Arrow's impossibility theorem
Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, American economist Kenneth Arrow showed no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrela
Metadata
- Slug: 00027-arrow-s-impossibility-theorem
- Type: PARADOX
- Tags: economics, decision, choice
- Sources: 1
Axioms
- Assume the rules of the domain apply uniformly.
- Assume the observer’s criteria remain fixed.
- Assume classification boundaries stay consistent.
- Assume the model describes the real case.
- Assume repeated steps do not change the outcome.
- Assume no hidden variables are introduced midstream.
Contradictions
- Two reasonable lines of inference yield opposite conclusions
- A global rule conflicts with a local judgment
- A stable resolution appears to violate a starting premise
- Changing the framing reverses the outcome
- Intuition and formalism diverge at the same step
Prompts
- Which assumption is doing the most hidden work?
- What changes if you relax the smallest constraint?
- Does the paradox dissolve or relocate when reframed?
- What is conserved, and what is sacrificed?
Notes
Sources
Overview
Arrow’s impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, American economist Kenneth Arrow showed no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrela
Tension
- Two reasonable lines of inference yield opposite conclusions.
- A global rule conflicts with a local judgment.
- A stable resolution appears to violate a starting premise.
- Changing the framing reverses the outcome.
- Intuition and formalism diverge at the same step.
Why It Matters
This entry tests how a stable rule-set can yield unstable conclusions under certain assumptions.
Prompts
- Which assumption is doing the most hidden work?
- What changes if you relax the smallest constraint?
- Does the paradox dissolve or relocate when reframed?
- What is conserved, and what is sacrificed?