Introduction to Decision-Making and Rational Choice

Every day you face a stream of choices—what to eat, how much to save, whether to take a risk. Some are small, some life-changing. This chapter gives you a clear way to think about decisions, starting with models that assume we are perfectly rational. These models will be our baseline for the journey into real human behavior.

The Big Picture#

We all want to make good decisions, but what does “good” even mean? This chapter lays down the classic economic answer: a good decision is one that best satisfies your own preferences, given the information you have. We’ll build the toolkit of rational choice theory—utility functions, expected utility for risky situations, and exponential discounting for choices spread over time. Think of these as the standard “ideal decision-maker” models. Later in the course we’ll see how real people often depart from them, but you can’t understand the departures until you know the ideal. So here we start with the benchmark.

What Is a Decision?#

A decision happens whenever you pick one option from several possible ones. Sit down at a restaurant and you face a menu—that’s a decision. Choose a university major, a savings plan, or whether to buy insurance—all decisions. To study decisions clearly, we break them into a few basic pieces:

• Options (alternatives): the things you can choose from.
• Outcomes: what happens after you choose, often not fully predictable.
• Uncertainty: many outcomes depend on chance—rain tomorrow, a stock price move.
• Time: some outcomes happen now, some later, and you might care differently about now versus later.

When we talk about “rational” choice, we mean a choice that is coherent with your own goals and consistent across similar situations. It does not mean the choice is cold, selfish, or even “smart” in some objective sense—it simply means you have clear preferences and you act on them without contradiction.

The first step toward a model is to represent how much you like each possible outcome. That representation is called utility.

Utility: A number that represents the satisfaction or value you derive from an outcome. Higher utility means you prefer that outcome more.

We won’t try to measure utility directly in your brain; we’ll infer it from your choices. And once we assign utility numbers to outcomes, we can describe a decision-maker as someone who picks the option that gives the highest utility—utility maximization.

📝 Section Recap: A decision has options, outcomes, uncertainty, and time. Utility is a numerical score of liking, and rational choice means picking the option with the greatest utility.

The Rational Choice Framework#

The rational choice model rests on a few simple assumptions about how you rank things. Let’s imagine you are comparing any two items, say A and B. The framework assumes:

1. Completeness: You can always compare A and B. You either prefer A, prefer B, or are indifferent between them. No “I can’t decide.”
2. Transitivity: If you prefer A to B and B to C, then you must prefer A to C. Your preferences don’t cycle.
3. Independence (for risky choices, later): Your preference between two gambles shouldn’t change if both are mixed with the same third gamble in the same way.

When your preferences satisfy completeness and transitivity, we can represent them with a utility function . For two outcomes and , you prefer over if and only if . Indifference means .

This is an ordinal concept—only the ranking matters, not the absolute numbers. If and , that doesn’t mean you like pizza twice as much; it just means you rank pizza higher. You could rescale the numbers and the choice predictions wouldn’t change, as long as the order is preserved.

Utility maximization: The principle that a rational decision-maker picks the option with the highest utility among those available.

Why is this useful? Because it lets us predict behavior. If we know your utility function (inferred from your past choices), we can guess what you’ll choose in a new situation. This is the core engine behind most economic models.

To see it in a simple, risk‑free setting: suppose you have $10 and can buy either a burger () or a wrap (). Utility maximization predicts you buy the wrap. No probabilities involved yet—that’s next.

📝 Section Recap: Rational choice assumes preferences are complete and transitive, so we can rank options with a utility function. The decision maker then chooses the highest‑ranking option available.

Decisions Under Risk: Expected Utility Theory#

Most interesting decisions involve risk—you don’t know exactly what will happen. Do you take an umbrella? If it rains, you stay dry; if not, you carried it for nothing. In such cases, we weigh the utility of each possible outcome by its chance of occurring. The result is expected utility.

Imagine a simple gamble: you flip a fair coin. Heads you win $100, tails you win nothing. How do you evaluate this? You wouldn’t just look at the best or worst outcome; you’d combine the possible outcomes with their chances. Expected utility does exactly that, but using utilities rather than dollar amounts directly.

Expected utility (EU): The probability‑weighted sum of the utilities of all possible outcomes.

Here is the probability of outcome , and is its utility. The theory says a rational person maximizes expected utility when facing risk.

Example: Suppose your utility for money is (a concave function—more on that in a moment). A gamble offers a 50% chance of $100 and a 50% chance of $0. Expected utility is . If you could instead take a sure $25, its utility is , so you’d be indifferent. If the sure amount were $30 (utility ), you’d choose the sure thing over the gamble.

This example highlights risk aversion. Most people dislike risk and would take a guaranteed amount less than the expected monetary value (here $50) to avoid the gamble. In expected utility theory, risk aversion is captured by a utility function that curves downward—concave—so that extra dollars add less and less additional happiness (diminishing marginal utility).

Risk aversion: Preferring a certain outcome over a risky one that has the same expected monetary value. It is modeled with a concave utility function .

Expected utility theory became the dominant model of choice under risk because it is simple, general, and follows logically from a few compelling axioms. It’s the normative benchmark: if you want to be consistent in the face of uncertainty, this is how you should combine probabilities and outcomes. Real people, however, often violate these axioms—but that’s a story for later chapters.

📝 Section Recap: Expected utility weights the utility of each outcome by its probability, giving a single number to evaluate risky options. A concave utility function explains risk aversion—declining marginal utility of wealth.

