# Difference Between Cardinal and Ordinal Utility

Cardinal utility and ordinal utility are two different ways of measuring and comparing the satisfaction or preferences of individuals. Cardinal utility assumes that the satisfaction derived from consuming a good or service can be measured and assigned a numerical value, allowing for direct comparisons of utility between different goods and individuals.

Ordinal utility only focuses on the relative ranking of preferences, without assigning specific numerical values to the level of satisfaction. Ordinal utility simply states that an individual prefers one bundle of goods over another, without quantifying the magnitude of that preference. While cardinal utility allows for the comparison of utility differences and the calculation of marginal utility, ordinal utility is more limited in its scope and only provides information about the ordering of preferences.

However, ordinal utility is considered a more realistic and practical approach, as it does not require the assumption that individuals can accurately assign numerical values to their satisfaction levels.

## What is Cardinal Utility?

Cardinal utility is an economics theory that the level of satisfaction a consumer gets after the consumption of a good is measurable. The unit of this measurement is utils. The theory of marginal says that the unit of measurement for the consumption of a good is the cost.

That means the measurement of satisfaction that a person gets after consuming a product is based on the cost of that product. The level of satisfaction after increased consumption is determined by diminishing marginal utility, which says that the more a person consumes something, the less they are willing to pay for additional units.

Cardinal utility assumes that there is an absolute standard by which we can measure how good something is. The theory says that the usefulness of a good is dependent on its quantity, and assigns a number to the utility of a product or service.

An example can explain it better. If you went to a restaurant at a friend’s invitation and found him having ordered water and wine, the cardinal utility would be measured based on how much water or wine you have consumed so far. If water costs 20 dollars and wine 120 dollars, the utility would be either 20 dollars or 120dollars.

### History and Development

The concept of cardinal utility was first introduced by economists such as Jeremy Bentham and John Stuart Mill in the 18th and 19th centuries. They believed that utility could be measured and used to make decisions based on the greatest happiness principle. However, the idea of cardinal utility was later challenged by economists like Vilfredo Pareto and Paul Samuelson, who argued that utility is subjective and cannot be measured precisely.

### Assumptions and Characteristics

Cardinal utility theory makes several assumptions:

#### Quantifiable Utility

It assumes that utility can be measured and assigned a specific numerical value. For example, if I consume a pizza and derive a utility of 10 units, and then consume a burger and derive a utility of 5 units, I can say that the pizza provides twice as much satisfaction as the burger.

Also Read:   Airport vs Railway Station – Difference and Comparison

#### Interpersonal Comparisons

Cardinal utility allows for interpersonal comparisons of utility. This means that we can compare the utility derived by different individuals from consuming the same good or service. For instance, if I derive 10 units of utility from a pizza and my friend derives 8 units, we can say that I enjoy the pizza more than my friend does.

Cardinal utility assumes that the total utility derived from consuming multiple goods or services is the sum of the utilities derived from each individual good or service. If I derive 10 units of utility from a pizza and 5 units from a burger, my total utility from consuming both would be 15 units.

### Limitations and Criticisms

Despite its intuitive appeal, cardinal utility theory has several limitations and has been criticized by many economists:

#### Subjectivity and Measurability

The main criticism of cardinal utility is that utility is subjective and cannot be measured precisely. It is difficult to assign a specific numerical value to the satisfaction or happiness derived from consuming a good or service. Different individuals may have different preferences and derive different levels of utility from the same good.

#### Interpersonal Comparisons

The assumption that utility can be compared across individuals is also problematic. It is difficult to determine whether one person’s utility is greater or less than another person’s utility, as preferences and satisfaction levels vary from person to person.

### Examples of Cardinal Utility

1. Money: People assign a numeric value to money, like saying, “I’d pay \$50 for that concert ticket.”
2. Temperature: We measure temperature on a scale, such as 72°F or 22°C.
3. Weight: When you step on a scale, you get a specific number, like 150 pounds or 68 kilograms.
4. Time: We quantify time in hours, minutes, and seconds, like “I spent 2 hours on that project.”
5. Distance: We measure distance in miles or kilometers, such as “The store is 3 miles away.”

## What is Ordinal Utility?

The ordinal utility is a measure of the relative satisfaction that a consumer obtains after consuming goods. It does not measure how much utility is obtained from a product, but rather how much higher or lower the level of satisfaction is when compared with another product.

Economists define ordinal utility as the level of satisfaction a consumer obtains after consuming a certain product is not absolute, but relative to the satisfaction obtained from other products.

According to this theory, the usefulness of a good is dependent on how it ranks in comparison to other goods.

For example, if you had two products, water and soda, their ordinal utility would be measured based on which one tastes better to you at any given time. You might naturally prefer soda at the beginning, but after drinking it, its preference goes down to a level where water becomes more attractive.

This means that it is possible for a consumer to be more satisfied with one purchase than another, even if the total utility of both purchases is equal. Ordinal utility can be used to determine which product is better for a consumer because it considers the individual’s personal preferences and values.

### Key Features of Ordinal Utility

1. Ranking of preferences: Ordinal utility focuses on the relative order of preferences rather than the magnitude of satisfaction derived from each option.
2. No specific numeric values: Unlike cardinal utility, ordinal utility does not assign numeric values to the level of satisfaction or utility gained from each choice.
3. Transitivity: If I prefer A to B and B to C, then I must also prefer A to C. This is known as the transitivity property of ordinal utility.

