Arrow's Impossibility Theorem

Theorem

Let voters be given $3$ or more distinct choices to choose from.

Then there is no ranking system which can aggregate the individual preferences of two or more individuals so that $4$ apparently reasonable conditions are met.



This article is complete as far as it goes, but it could do with expansion.
In particular: Make this rigorous and provide examples
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Proof


This theorem requires a proof.
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Source of Name

This entry was named for Kenneth Joseph Arrow‎.


Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Arrow's Impossibility Theorem
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Arrow's Impossibility Theorem
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