Ordinal vs. Cardinal Utility

Ordinal utility is simply ranking your preferences, like placing 1st, 2nd, and 3rd in a race. In contrast, cardinal utility attempts to measure the magnitude of your preferences, like a stopwatch recording the exact time difference between each racer. So, while you might prefer coffee to tea (ordinal), claiming you get 'twice the satisfaction' from coffee is a cardinal statement.

Ask this: When I state a preference, am I just ranking my options, or am I trying to measure the gap in satisfaction between them?

Ordinal utility is the standard in modern microeconomics because it makes fewer assumptions. It only requires that we can consistently rank our choices, such as preferring a latte over a cappuccino, without needing to say by how much.

This ranking can often be observed through our actions, a concept known as revealed preference.

Cardinal utility makes the stronger claim that we can measure and compare satisfaction with numbers. While it's hard to prove you get exactly 'twice' the happiness from something, this framework is crucial for decisions involving risk.

For example, buying insurance requires cardinal thinking. You implicitly weigh the certain small cost of the premium against the small probability of a very large financial loss, comparing the magnitude of outcomes.

At work, you use ordinal utility to rank projects by priority (A is more important than B). You switch to cardinal thinking when allocating a budget, estimating how much more of a return Project A will generate than Project B.

Early utility theory, influenced by utilitarian philosophers, was cardinal, aiming to directly measure units of happiness or 'utils'. This approach faced criticism for its strong psychological assumptions, leading to the 'ordinal revolution' in the 1930s. A specific form of cardinal utility was later reintroduced to analyze decisions involving risk. [4]

• John Hicks and R.G.D. Allen (1934) were instrumental in establishing the dominance of ordinal utility in standard consumer theory. They used indifference curves to model choice without assigning numerical values to satisfaction. [1]

• John von Neumann and Oskar Morgenstern (1944) revived a form of cardinal utility for their influential Expected Utility Theory. They showed that if an individual's choices under risk follow certain logical axioms, their behavior can be described as if they are maximizing the expected value of a measurable utility function. [2]

• Daniel Kahneman and Amos Tversky (1979) later challenged this with Prospect Theory, showing that people's valuation of outcomes is often cardinal but is relative to a reference point (a gain or a loss) rather than based on absolute states of wealth. [3]

The primary critique of cardinal utility is the interpersonal comparison problem. There's no objective way to know if one person's '10 utils' of satisfaction is the same as another's, making it difficult to use for social welfare policy.

Ordinal utility avoids this problem but is less powerful. It cannot capture the intensity of preferences, which is vital for questions like whether giving $100 to a poor person creates more overall welfare than giving it to a rich person.

Both models traditionally assume that people have stable and consistent preferences. However, behavioral economics research shows that context, framing, and emotions frequently cause preferences to shift in ways these models don't predict.