When it comes to decisions, few things influence us more than risk. We're constantly faced with uncertainty, and for most of us, that's an uncomfortable and halting feeling. Whether we’re thinking of changing majors, taking a gamble with investments, or even telling someone special how we feel, there is an element of uncertainty associated with all of these actions. Uncertainty comes with a variety of negative emotions which we have evolved to avoid: fear, loss, disappointment, this list goes on.

We’re gonna go over a formulaic method of navigating decision making, look into what exactly makes decision making so difficult, and discuss a useful framework to help us navigate and reframe this.

What is Decision Theory?

At its core, Decision Theory is all about how we make choices when we're faced with uncertainty. Think about it as a framework for understanding and improving your individual decision-making process. We deal with different levels of uncertainty, and it's helpful to categorize them:

• Decisions under risk: This is when you know all the possible outcomes and can assign a probability to each one. For example, when you flip a coin, you know the two outcomes (heads or tails), and you know the probability of each is 50%.
• Decisions under uncertainty: This is a trickier situation where you know the possible outcomes, but you can't assign a specific probability to them. What's the chance your new business will succeed? No one knows for sure, but you can still make an educated guess.
• Decisions under ignorance: This is when you don't even know what all the possible outcomes are – the most uncertain form of decision theory.

Expected Utility, Rationality, and Risk

Intro: Expected Utility Theory (EUT)

According to the EUT, when faced with a choice between uncertain outcomes, we will choose the option that maximizes their expected utility. Utility, in this context, is not merely a synonym for money or happiness, but rather a formal measure of an individual's preference for a particular outcome. Here’s how it’s broken down mathematically:

• For any given gamble or lottery (L), which offers a set of outcomes x1, x2,…,xn with respective probabilities p1,p2,...,pn, its expected utility is calculated as the sum of the utility of each outcome multiplied by its probability:

  $$ EU(L)=\sum_{i=1}^{n}p_{i}\cdot u(x_i) $$

• Here, u(xi) represents the utility function, which assigns a numerical value to each outcome.

For example, say you have the option of taking a gamble with two options:

1. A 50% chance you gain 2 million dollars
2. A 50% chance you lose 1 million dollars

Based on a simple calculation of the Expected Monetary Value (EMV), you should take the gamble as the EMV outweighs not taking the offer:

• EU = 0.50 x $2M + 0.50 x -$1M = +$0.5M