# Taking responsibility and partial derivatives

A common pattern for myself over the years is to get into some kind of interpersonal ~"conflict", feel mildly to extremely indignant about how the other person is at fault, then later either through confrontation or reflection, realize that I actually held substantial responsibility. I then feel [very guilty](https://www.lesswrong.com/posts/GBkc5yRgomstBkabn/the-proper-response-to-mistakes-that-have-harmed-others).

(When I say "conflict" I mean something broader, e.g. I mean to include cases where you're mad at your boss even if you never actually confront them.)

I noticed this pattern some years ago such I did become skeptical of my indignation even when I couldn't yet see where I was responsible. Yet this led me to a feeling of frustration. How is it that I'm always at fault? Why can I never be justifiably indignant at someone else?

I believe the answer to this can be explained via partial derivatives. It doesn't have to be explained via partial derivatives, but I think partial derivatives are this super great concept that's helpful all over the place[^h8qu7ubo1pv], so I'm going to invoke it. See this footnote for a quick explanation[^6wvubrq19l8].

Suppose we have a Situation in which there is a Problem. In the real world, any Situation is composed of a large number of parameters. The amount of Problem there is is a function of the parameters. And for any interpersonal situation, different parameters are controlled by the different parties involved in the situation.

The needlessly mathematical Partial Derivative Model of Interpersonal Conflict says that for any nontrivial situation, likely both partners control parameters that have non-negligible impact on how much of a Problem there is.

In other words, if you want to blame the other person, you'll succeed. And if you want to blame yourself, you'll succeed.

I have been good at doing those serially, but might be a better model to them in parallel: see all the ways in which each of you are contributing to the amount of Problem.

This isn't to say that always everyone is equally to blame. If someone runs a red light and hits your car, they're at fault even if you could have chosen to work from home that day. In many cases, it's less clear cut and I think it's worth tracking how each person is contributing.

The asymmetry in the situation is that by definition you control the parameters you're in control of, so it's worthwhile paying attention them. If you can get over being Right and instead focus on the outcomes you want, you might be able to attain them even if you're compensating for the mistakes of the other person.

(A note on compensating for the mistakes of the other person. This might get you the outcomes you want, but I think can be unhealthy or unbalanced. If I have a colleague who feels easily insulted and I do extra emotional work to avoid doing that, it might work, but it's imbalanced. I venture that imbalanced situations between adults and children, and \[senior\] managers and \[junior\] employees are okay, but between peers, you want balance. You want to be making and compensating for mistakes in equal measure, not one person enabling the flaws of the other.

Possibly the best thing to do if you think someone is at fault and you're at risk of compensating for it, is it to go have a conversation with them about it – but do so in an open-minded way where you're open to the possibility you're more at fault than you realize.)

Something to note is that while I've framed this is the Problem as a function of the parameters, as though we have a function evaluated at single point in time, in fact interpersonal situations have more of a "game" (in the game theory sense) element to them. The other person's behavior might be a response to your behavior and their models of you, your behavior might be a response to their behavior and your models of them, recursively. If so, question whether you want to play the game of "I'll change if they change first" or just go break the cycle or whatever.

Having thought about this, my takeaway is that in situations of interpersonal conflict, I should:

*   Try to map out the partial derivatives of outcome with respect to each party's behavior.
    *   Likely this requires more effort to model how I am contributing to any Problem, since while upset it's easier for me to find fault in the other
    *   Likely requires developing more empathy and perspective-taking if I'm really to get why the other person is responding how they are.
*   Take note of the parameters that I do control and think about what I can do to get good outcomes above and beyond blaming the other
    *   sometimes it doesn't matter who is wrong or right, it's best to just take actions that get good outcomes
    *   sometimes it does matter who is at fault. If it was you, [make amends and take meaningful action to prevent doing it again](https://www.lesswrong.com/posts/GBkc5yRgomstBkabn/the-proper-response-to-mistakes-that-have-harmed-others#Apologize_and_make_amends). If it was the other person, take strategic action in response to that (e.g. a confrontation aimed at effecting change rather than at venting your anger or punishing the other).

[^h8qu7ubo1pv]: My favorite use of the partial derivatives concept is as an alternative to "bottlenecks" in the theory of constraints sense. "We should work on the bottlenecks" people say. If you have a true bottleneck (e.g. a linear conveyor belt assembly line), productivity can only be increased at the bottleneck. That's rarely the care for what most people are working on. It's more accurate to say that you want to do is work on the parts of your system/process that have the greatest partial derivative of outcome. 

[^6wvubrq19l8]: Mini crash course in partial derivatives: suppose you have a function F that is a function of x, y, z; for example: \(F(x,y,z) = 2x^3 + 3y^2 + 5z\)F has partial derivatives with respect to each of its parameters, i.e. how much F changes if you change that parameter. You calculate this by taking the derivative with respect to one of the parameters, e.g. x, and treating the others as constants. For F, this give the partial derivative with respect to x is \(6x^2\), partial derivative with respect to y is 6y, with respect to z is 5.)