Model Answer
0 min readIntroduction
Social choice theory, a cornerstone of welfare economics, attempts to aggregate individual preferences into a collective decision. However, the inherent complexities of this process were brought to the forefront by Kenneth Arrow in his seminal work, "Social Choice and Individual Values" (1951). Arrow demonstrated that under certain seemingly reasonable conditions, it is impossible to design a social welfare function that consistently translates individual preferences into a rational social ordering. This is known as Arrow’s Impossibility Theorem. While profoundly influential, the theorem has been subject to scrutiny, notably by Amartya Sen, who proposed modifications to address its limitations and enhance its relevance for social welfare maximization.
Arrow’s Impossibility Theorem: A Detailed Examination
Arrow’s Impossibility Theorem states that no social welfare function can simultaneously satisfy a set of five conditions:
- Unrestricted Domain: The social welfare function must be able to accept any possible set of individual preferences.
- Non-Dictatorship: The social welfare function cannot be dictated by the preferences of a single individual.
- Pareto Efficiency (or Unanimity): If every individual prefers alternative A to alternative B, then the social welfare function must also prefer A to B.
- Independence of Irrelevant Alternatives (IIA): The social ranking of alternatives A and B should not change if a third alternative C is introduced or removed.
- Universal Domain: Rational preferences are assumed for all individuals.
The theorem’s significance lies in its demonstration that collective decision-making, even in a democracy, is fraught with inherent difficulties. It suggests that any social choice mechanism will inevitably violate at least one of these seemingly desirable conditions. The IIA condition is often considered the most problematic, as it implies that preferences should be insensitive to the introduction of dominated alternatives.
Sen’s Modification and the Capability Approach
Amartya Sen, in his work "Collective Choice and Social Welfare" (1970), challenged the strict assumptions of Arrow’s theorem, particularly the requirement of complete and transitive individual preferences. Sen argued that individuals often have incomplete preferences – they may not be able to compare all possible alternatives. He proposed relaxing the IIA condition, arguing that it is often rational for social preferences to change when irrelevant alternatives are introduced, especially when these alternatives reveal information about underlying values.
Sen’s primary contribution lies in the development of the capability approach. This approach shifts the focus from preference satisfaction (as assumed by Arrow) to the actual freedoms individuals have to achieve well-being. Instead of simply asking what people prefer, the capability approach asks what people are actually able to *do* and *be*. This involves considering factors like health, education, political freedoms, and economic opportunities.
Key Differences between Arrow and Sen
| Feature | Arrow’s Theorem | Sen’s Modification |
|---|---|---|
| Preference Structure | Complete and transitive preferences | Incomplete and potentially intransitive preferences |
| IIA Condition | Strict adherence | Relaxation of IIA; allows for rational changes in social preferences with irrelevant alternatives |
| Focus of Welfare | Preference satisfaction | Capability and freedom to achieve well-being |
| Social Welfare Function | Impossibility of a universally satisfying function | Possibility of a function based on capability aggregation |
Sen’s modification doesn’t entirely overcome the impossibility result, but it expands the possibility space for designing social welfare functions. By focusing on capabilities, Sen provides a framework for evaluating social outcomes that goes beyond simply aggregating preferences. This is particularly relevant in contexts where individuals may be systematically disadvantaged or have limited opportunities to express their preferences freely.
Furthermore, Sen introduced the concept of rights-based welfare functions, which prioritize the protection of certain fundamental rights and capabilities, even if doing so might conflict with the preferences of some individuals. This approach acknowledges that social welfare maximization is not solely about maximizing aggregate utility but also about ensuring justice and fairness.
Conclusion
Arrow’s Impossibility Theorem remains a foundational result in social choice theory, highlighting the inherent challenges of aggregating individual preferences. However, Amartya Sen’s critique and modification, particularly through the capability approach, offer a valuable framework for addressing these challenges and promoting social welfare maximization. By shifting the focus from preference satisfaction to actual freedoms and capabilities, Sen provides a more nuanced and ethically grounded approach to collective decision-making. While a perfect social welfare function remains elusive, Sen’s work demonstrates that meaningful progress can be made by relaxing unrealistic assumptions and prioritizing the well-being and agency of individuals.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.