Two Theories on Decisions (2024-02-26)

How (Not) To Be Wrong

Recently I’ve been spending some time figuring out what I want to do after college. I had a few options that were pretty different directions, so it was a little hard to ask people for advice; I do not think anyone gave me any particularly convincing advice of the form “you should do X and not Y because Z,” although I certainly heard plenty of such statements. Some people answered questions about X and Y and were thus quite helpful, but still they were not very helpful about comparing the two. On the other hand, I did receive some useful advice on making decisions, which I share here.

Idea 1: The hardest decisions do not matter.

This is a game theory-type observation. If you are making a decision and one option is clearly better, then the decision is easy. On the other hand, when a decision is hard, it is because you are deciding between options that seem equally good (or equally bad). For example, in rock-paper-scissors, it is “hard” to pick between the three choices, because they are roughly the same. In fact, game theory suggests something even more interesting, which is that you should randomize between equally good options. In other words, when a decision is truly impossible, it is not only impossible to make a correct choice, but also you should be randomly deciding between the options.

(Note that the game-theoretic analysis only applies to multiplayer games; in single-player games the analysis tells you that your decision literally does not affect your outcome. For example, in poker you cannot just go “I feel like playing on, let’s call every hand”, but in blackjack it’s fine to just always hit on 50/50 situations.)

But not all decisions are rock-paper-scissors. Decisions can also be hard because the options are hard to compare — this was the case for me. In this case still, this idea is nevertheless useful. The difficulty of the decision itself still implies that one route is not clearly better than the other. The point is somewhat tautological: If no choice is much worse than the others, then it is impossible to be very wrong. (Here, it’s possible to be wrong in retrospect, but if you think your information-gathering was sound, then it seems wrong to judge the decision based on future knowledge.)

Idea 2: You should make as many hard decisions as possible.

Suppose you imagine life as a massive tree of decisions. Then, all the easy decisions are basically predetermined/forced. So, you proceed through the tree, and the only times when things branch off are when you actually have to make a hard decision. In other words, the hard decisions not only matter, but they are the only ones that do. A corollary of this model is that if you are not making hard decisions, then you have essentially lost all of your agency. Since agency maximization is good (it means you have more options and more control), you should also try to make some really hard decisions.

Another observation is that hard decisions force you to become more introspective. In particular, when you have to compare two things that are hard to directly compare, then you are forced to think hard about which values actually matter to you. In this way, hard decisions force you to understand your own motivations better.

In fact, you can learn about more than just yourself. Forcing yourself to make decisions, even if they are just by considering alternatives to your current path, lets you better understand your current path. You can make observations when comparing two things that you cannot make (or that become harder to make) by considering them individually. This is why foils are such useful literary tools; it is also why reductions (i.e. comparing difficulties of problems) is such a powerful tool in modern theoretical CS. Therefore, forcing yourself to make decisions allows you to also better understand your choices, which is beneficial irrespective of the actual decision itself.

Neither of these theories are actually helpful in terms of how you should make the decision itself; that ends up being too personal of a process for me to make any generalizations from. However, I found them to be quite reassuring; they implied that, by virtue of being in the position that I was in, I had already made it onto the right path.

Thanks to Rohan K., Edgar W., Oliver Y. for reading and feedback.