Min-max search your own arguments

Essentially, when thinking about something, don't try to prove why you're right; try to prove why you're not. Try as hard and as geniuenly as you can to refute yourself. If you can't, you might be right after all. But keep an open mind.

What is min-max search?

Min-max search is a search algorithm. Most uses I've heard of "min-maxxing" outside of a computer science class really just mean in effect plain maximizing. I think people think it's "min-maxxing" since you might need to not only increase some factor but decrease some other one to reach the best result... which can be modeled as just maximizing some objective function. You're just maximizing. So, if you want to be pedantic/annoying, you point out that this is wrong if someone says it.

So what is actual min-max search? Well, I said search because min-max is a strategy you use on search algorithms in turn-based 0-sum games (or problems modeled as such).

The classic example is chess, where for every move you do you want to anticipate what the best response of the opponent is. In this sense, when doing a search you want to find moves that benefit you, but to see how good they are you need to examine what other moves can be played against you. Therefore, you need to search your opponent's moves, and here it's completely useless to search the moves that are best for you. The best move for you that an opponent might make is probably hanging the queen or similar, but of course your opponent just... won't play that.

But if you search all possible moves doing min-max, you will find the objectively best move.

There is a wrinkle in human chess in the sense that you can try to take into account how likely each opponent move will do, so there might be moves that are optimal assuming optimal play from the opponent but if every move except a very hard-to-see one is awful, you might risk it, play that move, and hope your opponent doesn't find how to save himself. This probably happens most often accidentally. While pragmatically useful, it's useless if you want to find the objectively best move.

Why min-max your arguments?

I think it's fairly "intuitively clear" to see the relation from the opening sentence to the example of chess in min-max. If we want to be rigorous it's not that obvious though, mainly because... where is the turn-based 0-sum game here? In essence it's "the debate". However it might be weird to call it a 0-sum game. Or even turn-based, really. For the turn-based, we can pretend that each time the speaker changes it's a turn. They might not be arbitrated, you might get cut off, but hey we never said that can't happen. And it doesn't matter that much because in practice getting cut-off doesn't change the crux of the argument.

Now, why would it be 0-sum? I think it sounds bad to say that a debate is 0-sum. Generally, in a lot of things, no one-side is completely right. What we are assuming is that, in the end, there is an objective reality and if you define properly your terms then there is an objective truth to a false and true statement. This sounds nice in theory, but is messy in practice, since there are few things you can say with certainty about anything. But that's why there exist quantifiers like "in general" or specifying some set of conditions. If we assume this is possible (which I argue it basically is), then the "debate game" is essentially 0-sum since there is no way to generate more true statements.

Here you could say that if someone changes an opinion then it is not 0-sum! Since both people can "win" (or lose lol). But it's important to note that I am modeling that the players are the ideas, not the people. And the argument is either right or wrong or ambiguous or whatever, but in theory it doesn't change. If the argument changes, it's a different game.

So under those assumptions, exhaustive min-max search will give you the best result! Oh, but exhaustive min-max searching is clearly impossible because you are not going to be able to go through all arguments... In fact, I would say it notoriously hard to come up with good counter-arguments on your own.

So... is min-max search for your arguments totally useless? Mathematically, it might be, because the conditions for which it is guaranteed to be good for are not necessarily upheld in real life. In practice, it's extremely useful. Thinking about the actual mathematical algorithm can help understand the technique a bit better but let's not confuse it with the unbreakable rigor of math.

How to min-max your arguments

The opening paragraph explains the main concept. As practical tips:

• Note that the "min" part of the argument is no less important than the "max" part. We tend to think way more about arguments in our favor so it's important to keep in mind to think about arguments against you.
• Even if you think all you can about counter-arguments, it's still hard to think of good counter-arguments. The people that disagree with an idea are generally the people that are the best/most passionate at providing counter-arguments, so embrace them! Even ask for them (but don't be paternalistic or a "debate bro").
• The 0-sum part is in the ideas, not the people. Also, whether an idea is right or wrong is fixed. If by some argument some idea is wrong and you can't find a way to disprove it, there is no logical optional but to just change ideas.
• Again, assume you're wrong! You probably are wrong! If good scientists are so coy with the statements they say about the most studied aspects of the universe, you probably shouldn't be thaaat confident in anything (but don't be too much of a pushover either!).

Simple models that assume a "closed-world" rarely work perfectly in "real life". Even the chess example, which is the archetypical example of min-max search, isn't 100% accurate in real chess. I tried to give practical tips, but almost every tip has a corresponding "don't overdo it" which might seem contradicting. In life, you generally shouldn't aim at maximizing any single thing. Even though it seems contradictory, I think it's good to think about how the world works, do your best, note down when you fail, and do better next time.

Merry Christmas :)