101 lines
5.8 KiB
Markdown
101 lines
5.8 KiB
Markdown
---
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title: Rational Choice Theory 101
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date: 2026-XX-XX
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published: true
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tags:
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- '101'
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---
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I have never had a strong intuition for understanding the behaviour of other people around me, but when I learned to look at the world through the lens of rational choice theory, it all started to make so much more sense.
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**Rational choice theory** is a framework for modeling strategic decision-making. It is based on the assumption that decision-makers are **rational agents**, each of whom considers the costs and benefits of their options and chooses a course of action that is in their own individual best interest.
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## Preference Relations
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How do we know what constitutes an agent's "best interest"? We use a **preference relation** to represent an agent's preferences among the options they have. **Preference** is a binary relation that compares any pair of options and says either:
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- which one the agent prefers, or
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- that the agent is indifferent
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A rational agent simply chooses whichever action(s) are most likely to lead to their most preferred outcome.
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### Example: Work-Life Balance
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Here's an example. Let's say that I have the following preference relation: work-life balance ≻ overwork ≻ default on my mortgage. Given these preferences, the only rational course of action is to balance work and life. It would be irrational of me to work more than I need to, but it would also be irrational to quit my job and default on my mortgage.
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Let's say that like many people I would most prefer an outcome where I could quit my job and keep my home. Since I have no actions that would lead to this outcome, the rational choice is continue on as a weekend warrior. However, if I won the lottery or came into a sufficiently large inheritance, then the rational choice would be to quit my job and live off my wealth.
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### Example: Cracking the Egg
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A simple understanding of preference functions is already very powerful. Another example: if you don't understand why someone would undergo a gender transition, look through the lens of rational choice theory. Someone who transitions communicates with their actions that gender dysphoria is more miserable to live with than all the social stigma, political scapegoating, increased mortality rates, etc. Gender dysphoria is not something that I can easily imagine, but based on the fact that trans people would subject themselves to a bunch of horrible stuff (that I *can* understand) in order to avoid it, I know that it must be agonizing, and I feel for them.
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## Utility Functions
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A preference relation can usually also be represented by a **utility function**, which assigns quantitative values to an agent's options. Utility can be thought of as a measure of an agent's satisfaction with a choice. Numerical utility functions are useful because you can apply much more math to them than you can to simple ordinal preference relations. When you use a utility function, rational choice becomes a matter of optimizing the value of the utility function.
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Perhaps the most salient example of a utility function is simply monetary value. An agent whose utility function is based on monetary value seeks to cut expenses while increasing income.
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### Example: Minimum Order for Free Shipping
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Here's an example. My laptop's charger has broken and I need to replace it. A replacement charger costs $20 with a $10 shipping fee for orders less than $25. The manufacturer also sells stickers for $1 apiece (for the sake of the example, I derive neither joy nor inconvenience from the stickers). If I simply buy the charger, my utility is -30. It's clear that if I buy 5 stickers, I will hit the threshold for free shipping, and my utility will be -25. Any fewer stickers and I'll have to pay the shipping fee PLUS the money for the extra stickers. Any more stickers and the price will simply go up. Five stickers is the sweet spot — the **optimum** where my utility is maximized (or my **loss** is minimized). In other words, the rational choice is for me to order the charger with five stickers in order to minimize my losses.
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## Expected Utility
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In situations where outcomes of actions are uncertain, we simply use **expected utility**, where the value of each possible outcome is weighted by the probability of it being realized.
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### Example: Scratchers
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For example, consider a lottery scratcher that costs $5. Let's say there's a 10% chance of winning $10 and a 1% chance of winning $100. The expected utility of not buying the scratcher is $0. The expected utility of buying the scratcher is:
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$$-\$5 \text{ (for the cost of the scratcher)} + \$10\cdot10\% + \$100\cdot1\% = -\$3$$
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If you were to buy a very large number of scratchers, you should expect to have lost about $3 for each card you bought. Since the expected utility is negative, buying a scratcher is clearly not in your best interest if you derive utility only from monetary value. The rational course of action is to not buy a scratcher in the first place.
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## Reinforcement Learning
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**Reinforcement learning**, one of the three fundamental categories of classical machine learning, is essentially a computational approach to rational choice theory.
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<!--TODO expand-->
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## Economics (Supply & Demand)
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## Utility Functions for Humans
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### Beliefs and Values
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### Personal Rules
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### Dopamine
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## Game Theory
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To this point, we've been talking about **decision theory**, which is concerned with the behavior of a single rational agent in an uncertain environment. On the other hand, **game theory** is a study of the interdependence
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### Nash Equilibrium
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### Pareto Optimality
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- Rational choice theory
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- mathematical approach to strategic decision making
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- one or more agents*
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- *one agent typically called decision theory; game theory typically multi-agent
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- it's everywhere: behavioural psychology, reinforcement learning, economics,
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- optimizing the objective function
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- Cui bono? |