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Interpersonal Comparison of Utility and the Aggregation Problem
1. Introduction
In economics, utility represents satisfaction or well-being derived from consuming goods and services. However, a key challenge in welfare economics is whether we can compare utility across individuals—this is known as the interpersonal comparison of utility problem.
The aggregation problem arises when trying to combine individual utilities into a single measure of social welfare. Since preferences and satisfaction levels are subjective, economists debate whether social welfare can be meaningfully assessed.
2. The Problem of Interpersonal Comparison of Utility
✔ Definition: Interpersonal comparison of utility refers to the attempt to compare the level of happiness or satisfaction between different individuals.
✔ Challenge: Utility is subjective and unobservable, making it difficult to measure and compare across people.
📌 Example:
- If Person A says they enjoy an apple twice as much as Person B, can we quantify and verify this?
- If a rich person gains $100 and a poor person loses $100, can we assume equal happiness changes?
🔹 (1) Cardinal vs. Ordinal Utility in Interpersonal Comparisons
✔ Cardinal Utility Approach (Early Neoclassical View)
- Assumes utility can be measured numerically (e.g., “I get 10 utils from coffee, you get 5 utils”).
- This approach allows direct comparison of happiness between individuals.
- Used in Benthamite utilitarianism (maximize total happiness).
✔ Ordinal Utility Approach (Modern Economics)
- Assumes utility can only be ranked but not measured (e.g., “I prefer coffee to tea, but not by how much”).
- Since utility is not measurable, comparisons between individuals become problematic.
📌 Example:
- If Person A prefers apples to bananas and Person B prefers bananas to apples, we cannot say who enjoys their choice more in an ordinal system.
🔹 (2) The Difficulty in Measuring Happiness
✔ People have different psychological thresholds for satisfaction.
✔ We cannot observe internal feelings, only choices and behaviors.
✔ Even if we measure happiness through surveys or neuroscience, there is no objective scale for comparison.
📌 Example:
- A millionaire losing $10,000 may feel little impact, while a low-income worker losing $10,000 faces significant distress. Can we objectively compare their suffering?
3. The Aggregation Problem in Welfare Economics
Even if we could compare utility, the aggregation problem arises when we try to combine individual utilities into a single measure of social welfare.
✔ Key Question:
- How should we sum up individual utilities to measure total social welfare?
🔹 (1) Utilitarian Approach (Total Utility Maximization)
✔ Proposed by Jeremy Bentham – Society should maximize the total sum of utilities.
✔ Formula: W=U1+U2+…+UnW = U_1 + U_2 + … + U_n
✔ Problem: It ignores fairness and distribution.
📌 Example: A policy that benefits the rich a lot but harms the poor slightly could still increase total welfare under this model.
🔹 (2) Rawlsian Approach (Maximin Rule)
✔ Proposed by John Rawls, it focuses on maximizing the welfare of the poorest person.
✔ Formula: W=min(U1,U2,…,Un)W = \min(U_1, U_2, …, U_n)
✔ Problem: It may discourage economic growth by penalizing high earners to redistribute wealth.
📌 Example:
- Heavy taxation on the rich to lift the poor might reduce investment and innovation.
🔹 (3) Bergson-Samuelson Social Welfare Function
✔ A general framework that weights individual utilities differently: W=f(U1,U2,…,Un)W = f(U_1, U_2, …, U_n)
✔ Allows different ethical considerations (e.g., prioritizing equality, growth, or efficiency).
📌 Example:
- A democratic society may choose a balanced weighting between economic growth and social welfare.
4. Practical Applications and Policy Implications
✔ Public Policy: Welfare programs like progressive taxation and social security rely on some level of interpersonal utility comparison.
✔ Happiness Economics: Surveys on life satisfaction attempt to measure well-being, but results vary across cultures and individuals.
✔ Cost-Benefit Analysis: Governments often assume diminishing marginal utility of income, meaning policies that transfer money from the rich to the poor improve social welfare.
📌 Example:
- Universal Basic Income (UBI) assumes that $1,000 to a poor person increases happiness more than $1,000 to a billionaire.
5. Criticism of Interpersonal Utility Comparisons
✔ Subjectivity – Utility is a mental state, making comparisons unreliable.
✔ Cultural Differences – People in different societies may value happiness differently.
✔ Ethical Concerns – Should we sacrifice one person’s happiness for the greater good?
📌 Example:
- Some argue redistribution policies are unfair if they harm productive individuals, even if they increase overall happiness.
6. Conclusion
✔ Interpersonal utility comparisons are difficult because happiness is subjective and unobservable.
✔ The aggregation problem complicates how we define and measure total social welfare.
✔ Different social welfare functions offer trade-offs between efficiency and equity.
✔ Governments and economists use simplified models to make policy decisions, even if perfect comparison is impossible.