evidence is however not evidence of absence. But another possibility is that we have observed that doing B seems to be associated with poor outcomes, not realizing that there were hidden factors that always accompanied our choice of B that made it look like B was a losing proposition. As I noted above, randomly doing B in some cases but A in the rest is a way of producing information about the true value of B, free of the confounding effects of hidden factors and thus helping to overcome a biased belief about it. Experimental design is thus a particular case of using randomness to overcome potentially self-confirming biased beliefs that arise because of hidden factors that mislead us about the consequences of actions.

Of the three paths to revelation through randomness, the third principle of acting at random is the least intuitive. Should we really set out to tackle life with our dice in hand? If we (admit we) are not omniscient- our beliefs could be biased- the answer is a definite and perhaps disturbing- “yes”.

The problem is that we don’t really know how often to roll the dice. A good thumb rule is to roll them more often in situations where we know that we don’t know enough — i.e., where we suspect our beliefs could be biased- but where the worst outcomes even if we select randomly are still not likely to be too bad. For instance, if you decided at random between taking the lift and walking off the edge of the balcony to get to the ground floor from your 7th floor apartment, you are a candidate for the Darwin Awards. But if you decide to pick at random between the familiar and unfamiliar restaurant, you might learn something useful and are at worst going to experience a bad meal.

Here’s a more practical example of a situation where we might know that we are likely to not know. Past data can be helpful in making predictions, and that is indeed the promise of predictive analytics through machine learning. However, learning from the consequences of past actions, as we saw above, can leave you a victim to self-confirming biased beliefs. Let’s suppose your HR department was biased against a particular race or gender, and rarely hired them. Then the data on your past hires and how well they performed may not suffice to eliminate this bias. If you train a machine learning algorithm on this data, you may even have locked yourself into inadvertently reinforcing past mistakes.

But if we know this risk exists, a solution is to hire (at least some) at random. This may come with some short-term costs, but it can significantly improve the prediction accuracy of the models used in the evaluation of future candidates. Think of the short-term costs as the acceptable sacrifices required to de-bias your selection process- the modest price of enlightenment through randomness.

But let’s be honest, our thumb rules on when to roll the die are usually just that — thumb rules.

Choosing to act randomly –to select actions that are inconsistent with current beliefs- is hard because it requires us to recognize the possible imperfection of those beliefs. In a culture that worships rationality as consistency, and too often equates confidence with competence, the license to randomize is not easy to obtain.

Sometimes that license is hidden within ritual and custom. Consider the practice of the examination of animal entrails, the observation of the flight of geese or the perusal of the weekly horoscope. Each can serve to inject randomness into the process of decision making and may perhaps lead to the discovery of better actions (or it may not)- not to mention making you inscrutable to your enemies. Randomized experiments may be seen as rituals that have obtained social sanction to do this — we know this is just a “trial” or a “test”, so that we support their conduct, even if unconvinced by the reasoning behind the claims being tested (if we were completely convinced, why bother testing them)?

And then there is just plain old error. The unintentional error, the misguided error, the pig-headed colleague with erroneous views, and the case of sheer bad luck- all are sources of randomness in decisions. Breakdowns in communication can be also quite useful in this way. In most organizations of even modest size, there is a separation between belief and action- managers may form beliefs about what to do, but their subordinates are the ones doing the doing. Miscommunication or misalignment between the former and the latter can produce random deviations from the intentions of the former, and to some degree these are even tolerated as the costs of providing autonomy to the subordinates. Yet, all of these sources of error may also have some value in helping us escape self-confirming biased beliefs.

When I started out as a graduate student, it was still possible to see papers that equated rationality with “doing what makes the most money”. Soon that gave way to the more enlightened sounding (but harder to pin down) “whatever maximizes utility”. Then, having realized that our beliefs about what maximized anything were often far from accurate, we switched to “maximizing subjective expected utility”- which is really nothing more than saying we should act consistently with our beliefs about what we think is the best course of action. But even consistency, as we have seen above, may not always be adaptive. Acting inconsistently with our beliefs — in essence at random- is sometimes the right thing to do to escape our biased beliefs.

Only the omniscient can afford to be consistent. It might behoove the rest of us to wonder if the “war on error” that formalization, automation, and mechanization represent, is at least to some degree misguided.

The ideas in this essay draw on those in one of my favorite papers by the late James G March, “The Technology of Foolishness”, from a lecture I gave on “Exploration in Organizations” in his memory at Carnegie Mellon University in 2019, and from the paper “Self-confirming biased beliefs in organizational learning by doing” (with Sanghyun Park, Complexity, 2021).