#### Simplicity

One of the main advantages of ordinal utility is its simplicity. It’s much easier for me to rank my preferences in order than to assign specific numeric values to my level of satisfaction. I don’t need to worry about the exact difference in satisfaction between my first and second choices; I just need to know which one I prefer more.

Also Read:   Center vs Centre - Difference and Comparison

#### Avoiding Interpersonal Comparisons

Ordinal utility also helps avoid the problem of interpersonal utility comparisons. It’s difficult, if not impossible, to compare the level of satisfaction that different people derive from the same thing. By focusing on the ranking of preferences rather than the magnitude of satisfaction, ordinal utility sidesteps this issue.

### Limitations of Ordinal Utility

#### Lack of Precision

While the simplicity of ordinal utility is an advantage, it can also be a limitation. By not assigning specific numeric values to my preferences, I lose some precision in expressing the strength of my preferences. Ordinal utility doesn’t tell me how much more I prefer my first choice to my second choice.

#### Difficulty in Complex Decisions

Ordinal utility can become less useful when I’m faced with complex decisions involving many options or criteria. In these cases, it may be challenging to rank all of my preferences in a clear order, and I may need to use more sophisticated decision-making tools.

### Applications of Ordinal Utility

#### Consumer Choice Theory

Ordinal utility is a fundamental concept in consumer choice theory. Economists use ordinal utility to model how consumers make decisions based on their preferences and budget constraints. By understanding the ranking of preferences, economists can predict how changes in prices or income might affect consumer behavior.

#### Voting Systems

Ordinal utility is also relevant to the design and analysis of voting systems. Some voting systems, such as ranked-choice voting, ask voters to rank their preferences for candidates in order. These systems rely on the principles of ordinal utility to determine the winner of an election based on the collective preferences of the voters.

### Examples of Ordinal Utility

1. Movie ratings: When you rate a movie on a scale of 1 to 5 stars, you’re giving it an ordinal value.
2. Pain scale: Doctors ask patients to rate their pain on a scale of 1 to 10, which is an ordinal measurement.
3. Satisfaction surveys: When you fill out a survey and rank your satisfaction as “Very Satisfied,” “Satisfied,” “Neutral,” “Dissatisfied,” or “Very Dissatisfied,” you’re using ordinal utility.
4. Preference ordering: If you say, “I prefer vanilla ice cream to chocolate, and chocolate to strawberry,” you’re expressing an ordinal preference.
5. School grades: Letter grades like A, B, C, D, and F are ordinal measurements of academic performance.

## Difference Between Cardinal Utility and Ordinal Utility

Basic Definitions

1. Cardinal Utility: This is a measure of satisfaction that assigns a specific numerical value to the level of satisfaction gained from consuming a good or service. It assumes that the difference between these values has meaning and can be compared across individuals.
2. Ordinal Utility: This is a measure of satisfaction that ranks preferences in order, without assigning specific numerical values. It only considers the relative ordering of preferences and doesn’t assume that the difference between ranks has any meaning.

Measurability

1. Cardinal Utility: It assumes that utility can be measured and quantified using a specific unit, such as utils or dollars. For example, if you assign a utility of 10 to a pizza and 20 to a burger, it implies that the burger gives you twice as much satisfaction as the pizza.
2. Ordinal Utility: It doesn’t assume that utility can be measured or quantified. It only focuses on the ranking of preferences. For example, if you prefer a burger to a pizza, and a pizza to a salad, ordinal utility only captures this ranking without assigning any numerical values.

Interpersonal Comparisons

1. Cardinal Utility: Since it assigns specific values to utility, cardinal utility allows for interpersonal comparisons of utility. This means you can compare the utility gained by different individuals and make statements like “Alice gains more utility from a pizza than Bob.”
2. Ordinal Utility: Due to its focus on relative rankings, ordinal utility doesn’t allow for interpersonal comparisons. You can’t compare the utility gained by different individuals, as the rankings are specific to each person’s preferences.

Mathematical Operations

1. Cardinal Utility: Because cardinal utility assigns numerical values, you can perform mathematical operations on these values, such as addition or multiplication. This allows for the calculation of total utility, marginal utility, and the application of advanced utility theories.
2. Ordinal Utility: Since ordinal utility doesn’t assign numerical values, mathematical operations are not applicable. You can only make statements about the relative ordering of preferences, such as “A is preferred to B.”

Assumptions

1. Cardinal Utility: It assumes that individuals can accurately quantify their level of satisfaction and that these values have a consistent meaning across different goods, services, and individuals. This is a strong assumption that has been criticized by many economists.
2. Ordinal Utility: It has fewer assumptions compared to cardinal utility. It only assumes that individuals can rank their preferences consistently, without the need for quantifying satisfaction or assuming the consistency of satisfaction across different contexts.

Practical Applications

1. Cardinal Utility: Despite its limitations, cardinal utility is still used in some economic models and theories, such as expected utility theory in decision-making under uncertainty.
2. Ordinal Utility: Due to its fewer assumptions and focus on relative rankings, ordinal utility is more widely used in modern economic analysis, particularly in consumer theory and the study of consumer behavior.