The best output given two inputs

Once upon a time, I had an interview question that went something like this. You are trying to predict some event $E$, and you have a model $M$ with which to do so. Suppose there is some other model $N$. How should you personally value model $N$?

Here is the naive answer. Suppose $P(M)$ and $P(N)$ are the performances of models $M$ and $N$, respectively. (Maybe $P(M)$ is the amount of money that $M$ makes you.) Then the value of model $N$ is $P(N) - P(M)$ if $P(N) > P(M)$, and otherwise $N$ is worthless to you. Basically, the value of $N$ is how much better $N$ does than $M$.

But this is very much the wrong answer. The value of $N$ is based on the best model you can get by combining $M$ and $N$. Let me illustrate this for you with a concrete example.

Suppose I have a model $M$ to predict yes/no events. It is correct only $2/3$ of the time. Suppose you and your friend have two models $N_1$ and $N_2$ which do the same. Individually, they are no better than guessing. However, the models have an interesting relation: The majority vote of the models is always correct. Simply put, if at least two of the models think the answer is “yes”, then it is “yes”. Likewise for “no”.

1. correct, correct, incorrect
2. correct, incorrect, correct
3. incorrect, correct, correct

Do you see how by acquiring $N_1$ and $N_2$, models which individually do just as well as $M$, combined with $M$ do much better?

Now this is a bit of a contrived example. But the point remains the same. This is quite literally a mathematical example of the power of teamwork.

What’s the upshot? A lot of people implicitly hold the naive view that because they are worse than someone else in their group or team, they hold no value in it.¹ Two years ago, I wrote about how I don’t believe this is the case for creative fields. Two years later, I am glad to report that this is this is the case even for fields with objectively right answers. That group test? Unless Alice is literally perfect, the A-student Alice and B-student Bob do better than Alice could alone, even though Alice gets better scores than Bob every test.

On a related note, there are some people who believe that generative AI will render humans completely useless. Again, this is not the case. Even if a moron with generative AI can produce code faster than a skilled software engineer working alone,² that skilled software engineer will be leagues more useful with generative AI.