Background
Arrow’s impossibility theorem, also known as Arrow’s paradox, is a pioneering concept in social choice theory formulated by economist Kenneth Arrow. The theorem demonstrates that it is impossible to create a flawless method for transforming individual rankings of preferences into a collective ranking that satisfies a set of desirable conditions.
Historical Context
Kenneth Arrow introduced the theorem in his seminal 1951 book, “Social Choice and Individual Values.” His work fundamentally challenged the assumption that democratic societal preferences could represent individual preferences cohesively and without contradictions.
Definitions and Concepts
Arrow’s impossibility theorem outlines a proof that no aggregation process can perfectly convert individual rankings of choices into a coherent collective ranking while meeting a specific set of desirable axioms.
Key Axioms:
1. Independence of irrelevant alternatives (IIA):
- Adding a new option should not affect the initial ranking of the existing options; the collective preference over the remaining options should remain unchanged.
2. Non-dictatorship:
- The collective ranking should not be determined by the preferences of a single individual; no one person’s preferences can override everyone else’s.
3. Pareto criterion (Pareto efficiency):
- If every individual prefers one option to another, then the society’s collective ranking should mirror this unanimous preference.
4. Unrestricted domain:
- The collective choice mechanism must be able to accommodate any conceivable set of individual rankings.
5. Transitivity:
- The collective ranking must be transitive; if society prefers option A over B, and B over C, then it must also prefer A over C.
Major Analytical Frameworks
Classical Economics
Although Arrow’s theorem emerged in the mid-20th century, its findings challenge some classical concepts of individual and collective rationality.
Neoclassical Economics
Neoclassical economics, with its focus on consumer choice and utility maximization, requires a robust aggregation rule, making Arrow’s theorem particularly relevant by highlighting the irrationalities and inconsistencies that can arise.
Keynesian Economic
In Keynesian frameworks, especially those focusing on fiscal policy and decision-making, Arrow’s insights reveal the complexities involved in achieving optimal social preferences.
Marxian Economics
For Marxian economics, which often critiques the process of social decision-making and power structures, Arrow’s theorem underlines the challenges in aggregating individual preferences within societies governed by diverse power dynamics.
Institutional Economics
Institutional economics considers the rules and norms governing economic behavior. Arrow’s theorem highlights the necessity for robust institutional frameworks to handle preference aggregation.
Behavioral Economics
Behavioral economic models that delve into human psychology and decision-making irrationality can utilize Arrow’s theorem as a foundation for investigating inconsistencies in collective choice processes.
Post-Keynesian Economics
Post-Keynesian approaches often criticize mainstream methods and emphasize the role of uncertainty and time; Arrow’s theorem contributes to the discourse on collective decision-making under uncertainty.
Austrian Economics
Austrian economists, who advocate for individual choice and market self-regulation, might view Arrow’s theorem as evidence of the difficulties inherent in centralized or collective decision-making.
Development Economics
In development economics, which focuses on improving the economic and social well-being of people, Arrow’s theorem highlights challenges in crafting collective decisions that reflect diverse preferences within populations.
Monetarism
Even within monetarist perspectives, which prioritize the role of monetary policy, Arrow’s findings underscore the complications that can arise when aggregating individual economic preferences.
Comparative Analysis
When examining different economic schools of thought, Arrow’s theorem consistently illustrates the challenge of forming a collectively rational decision-making process from individual preferences, a theme that reveals the limitations and complexities innate in various economic paradigms.
Case Studies
Understanding practical applications of Arrow’s impossibility theorem can be linked to real-world voting systems, public choice dilemmas, and democratic decision-making processes that struggle with aggregation rules leading to paradoxes like the Condorcet paradox.
Suggested Books for Further Studies
- “Social Choice and Individual Values” by Kenneth Arrow
- “Collective Choice and Social Welfare” by Amartya Sen
- “Handbook of Social Choice and Welfare” edited by Kenneth J. Arrow, Amartya Sen, and Kotaro Suzumura
Related Terms with Definitions
Collective Choice: The process of making decisions that affect a group based on individual preferences aggregated using various methods.
Interpersonal Comparisons: Evaluating and comparing utilities or preferences across different individuals.
Voting Systems: Mechanisms and rules designed to aggregate individual votes into a collective decision, susceptible to the limitations highlighted by Arrow’s theorem.
