We all make a million decisions a day, both big and small. There are decisions like what to eat for lunch or what clothes to wear, but also big policy decisions that politicians make, decisions for medical treatment, and so on. We all strive to make decisions ‘rationally’, but most people aren’t actually on the same page for what this means. As a basis to understand the rest of this blog, and really all of rational thinking, we need to develop a clear understanding of what makes decisions good or bad.
Decision theory is the field that studies how individuals should behave rationally under uncertainty. Breaking this sentence down, first see that it’s about how individuals should behave, not how they actually do behave. Of course, how people actually behave is extremely important but that’s categorized into other fields like psychology and behavioral economics. Next, ‘rationally’ here means that the decision is in service to some goal, often referred to as an ‘objective’. Finally, the phrase ‘under uncertainty’ means that there is some unknown information or randomness that will affect the outcome.
You could spend your life studying decision theory, but for our purposes we just need to establish what exactly an objective is, and how to start thinking about decision making under uncertainty.
Whenever you are making a decision, the first thing you need to do is identify what your objective is. Your objective is your goal, is the quantity or quantities that you are trying to maximize or minimize. It will depend on your personal goals, or the goals of whatever organization you are acting for. For example, if you’re playing poker you might want to maximize your winnings, or if you’re running a public health effort you might want to minimize deaths. Before you start making important decisions, you need to clearly choose a good objective because it will drive the whole rest of the decision making process. Once you choose your objective, then comes the optimization: trying to figure out what the optimal (best) decisions are to achieve your objective.
If your objective is off-target from what you really care about, then it won’t matter how good your are at optimizing because you’ll be aiming for the wrong goal. If you’re shooting an arrow at the wrong target, it doesn’t matter if you’re the world’s greatest archer because you’ll just end up landing spot-on at the wrong place.
This might seem completely obvious, but people and even whole institutions often make big mistakes here, for a variety of reasons. One of these reasons is people confusing measures of an objective with the actual objective, and trying to improve the measure instead of the objective. More on that here.
When setting objectives in different contexts, it’s helpful to consider an appropriate scope for each given situation. Your life’s goal may be to maximize your own happiness, or maximize the happiness of the human race, or something else entirely. But these kinds of goals are not practical to think about when making most of your day-to-day decisions. When driving to work you probably are mostly trying to get there safely and quickly, and not wondering if each right or left turn will lead to a happier life. You’ve already decided some time ago that going to work is a good idea, so you can just focus on how to get there for now.
So in general, you want to choose the right scope of objective for any given decisions: large enough that it captures what’s important for the decision, but as small as possible so that the decision is practical to actually make. This can be a tricky line to walk, so it’s important to keep in mind the bigger picture even if you are focusing on something more specific at the moment. A heart doctor’s narrow goal may be to minimize the probability that their patient has a heart attack, but it’s still important that they consider if medication they prescribe hurts the patient in non heart-related ways.
For almost any decision you make there is some uncertain information that can affect the outcome. I like the weather as an example of this, because weather forecasts give actual percentage chances of different outcomes. Should you take your umbrella with you when you leave in the morning? If it rains later you’ll be glad you did, but if it doesn’t then it would be a waste of effort. There is no decision here that will always be best in hindsight, regardless of the weather.
For example, suppose you’re heading to an amusement park and it looks like it might rain. You can buy a cheap umbrella before you, but then if it doesn’t rain you’ll have no use for it. Or, you can wait to see if it rains and buy an expensive umbrella at the park. What should you do?
Let’s say all you care about is spending as little money as possible while staying dry. Well, since probabilities are involved you can’t actually always achieve this: if you buy the cheap umbrella and it doesn’t rain you could have saved by waiting, but if you forgo the cheap umbrella and it rains you could have saved by not waiting. So really your objective is minimizing the expected amount of money that you spend, where ‘expected’ just means average in economics language. Knowing the exact price of the umbrellas and the probability it will rain, you could work out for example that buying the cheap umbrella costs $5 in expectation (on average), and waiting to see if it rains will cost $6 in expectation. Then you should go with the cheap umbrella.
Sometimes it’s not the expected loss exactly that you are trying to minimize, because of the effect of risk: a big gain may be nice, but a big loss may be disastrous to you. Fully understanding the effect of risk may be beyond what most people are mathematically comfortable with, so instead you can think about minimizing (or maximizing) the expected value of your objective, plus some consideration for the effect of risk added on top.
In summary, what’s important to understand is that when making decisions you are really trying to minimize or maximize the expected value of your objective. And so just because your decision didn’t lead to the best possible outcome in hindsight, it doesn’t mean you didn’t make the right decision at the time. If you buy the cheap umbrella but it doesn’t rain, it doesn’t mean you shouldn’t have bought it.