Arrow’s impossibility theorem shows that no social-choice rule can turn individual preference rankings into a collective ranking while satisfying several natural fairness conditions at the same time.
The intuition
People often want a voting rule that is fair, consistent, and respectful of individual preferences. Arrow proved that once there are at least three options, those goals conflict. If you demand too many attractive properties at once, no decision rule can satisfy all of them.
Why this matters in economics
The theorem is important because welfare economics and public choice often rely on some way of aggregating individual preferences into social decisions. Arrow’s result warns economists not to assume that a clean, value-free social ordering can always be constructed from private rankings.
What the theorem does not say
It does not say collective choice is impossible in practice. Real political systems still choose. The theorem says there is no perfect aggregation rule meeting all the specified criteria simultaneously. That forces economists and policymakers to confront trade-offs rather than pretend they disappear.