Decision making made complex • Kiran Johns

This post is not a theoretical or generalized framework for decision-making! It’s how I have been thinking about decision-making and modelling my own mental model.

What is a decision? A decision is a choice or judgment that you make after considering various possibilities. Well, at least that’s the dictionary definition.

I fundamentally see the process of decision-making as a multivariate mathematical function that computes and outputs a distribution, or at least this is my current mental model of it!

To keep it simple, my decision of carrying an umbrella is influenced by the weather forecast and whether or not I like getting drenched in the rain.

$D(\text{Carry an umbrella?} \mid \text{forecast}, \text{tolerance}) = \text{Yes} / \text{No}$

For a lot of people, including myself, who face trouble with decision-making, it’s not the process that is hard—it’s usually:

Too Many Outputs

A classic example of this is choosing which ice cream flavor you want! The problem here is not whether you want or don’t want ice cream, but more about which of the 100 flavors will make you happy.

$D(\text{What flavor?} \mid$

\begin{aligned} &\text{availability}, \\ &...\text{bias}) = \\ &\{\text{Vanilla}, \text{Chocolate}, \text{Spanish Delight}, ..., \\ &\text{Ice Cream Flavor 98}, \text{Choco Chilly Pepper}\} \end{aligned}

FYI, Spanish Delight is the best ice cream flavor, mic drop.

Input Overload

Take the ice cream example again but with just two choices: chocolate and vanilla.

$D(\text{What flavor?} \mid$

\begin{aligned} &\text{past experiences}, \\ &\text{mood}, \\ &\text{influence}, \\ &\text{availability}, \\ &\text{bias}) = \{\text{chocolate}, \text{vanilla}\} \end{aligned}

The number of inputs (x1, x2, …, xn) can clog your decision-making process, especially if the decision has a lot of long-term consequences!

But for our case, just get both flavors and move on! Or, just get vanilla if they serve brownies too.

Unknown Outcomes

Your decision-making process can also feel like a black box! You don’t know what will happen! Your brain might also consider the opportunity cost and wonder about the second-order effects of your initial outcome. For example, will choosing strawberry make me happy?

Minimize Clogging Your Brain

Eliminate Outputs

I don’t want any other flavors—just give me Spanish Delight! Or, if I’m feeling adventurous, I ask the ice cream guy how good the Choco Chilly Pepper is and just live with that choice. For complex decisions, I use this approach of elimination to remove the choices I already know won’t sustain or have less significant consequences.

Eliminate Inputs

$D(\text{flavor} \mid \text{do they have brownies?}) = \begin{cases} \text{Vanilla} & \text{if they do} \\ \text{Chocolate} & \text{if they don't} \end{cases}$

However, this approach can have large consequences for complex decisions that require a lot of thought. It’s advisable to think through all your inputs before eliminating any; you don’t want to eliminate the inputs that have a lot of weight toward generating a major result with greater second- or third-order impacts!

Complex Decisions & First and Second-Order Effects

For many of us, everyday complex decisions might be composite functions. For example, a general decision of whether or not to pursue Engineering could be framed as:

$D(\text{Engineering} \mid x, y, z)$ where:

$x \rightarrow f(\text{education},$ $\text{experience}, \text{talents})$
$y \rightarrow g(\text{job market trends},$ $\text{industry growth})$
$z \rightarrow h(\text{hobbies},$ $\text{intrinsic motivation},$ $\text{work-life balance})$

Each of these inputs might also be weighted, meaning that $y$ might influence $D$ more than $x$ or $z$ in your decision!

Foundationally, this is how I see first- and second-order thinking too. Decisions made when you decided $D(\text{education} \mid x_1, x_2, ... x_n)$ can influence $D(\text{Engineering} \mid x, y, z)$ .

A general mental model in my brain is:

$f(w_1x_1, ... , w_nx_n)$ where $w$ is a weight and $x$ can be an input or a function or a composite function.

Dealing with Time-Bound Decisions

Easy! Eliminate unnecessary or low-weight inputs and functions, define if time has a maximizing or minimizing weight, eliminate outputs you think are wrong, and live with your decision!

Making This More Complex!

Sometimes, instead of weighted inputs, I think in terms of partial derivatives to eliminate and determine outputs, especially when it comes to time-bound decisions. These are generally good for when you already have a bias!

My choice of engineering was a direct influence of my sensitivity to math and computers, and my thesis that I will find more opportunities in this field as my interest in engineering, computers, or math increases. That’s the second derivative! Another way to think of first- and second-order outcomes!

TL;DR

You do all of this without thinking about all these complications, and you’ll never need to think of this mathematically! The only two cents I have from this post are: input and output elimination and live with your choices. No one else is going to make decisions for you!