Decisions Over Time: Exponential Discounting#

Many decisions involve trade‑offs between now and later. Save $100 this month or spend it? Exercise today or binge‑watch a series? The standard model for choices over time is exponential discounting.

Imagine you will receive a reward in the future. Most people would rather have $100 today than $100 a year from now. That’s called time preference. We model it by multiplying future utility by a discount factor—a number between 0 and 1 that shrinks the value of future payoffs. The further away the reward, the more it is discounted.

Discount factor (δ): The weight given to utility received one period later, relative to receiving it now. If , then a utility of U in one period is worth today.

With exponential discounting, the value today (present value) of a stream of utilities over time is:

where is the utility at time , and is constant per period. The key property here is that the discount rate between any two adjacent periods is the same. Delaying a reward by one extra year always reduces its value by the same proportion , regardless of whether that delay starts now or ten years from now. This is called time consistency: your future self won’t reverse the plans your current self makes today, because you apply the same discounting rule at every point in time.

Why exponential? Think of it like compound interest in reverse. Just as money grows by a constant factor per period, its subjective value decays by a constant factor per period you wait. If per year, receiving $100 in one year feels like $95 today; receiving it in two years feels like 90.25$ today.

Exponential discounting is the rational benchmark for intertemporal choice. It ensures you never have “preference reversals”—a situation where you plan to be patient next month but when next month arrives you become impulsive. We’ll later see that real people often show exactly such reversals, which has led to richer models like hyperbolic discounting. But for now, exponential discounting gives us the ideal of a consistent planner.

Time consistency: A decision maker’s planned future actions remain optimal when that future time arrives, because the discounting rule doesn’t change with the passage of time.

📝 Section Recap: Exponential discounting values future outcomes by multiplying with a constant discount factor per period. It produces time‑consistent plans, serving as the normative benchmark for intertemporal choice.

Revealed Preference: Learning from What You Choose#

How do we know what someone’s utility function looks like? We can’t peek inside their head, but we can observe their choices. The idea of revealed preference says: if you choose A over B when both are available, you have revealed that you (weakly) prefer A to B. With enough observations, we can piece together a utility function that is consistent with all your choices.

The logic is straightforward. Suppose you consistently pick burgers over salads when both are on the menu. That suggests . If you later pick salad over soup, we infer . Transitivity then implies , and indeed we should never observe you picking soup when a burger and soup are both available (unless something else changes, like price or hunger).

Revealed preference: The practice of inferring a person’s utility ranking from their observed choices, without needing to ask them directly.

There is a powerful check called the Weak Axiom of Revealed Preference (WARP). In a simple world with fixed budget, WARP says that if you pick bundle over bundle when both are affordable, you should never pick over later if both are still affordable. If you do, your choices are inconsistent—no single utility function could explain them.

Revealed preference gives us a way to test whether the rational model fits actual behavior. If someone’s choices satisfy the consistency checks, we can estimate a utility function and predict future choices. If they don’t, we know the model falls short—and that’s where behavioral economics steps in.

📝 Section Recap: Revealed preference means learning what you like from watching your choices. Consistency conditions like WARP tell us whether a single utility function can describe the behavior.

How We Should Decide vs. How We Actually Decide: Normative and Descriptive Models#

Here we come to a crucial distinction that runs through the whole course.

• A normative model tells you how you should decide if you want to be logically consistent and maximize your long‑term welfare. Expected utility theory and exponential discounting are normative models—they define rational benchmarks.
• A descriptive model tells you how people actually make decisions, with all their quirks, biases, and emotions. Real decision‑making often violates the normative benchmarks in systematic ways.

Normative model: A theory that prescribes the best or most logically consistent way to make a decision, according to some standard of rationality.

Descriptive model: A theory that explains and predicts actual human behavior, without necessarily saying it is optimal.

For decades, economics largely assumed that people act as if they follow the normative models—that they are “rational agents.” But psychologists and experimental economists found persistent, predictable deviations. For instance, people often overweigh small probabilities, care about gains and losses rather than final wealth, and procrastinate even when they know it hurts them. These findings spurred the growth of behavioral decision making, which modifies the rational models with psychological realism to build better descriptive accounts.

Understanding the normative models is essential because they serve as the baseline against which we spot anomalies. When we see a pattern that contradicts expected utility, we know we need a new explanation. Every chapter ahead will start from a normative benchmark and then show how real behavior departs—and why that matters for everything from personal finance to public policy.

So as we begin this journey, remember: the rational choice framework is not a description of what you will do. It’s a lens for thinking clearly about what a perfectly consistent decision‑maker would do, given their own goals. Keeping that lens handy will help you appreciate the fascinating ways in which all of us are a little less than perfect.

📝 Section Recap: Normative models prescribe optimal decisions (rational benchmarks); descriptive models capture real behavior. Behavioral decision making builds descriptive models by incorporating psychological insights, always starting from these benchmarks.

Summary#

We’ve built the first toolbox for thinking about decisions. We defined a decision, introduced utility and the idea of picking the option with the highest utility. Then we looked at risky choices, where expected utility weighs each outcome by its chance. A concave utility function explains why most of us dislike risk. For choices stretched over time, exponential discounting gives us a steady way to compare now and later. Finally, we saw how we can learn about preferences from observed choices and learned to separate how we should decide (normative) from how we actually decide (descriptive). The rest of the course will use these benchmark models to spot where real behavior surprises us.